# Quantum computing

> A knowledge graph covering quantum computing fundamentals, algorithms, hardware, and emerging applications.

Canonical URL: https://aristotree.com/darko/quantum-computing
Language: en
Creator: darko
Last modified: 2026-08-08T17:42:02.421Z
Concepts: 136
Relationships: 240

This is a public, user-curated knowledge graph. Follow the cited sources when verifying claims.

## Concepts

### Hilbert space

The mathematical concept of a Hilbert space generalizes the notion of Euclidean space.

Topics: instance of: mathematical concept, subclass of: uniformly convex space, subclass of: inner product space, named after: David Hilbert

Sources:
- https://en.wikipedia.org/wiki/Hilbert_space

### Poincaré sphere

The term Poincaré sphere refers to several distinct concepts across physics and mathematics. In optics, it is a graphical representation used to map and visualize the polarization states of light. In quantum mechanics, the related Bloch sphere provides a geometric representation of the state space of a two-level quantum system. In topology, the Poincaré homology sphere is a specific three-dimensional manifold that serves as a significant example of a homology sphere, demonstrating properties that distinguish it from the standard three-sphere.

Topics: instance of: wikimedia disambiguation page

Sources:
- https://en.wikipedia.org/wiki/Poincar%C3%A9_sphere

### Orthonormal basis

In mathematics, particularly linear algebra, an orthonormal basis for an inner product space with finite dimension is a basis for whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other.

Topics: subclass of: orthogonal basis, subclass of: orthonormal set

Sources:
- https://en.wikipedia.org/wiki/Orthonormal_basis

### Von Neumann entropy

In physics, the von Neumann entropy, named after John von Neumann, is a measure of the statistical uncertainty within a description of a quantum system.

Topics: instance of: scientific theory, subclass of: entropy, named after: John von Neumann

Sources:
- https://en.wikipedia.org/wiki/Von_Neumann_entropy

### No-communication theorem

In physics, the no-communication theorem is a no-go theorem in quantum information theory.

Topics: instance of: no-go theorem, part of: list of theorems, part of: quantum information

Sources:
- https://en.wikipedia.org/wiki/No-communication_theorem

### William Wootters

William "Bill" Kent Wootters is an American theoretical physicist, and one of the founders of the field of quantum information theory.

Topics: instance of: human, occupation: physicist, occupation: university teacher

Sources:
- https://en.wikipedia.org/wiki/William_Wootters

### Quantum teleportation

Quantum teleportation is a technique for transferring quantum information from a sender at one location to a receiver some distance away.

Topics: instance of: method

Sources:
- https://en.wikipedia.org/wiki/Quantum_teleportation

### Hidden-variable theory

In physics, a hidden-variable theory is a deterministic model which seeks to explain the probabilistic nature of quantum mechanics by introducing additional, possibly inaccessible, variables.

Topics: subclass of: quantum mechanics

Sources:
- https://en.wikipedia.org/wiki/Hidden-variable_theory

### Kochen–Specker theorem

In quantum mechanics, the Kochen–Specker (KS) theorem, also known as the Bell–KS theorem, is a "no-go" theorem proved by John S.

Topics: instance of: no-go theorem, named after: Simon B. Kochen, named after: Ernst Specker

Sources:
- https://en.wikipedia.org/wiki/Kochen%E2%80%93Specker_theorem

### Quantum contextuality

Quantum contextuality is a feature of the phenomenology of quantum mechanics whereby measurements of quantum observables cannot simply be thought of as revealing pre-existing values.

Topics: subclass of: physical phenomenon

Sources:
- https://en.wikipedia.org/wiki/Quantum_contextuality

### CHSH inequality

In physics, the Clauser–Horne–Shimony–Holt (CHSH) inequality can be used in the proof of Bell's theorem, which states that certain consequences of entanglement in quantum mechanics cannot be reproduced by local hidden-variable theories.

Topics: instance of: inequation, instance of: theorem, named after: Abner Shimony, named after: John Clauser

Sources:
- https://en.wikipedia.org/wiki/CHSH_inequality

### Local hidden-variable theory

In the interpretation of quantum mechanics, a local hidden-variable theory is a hidden-variable theory that satisfies the principle of locality.

Topics: subclass of: hidden-variable theory

Sources:
- https://en.wikipedia.org/wiki/Local_hidden-variable_theory

### Bell's theorem

Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the nature of measurement.

Topics: instance of: no-go theorem, instance of: correlation inequality, part of: list of theorems, named after: John Stewart Bell

Sources:
- https://en.wikipedia.org/wiki/Bell's_theorem

### Spherical coordinate system

In mathematics, a spherical coordinate system specifies a given point in three-dimensional space by using a distance and two angles as its three coordinates.

Topics: subclass of: orthogonal coordinate system, subclass of: curvilinear coordinate system

Sources:
- https://en.wikipedia.org/wiki/Spherical_coordinate_system

### Pauli matrices

In mathematical physics and mathematics, the Pauli matrices are a set of three complex matrices that are traceless, Hermitian, involutory and unitary.

Topics: instance of: mathematical concept, subclass of: two-by-two matrix, subclass of: hermitian matrix, named after: Wolfgang Pauli

Sources:
- https://en.wikipedia.org/wiki/Pauli_matrices

### Felix Bloch

Felix Bloch was a Swiss–American theoretical physicist who shared the 1952 Nobel Prize in Physics with Edward Mills Purcell "for their development of new methods for nuclear magnetic precision measurements and discoveries in connection therewith."

Topics: instance of: human, occupation: physicist, occupation: university teacher

Sources:
- https://en.wikipedia.org/wiki/Felix_Bloch

### Bloch sphere

In quantum mechanics and computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system (qubit), named after the physicist Felix Bloch.

Topics: instance of: representation, named after: Felix Bloch

Sources:
- https://en.wikipedia.org/wiki/Bloch_sphere

### WKB approximation

In mathematical physics, the WKB approximation or WKB method is a technique for finding approximate solutions to linear differential equations with spatially varying coefficients.

Topics: instance of: computation, subclass of: semiclassical approximation

Sources:
- https://en.wikipedia.org/wiki/WKB_approximation

### Field electron emission

Field electron emission, also known as field-induced electron emission, field emission (FE) and electron field emission, is the emission of electrons from a material placed in an electrostatic field.

Topics: subclass of: physical phenomenon

Sources:
- https://en.wikipedia.org/wiki/Field_electron_emission

### Josephson effect

The Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them.

Topics: instance of: physical phenomenon, instance of: macroscopic quantum phenomena, has part(s): Josephson energy, named after: Brian David Josephson

Sources:
- https://en.wikipedia.org/wiki/Josephson_effect

### Alpha decay

Alpha decay or α-decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle.

Topics: instance of: decay mode, subclass of: radioactive decay

Sources:
- https://en.wikipedia.org/wiki/Alpha_decay

### Scanning tunneling microscope

A scanning tunneling microscope (STM) is a type of scanning probe microscope used for imaging surfaces at the atomic level.

Topics: subclass of: electron microscope, subclass of: atomic resolution microscopy

Sources:
- https://en.wikipedia.org/wiki/Scanning_tunneling_microscope

### Rectangular potential barrier

In quantum mechanics, the rectangular potential barrier is a standard one-dimensional problem that demonstrates the phenomena of wave-mechanical tunneling and wave-mechanical reflection.

Topics: subclass of: local maximum, subclass of: obstacle

Sources:
- https://en.wikipedia.org/wiki/Rectangular_potential_barrier

### Quantum tunnelling

In physics, quantum tunnelling, barrier penetration, or simply tunnelling is a quantum mechanical phenomenon in which an object such as an electron or atom passes through a potential energy barrier that, according to classical mechanics, should not be passable due to the object not having sufficient energy to pass or surmount the barrier.

Sources:
- https://en.wikipedia.org/wiki/Quantum_tunnelling

### Superconducting quantum computing

Superconducting quantum computing is a branch of quantum computing and solid-state physics that implements superconducting electronic circuits as qubits in a quantum processor.

Topics: subclass of: quantum computing

Sources:
- https://en.wikipedia.org/wiki/Superconducting_quantum_computing

### John M. Martinis

John Matthew Martinis is an American physicist and Professor of Physics at the University of California, Santa Barbara.

Topics: instance of: human, occupation: physicist

Sources:
- https://en.wikipedia.org/wiki/John_M._Martinis

### Willow processor

The Willow processor is a 105-qubit superconducting quantum processor developed by Google's Quantum AI division, manufactured in Santa Barbara, California, and announced in 2024.

Topics: instance of: quantum processing unit, manufacturer: Google Quantum AI

Sources:
- https://en.wikipedia.org/wiki/Willow_processor

### Google Quantum AI

Google Quantum AI is a research division of Google focused on developing quantum computing technologies.

Sources:
- https://en.wikipedia.org/wiki/Google_Quantum_AI

### Hadamard transform

The Hadamard transform is an example of a generalized class of Fourier transforms.

Topics: subclass of: discrete transform

Sources:
- https://en.wikipedia.org/wiki/Hadamard_transform

### John Stewart Bell

John Stewart Bell was a physicist from Northern Ireland and the originator of Bell's theorem, an important theorem in quantum physics regarding hidden-variable theories.

Topics: instance of: human, occupation: mathematician, occupation: physicist

Sources:
- https://en.wikipedia.org/wiki/John_Stewart_Bell

### Bell state

In quantum information science, the Bell's states or EPR pairs are specific quantum states of two qubits that represent the simplest examples of quantum entanglement.

Topics: instance of: set, instance of: scientific theory, subclass of: pure state, named after: John Stewart Bell

Sources:
- https://en.wikipedia.org/wiki/Bell_state

### Entanglement swapping

In quantum mechanics, entanglement swapping is a protocol to transfer quantum entanglement from one pair of particles to another, even if the second pair of particles have never interacted.

Sources:
- https://en.wikipedia.org/wiki/Entanglement_swapping

### Gilles Brassard

Gilles Brassard is a Canadian computer scientist.

Topics: instance of: human, occupation: cryptographer, occupation: computer scientist

Sources:
- https://en.wikipedia.org/wiki/Gilles_Brassard

### Bessel's inequality

In mathematics, especially functional analysis, Bessel's inequality is a statement about the coefficients of an element in a Hilbert space with respect to an orthonormal sequence.

Topics: instance of: theorem, named after: Friedrich Bessel

Sources:
- https://en.wikipedia.org/wiki/Bessel's_inequality

### Compact operator

In functional analysis, a branch of mathematics, a compact operator is a linear operator that behaves, in several important respects, like a finite-dimensional operator such as a matrix.

Topics: subclass of: bounded operator

Sources:
- https://en.wikipedia.org/wiki/Compact_operator

### Parseval's identity

In mathematical analysis, Parseval's identity, named after Marc-Antoine Parseval, is a fundamental result on the summability of the Fourier series of a function.

Topics: instance of: identity, instance of: theorem, named after: Marc-Antoine Parseval

Sources:
- https://en.wikipedia.org/wiki/Parseval's_identity

### Quantum nonlocality

In theoretical physics, quantum nonlocality refers to the phenomenon by which the measurement statistics of a multipartite quantum system do not allow an interpretation with local hidden variables.

Topics: subclass of: quantum effect

Sources:
- https://en.wikipedia.org/wiki/Quantum_nonlocality

### Entropy of entanglement

The entropy of entanglement is a measure of the degree of quantum entanglement between two subsystems constituting a two-part composite quantum system.

Topics: instance of: Entanglement measure, subclass of: entropy

Sources:
- https://en.wikipedia.org/wiki/Entropy_of_entanglement

### Bell test

A Bell test, also known as Bell inequality test or Bell experiment, is a real-world physics experiment designed to test the theory of quantum mechanics in relation to Albert Einstein's concept of local realism.

Topics: instance of: scientific theory, subclass of: physics experiment, named after: Bell's theorem

Sources:
- https://en.wikipedia.org/wiki/Bell_test

### Quantum entanglement

Quantum entanglement is the phenomenon in which the quantum state of each particle in a group cannot be described independently of the state of the others, even when the particles are separated by a large distance.

Topics: instance of: physical phenomenon, subclass of: quantum information

Sources:
- https://en.wikipedia.org/wiki/Quantum_entanglement

### Hilbert projection theorem

In mathematics, the Hilbert projection theorem is a famous result of convex analysis that says that for every vector in a Hilbert space and every nonempty closed convex there exists a unique vector for which is minimized over the vectors ; that is, such that for every

Topics: instance of: theorem, part of: list of theorems

Sources:
- https://en.wikipedia.org/wiki/Hilbert_projection_theorem

### Parallelogram law

In mathematics, the simplest form of the parallelogram law belongs to elementary geometry.

Topics: instance of: identity, instance of: theorem

Sources:
- https://en.wikipedia.org/wiki/Parallelogram_law

### Banach space

In mathematics, more specifically in functional analysis, a Banach space is a complete normed vector space.

Topics: instance of: mathematical concept, subclass of: normed vector space, subclass of: Fréchet space, named after: Stefan Banach

Sources:
- https://en.wikipedia.org/wiki/Banach_space

### Cauchy sequence

In mathematics, a Cauchy sequence is a sequence whose elements become arbitrarily close to each other as the sequence progresses.

Topics: instance of: mathematical concept, subclass of: sequence of real numbers, named after: Augustin-Louis Cauchy

Sources:
- https://en.wikipedia.org/wiki/Cauchy_sequence

### Black box

In science, computing, and engineering, a black box is a system which can be viewed in terms of its inputs and outputs, without any knowledge of its internal workings.

Topics: instance of: type of system, subclass of: system, has part(s): input/output

Sources:
- https://en.wikipedia.org/wiki/Black_box

### Grover's algorithm

In quantum computing, Grover's algorithm, also known as the quantum search algorithm, is a quantum algorithm for unstructured search that finds with high probability the unique input to a black box function that produces a particular output value, using just evaluations of the function, where is the size of the function's domain.

Topics: instance of: search algorithm, instance of: quantum algorithm, named after: Lov Grover

Sources:
- https://en.wikipedia.org/wiki/Grover's_algorithm

### Riesz representation theorem

The Riesz representation theorem, sometimes called the Riesz–Fréchet representation theorem after Frigyes Riesz and Maurice René Fréchet, establishes an important connection between a Hilbert space and its continuous dual space.

Topics: instance of: theorem, part of: list of theorems, named after: Frigyes Riesz

Sources:
- https://en.wikipedia.org/wiki/Riesz_representation_theorem

### Self-adjoint operator

In mathematics, a self-adjoint operator on a complex vector space with inner product is a linear map that is its own adjoint.

Topics: subclass of: symmetric operator, part of: self-adjoint

Sources:
- https://en.wikipedia.org/wiki/Self-adjoint_operator

### Spectral theorem

In linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized.

Topics: instance of: theorem, part of: list of theorems

Sources:
- https://en.wikipedia.org/wiki/Spectral_theorem

### David Hilbert

David Hilbert was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of all time.

Topics: instance of: human, occupation: mathematician, occupation: university teacher

Sources:
- https://en.wikipedia.org/wiki/David_Hilbert

### Lp space

In mathematics, the Lp spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces.

Topics: subclass of: vector space, subclass of: function space

Sources:
- https://en.wikipedia.org/wiki/Lp_space

### Complete metric space

In mathematical analysis, a metric space M is called complete if every Cauchy sequence of points in M has a limit that is also in M.

Topics: subclass of: metric space

Sources:
- https://en.wikipedia.org/wiki/Complete_metric_space

### Logarithm of a matrix

In mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix.

Topics: instance of: matrix function

Sources:
- https://en.wikipedia.org/wiki/Logarithm_of_a_matrix

### Trace (linear algebra)

In linear algebra, the trace of a square matrix A, denoted tr(A), is defined as a sum of the elements on its main diagonal, .

Topics: subclass of: similarity invariance

Sources:
- https://en.wikipedia.org/wiki/Trace_(linear_algebra)

### John von Neumann

John von Neumann was a Hungarian and American mathematician, physicist, computer scientist and engineer.

Topics: instance of: human, occupation: mathematician, occupation: computer scientist, part of: The Martians

Sources:
- https://en.wikipedia.org/wiki/John_von_Neumann

### Thermodynamic equilibrium

Thermodynamic equilibrium is a notion of thermodynamics with axiomatic status referring to an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls.

Topics: instance of: type of equilibrium, subclass of: non-equilibrium steady state, subclass of: equilibrium point, has part(s): mechanical equilibrium, has part(s): chemical equilibrium

Sources:
- https://en.wikipedia.org/wiki/Thermodynamic_equilibrium

### Entropy (information theory)

In information theory, the entropy of a random variable quantifies the average level of uncertainty or information associated with the variable's potential states or possible outcomes.

Topics: instance of: mathematical expression, instance of: mathematical concept, subclass of: information content, subclass of: physical quantity

Sources:
- https://en.wikipedia.org/wiki/Entropy_(information_theory)

### Magic state distillation

Magic state distillation is a method for creating more accurate quantum states from multiple noisy ones, which is important for building fault tolerant quantum computers.

Topics: instance of: quantum algorithm

Sources:
- https://en.wikipedia.org/wiki/Magic_state_distillation

### Fault tolerance

Fault tolerance is the ability of a system to contain the propagation of faults.

Topics: subclass of: robustness, subclass of: control, part of: risk management, part of: reliability-centered maintenance

Sources:
- https://en.wikipedia.org/wiki/Fault_tolerance

### Fault tolerant quantum computing

In quantum information, fault-tolerant quantum computing (FTQC) is a regime of quantum processors that are both large-scale and that effectively incorporate quantum error correction to achieve arbitrarily low error rates (i.e.

Sources:
- https://en.wikipedia.org/wiki/Fault_tolerant_quantum_computing

### Qutrit

A qutrit is a unit of quantum information that is realized by a 3-level quantum system, that may be in a superposition of three mutually orthogonal quantum states.

Topics: instance of: unit of information, named after: trit, named after: qubit

Sources:
- https://en.wikipedia.org/wiki/Qutrit

### Generalizations of Pauli matrices

In mathematics and physics, in particular quantum information, the term generalized Pauli matrices refers to families of matrices which generalize the properties of the Pauli matrices.

Topics: subclass of: matrix

Sources:
- https://en.wikipedia.org/wiki/Generalizations_of_Pauli_matrices

### Unitary transformation

In mathematics, a unitary transformation is a linear isomorphism that preserves the inner product: the inner product of two vectors before the transformation is equal to their inner product after the transformation.

Topics: subclass of: linear map

Sources:
- https://en.wikipedia.org/wiki/Unitary_transformation

### Quantum information science

Quantum information science is an interdisciplinary field that combines the principles of quantum mechanics, information theory, and computer science to explore how quantum phenomena can be harnessed for the processing, analysis, and transmission of information.

Topics: instance of: branch of physics, instance of: branch of mathematics, subclass of: computer science, subclass of: quantum physics

Sources:
- https://en.wikipedia.org/wiki/Quantum_information_science

### Quantum state space

In physics, a quantum state space is an abstract space in which different "positions" represent not literal locations, but rather quantum states of some physical system.

Topics: subclass of: phase space

Sources:
- https://en.wikipedia.org/wiki/Quantum_state_space

### Qudit

In quantum computing, a qudit (/ˈkjuː/dɪt/) or quantum dit is the generalized unit of quantum information described by a superposition of states, where the number of states d is an integer equal to or greater than two.

Sources:
- https://en.wikipedia.org/wiki/Qudit

### Amplitude amplification

Amplitude amplification is a technique in quantum computing that generalizes the idea behind Grover's search algorithm, and gives rise to a family of quantum algorithms.

Sources:
- https://en.wikipedia.org/wiki/Amplitude_amplification

### Oracle machine

In complexity theory and computability theory, an oracle machine is an abstract machine that can query a black box called an oracle, which is able to give an answer to any instance of a certain problem ⁠⁠ in a single operation.

Topics: subclass of: abstract machine, subclass of: black box

Sources:
- https://en.wikipedia.org/wiki/Oracle_machine

### Lov Grover

Lov Kumar Grover is an Indian-American computer scientist.

Topics: instance of: human, occupation: computer scientist, occupation: engineer

Sources:
- https://en.wikipedia.org/wiki/Lov_Grover

### Query complexity

Query complexity in computational complexity describes the number of queries needed to solve a computational problem for an input that can be accessed only through queries.

Topics: instance of: Wikimedia disambiguation page

Sources:
- https://en.wikipedia.org/wiki/Query_complexity

### Quantum Fourier transform

In quantum computing, the quantum Fourier transform (QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform.

Topics: subclass of: linear map, subclass of: implementation

Sources:
- https://en.wikipedia.org/wiki/Quantum_Fourier_transform

### Modular exponentiation

Modular exponentiation is exponentiation performed over a modulus.

Topics: instance of: formula

Sources:
- https://en.wikipedia.org/wiki/Modular_exponentiation

### BQP

In computational complexity theory, bounded-error quantum polynomial time (BQP) is the class of decision problems solvable by a quantum computer in polynomial time, with an error probability of at most 1/3 for all instances.

Topics: instance of: complexity class, subclass of: computational problem, part of: AWPP, has part(s): BPP

Sources:
- https://en.wikipedia.org/wiki/BQP

### Peter Shor

Peter Williston Shor is an American theoretical computer scientist known for his work on quantum computation, in particular for devising Shor's algorithm, a quantum algorithm for factoring exponentially faster than the best currently-known algorithm running on a classical computer.

Topics: instance of: human, occupation: mathematician, occupation: computer scientist

Sources:
- https://en.wikipedia.org/wiki/Peter_Shor

### RSA cryptosystem

The RSA (Rivest–Shamir–Adleman) cryptosystem is a family of public-key cryptosystems, widely used for secure data transmission.

Topics: instance of: cryptosystem, subclass of: public-key cryptography, named after: Ron Rivest, named after: Adi Shamir

Sources:
- https://en.wikipedia.org/wiki/RSA_cryptosystem

### Integer factorization

In mathematics, integer factorization is the decomposition of a positive integer into a product of integers.

Topics: instance of: factorization, subclass of: factorization, part of: number theory

Sources:
- https://en.wikipedia.org/wiki/Integer_factorization

### Shor's algorithm

Shor's algorithm is a quantum algorithm for finding the prime factors of an integer.

Topics: instance of: quantum algorithm, instance of: integer factorization algorithm, named after: Peter Shor

Sources:
- https://en.wikipedia.org/wiki/Shor's_algorithm

### One-time pad

The one-time pad (OTP) is an encryption technique that cannot be cracked in cryptography.

Topics: instance of: cipher

Sources:
- https://en.wikipedia.org/wiki/One-time_pad

### Post-quantum cryptography

Post-quantum cryptography (PQC), sometimes referred to as quantum-proof, quantum-safe, or quantum-resistant, is the development of cryptographic algorithms that are currently thought, but not proven, to be secure against a cryptanalytic attack by a quantum computer.

Topics: subclass of: cryptography

Sources:
- https://en.wikipedia.org/wiki/Post-quantum_cryptography

### BB84

The BB84 protocol, named after its inventors Charles Bennett and Gilles Brassard in 1984, is a prepare-and-measure quantum key distribution (QKD) protocol, in which, one party performs the encoding by preparing the quantum states, and the other party measures them.

Topics: instance of: quantum key distribution, instance of: quantum cryptography protocol

Sources:
- https://en.wikipedia.org/wiki/BB84

### Quantum cryptography

Quantum cryptography is the exploiting of quantum-mechanical properties such as quantum entanglement, measurement disturbance, no-cloning theorem, and the principle of superposition to perform encryption tasks.

Topics: instance of: branch of science, part of: cryptography

Sources:
- https://en.wikipedia.org/wiki/Quantum_cryptography

### Steane code

The Steane code is a tool in quantum error correction introduced by Andrew Steane in 1996.

Topics: instance of: CSS code, named after: Andrew Steane

Sources:
- https://en.wikipedia.org/wiki/Steane_code

### Stabilizer code

In quantum computing and quantum communication, a stabilizer code is a class of quantum codes for performing quantum error correction.

Topics: subclass of: quantum error-correcting code, named after: stabilizer subgroup

Sources:
- https://en.wikipedia.org/wiki/Stabilizer_code

### Threshold theorem

In quantum computing, the threshold theorem states that a quantum computer with a physical error rate below a certain threshold can, through application of quantum error correction schemes, suppress the logical error rate to arbitrarily low levels.

Topics: instance of: theorem, part of: list of theorems

Sources:
- https://en.wikipedia.org/wiki/Threshold_theorem

### Physical and logical qubits

In quantum computing, a qubit is a unit of information analogous to a bit in classical computing, but it is affected by quantum mechanical properties such as superposition and entanglement which allow qubits to be in some ways more powerful than classical bits for some tasks.

Topics: subclass of: qubit

Sources:
- https://en.wikipedia.org/wiki/Physical_and_logical_qubits

### Shor code

In quantum computing, the Shor code or Shor nine qubit code is a foundational code in quantum error correction that protects quantum information against decoherence and operational errors.

Topics: instance of: Bacon–Shor code, instance of: CSS code, named after: Peter Shor

Sources:
- https://en.wikipedia.org/wiki/Shor_code

### Surface code

The surface code is a topological quantum error correcting code, and an example of a stabilizer code, defined on a two-dimensional spin lattice.

Topics: subclass of: CSS code

Sources:
- https://en.wikipedia.org/wiki/Surface_code

### Quantum error correction

Quantum error correction (QEC) comprises a set of techniques used in quantum memory and quantum computing to protect quantum information from errors arising from decoherence and other sources of quantum noise.

Topics: subclass of: error detection and correction

Sources:
- https://en.wikipedia.org/wiki/Quantum_error_correction

### Quantum capacity

In the theory of quantum communication, the quantum capacity is the highest rate at which quantum information can be communicated over many independent uses of a noisy quantum channel from a sender to a receiver.

Topics: instance of: extensive quantity

Sources:
- https://en.wikipedia.org/wiki/Quantum_capacity

### Holevo's theorem

Holevo's theorem is a result in quantum information theory.

Topics: instance of: theorem, named after: Alexander Holevo

Sources:
- https://en.wikipedia.org/wiki/Holevo's_theorem

### Quantum channel

In quantum information theory, a quantum channel is a communication channel that can transmit quantum information, as well as classical information.

Topics: subclass of: completely positive map, subclass of: channel

Sources:
- https://en.wikipedia.org/wiki/Quantum_channel

### Quantum tomography

Quantum tomography or quantum state tomography is the process by which a quantum state is reconstructed using measurements on an ensemble of identical quantum states.

Topics: subclass of: measurement in quantum mechanics

Sources:
- https://en.wikipedia.org/wiki/Quantum_tomography

### Quantum discord

In quantum information theory, quantum discord is a measure of nonclassical correlations between two subsystems of a quantum system.

Sources:
- https://en.wikipedia.org/wiki/Quantum_discord

### Superdense coding

In quantum information theory, superdense coding is a quantum communication protocol to communicate a number of classical bits of information by only transmitting a smaller number of qubits, under the assumption of sender and receiver pre-sharing an entangled resource.

Topics: subclass of: channel

Sources:
- https://en.wikipedia.org/wiki/Superdense_coding

### Quantum information

Quantum information is the information of the state of a quantum system.

Topics: subclass of: information, subclass of: physical quantity

Sources:
- https://en.wikipedia.org/wiki/Quantum_information

### Noisy intermediate-scale quantum computing

Noisy intermediate-scale quantum (NISQ) computing is characterized by quantum processors containing up to 1,000 qubits which are not advanced enough yet for fault-tolerance or large enough to achieve quantum advantage.

Topics: instance of: era, instance of: quantum information science

Sources:
- https://en.wikipedia.org/wiki/Noisy_intermediate-scale_quantum_computing

### Cross-entropy benchmarking

Cross-entropy benchmarking (XEB) is a statistical measure used to evaluate the performance in random circuit sampling experiments.

Topics: instance of: procedure

Sources:
- https://en.wikipedia.org/wiki/Cross-entropy_benchmarking

### Quantum simulator

Quantum simulators permit the study of a quantum system in a programmable fashion.

Sources:
- https://en.wikipedia.org/wiki/Quantum_simulator

### John Preskill

John Phillip Preskill is an American theoretical physicist and the Richard P.

Topics: instance of: human, occupation: physicist, occupation: university teacher

Sources:
- https://en.wikipedia.org/wiki/John_Preskill

### Computational complexity theory

In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and explores the relationships between these classifications.

Topics: instance of: academic discipline, subclass of: computability theory, subclass of: complexity theory, part of: mathematics, part of: theoretical computer science

Sources:
- https://en.wikipedia.org/wiki/Computational_complexity_theory

### Sycamore (processor)

Sycamore is a transmon superconducting quantum processor created by Google's Artificial Intelligence division.

Topics: instance of: quantum computer, developer: Google, followed by: Willow

Sources:
- https://en.wikipedia.org/wiki/Sycamore_(processor)

### Quantum supremacy

In quantum computing, quantum supremacy or quantum advantage is the goal of demonstrating that a programmable quantum computer can solve a problem that no classical computer can solve in any feasible amount of time, irrespective of the usefulness of the problem.

Topics: instance of: property

Sources:
- https://en.wikipedia.org/wiki/Quantum_supremacy

### Classical information channel

In quantum information science, a classical information channel is a communication channel that can be used to transmit classical information.

Topics: subclass of: channel

Sources:
- https://en.wikipedia.org/wiki/Classical_information_channel

### Copenhagen interpretation

The Copenhagen interpretation is a collection of views about the meaning of quantum mechanics, stemming from the work of Niels Bohr, Werner Heisenberg, Max Born, and others.

Topics: instance of: scientific hypothesis, subclass of: interpretation of quantum mechanics, named after: Copenhagen

Sources:
- https://en.wikipedia.org/wiki/Copenhagen_interpretation

### Double-slit experiment

In modern physics, the double-slit experiment demonstrates that light and matter can exhibit behavior associated with both classical particles and classical waves.

Topics: instance of: experiment

Sources:
- https://en.wikipedia.org/wiki/Double-slit_experiment

### Wave function

In quantum mechanics, a wave function is a mathematical description of the quantum state of an isolated quantum system.

Topics: instance of: concept in physics, subclass of: probability amplitude, subclass of: scientific model

Sources:
- https://en.wikipedia.org/wiki/Wave_function

### Wave interference

In physics, interference is a phenomenon in which two coherent waves are combined by adding their intensities or displacements with due consideration for their phase difference.

Topics: instance of: phenomenon, subclass of: physical law, part of: physics

Sources:
- https://en.wikipedia.org/wiki/Wave_interference

### Wave–particle duality

Wave–particle duality is the concept in quantum mechanics that fundamental entities of the universe, like photons and electrons, exhibit particle or wave properties according to the experimental circumstances.

Topics: instance of: physical law, instance of: quantum effect

Sources:
- https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality

### Schrödinger equation

The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system.

Topics: subclass of: partial differential equation, named after: Erwin Schrödinger

Sources:
- https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation

### Quantum superposition

Quantum superposition is a fundamental principle of quantum mechanics that states that linear combinations of solutions to the Schrödinger equation are also solutions of the Schrödinger equation.

Topics: subclass of: physical phenomenon, subclass of: mathematical concept, part of: quantum mechanics

Sources:
- https://en.wikipedia.org/wiki/Quantum_superposition

### Quantum key distribution

Quantum key distribution (QKD) is a secure communication method that implements a cryptographic protocol based on the laws of quantum mechanics, specifically quantum entanglement, the measurement-disturbance principle, and the no-cloning theorem.

Topics: subclass of: key distribution

Sources:
- https://en.wikipedia.org/wiki/Quantum_key_distribution

### Charles H. Bennett (physicist)

Charles Henry Bennett is an American physicist, information theorist and IBM Fellow at IBM Research.

Topics: instance of: human, occupation: physicist, occupation: computer scientist

Sources:
- https://en.wikipedia.org/wiki/Charles_H._Bennett_(physicist)

### Quantum network

Quantum networks form an important element of quantum computing and quantum communication systems.

Topics: subclass of: communication network

Sources:
- https://en.wikipedia.org/wiki/Quantum_network

### Quantum state

In quantum physics, a quantum state is a mathematical entity that represents a physical system.

Topics: subclass of: physical state

Sources:
- https://en.wikipedia.org/wiki/Quantum_state

### Clifford gate

In quantum computing and quantum information theory, the Clifford gates are the elements of the Clifford group, a set of mathematical transformations which normalize the n-qubit Pauli group, i.e., map tensor products of Pauli matrices to tensor products of Pauli matrices through conjugation.

Topics: subclass of: quantum gate

Sources:
- https://en.wikipedia.org/wiki/Clifford_gate

### Circuit complexity

In theoretical computer science, circuit complexity is a branch of computational complexity theory in which Boolean functions are classified according to the size or depth of the Boolean circuits that compute them.

Sources:
- https://en.wikipedia.org/wiki/Circuit_complexity

### Measurement in quantum mechanics

In quantum physics, a measurement is the testing or manipulation of a physical system to yield a numerical result.

Topics: subclass of: measurement, part of: quantum mechanics

Sources:
- https://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics

### Quantum algorithm

In quantum computing, a quantum algorithm is an algorithm that runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation.

Topics: subclass of: algorithm

Sources:
- https://en.wikipedia.org/wiki/Quantum_algorithm

### Quantum circuit

In quantum information theory, a quantum circuit is a model for quantum computation, similar to classical circuits, in which a computation is a sequence of quantum gates, measurements, initializations of qubits to known values, and possibly other actions.

Topics: instance of: model of computation

Sources:
- https://en.wikipedia.org/wiki/Quantum_circuit

### Monogamy of entanglement

In quantum physics, monogamy is the property of quantum entanglement that restricts entanglement from being freely shared between arbitrarily many parties.

Topics: instance of: quantum effect, named after: monogamy

Sources:
- https://en.wikipedia.org/wiki/Monogamy_of_entanglement

### Greenberger–Horne–Zeilinger state

In physics, in the area of quantum information theory, a Greenberger–Horne–Zeilinger (GHZ) state is an entangled quantum state that involves at least three subsystems.

Topics: subclass of: pure state

Sources:
- https://en.wikipedia.org/wiki/Greenberger%E2%80%93Horne%E2%80%93Zeilinger_state

### Schmidt decomposition

In linear algebra, the Schmidt decomposition refers to a particular way of expressing a vector in the tensor product of two inner product spaces.

Sources:
- https://en.wikipedia.org/wiki/Schmidt_decomposition

### Density matrix

In quantum mechanics, a density matrix is a matrix used in calculating the probabilities of the outcomes of measurements performed on physical systems.

Topics: subclass of: hermitian matrix, subclass of: positive-semidefinite matrix

Sources:
- https://en.wikipedia.org/wiki/Density_matrix

### Aspect's experiment

Aspect's experiment was the first quantum mechanics experiment to demonstrate the violation of Bell's inequalities with photons using distant detectors.

Topics: instance of: Bell test experiments, named after: Alain Aspect

Sources:
- https://en.wikipedia.org/wiki/Aspect's_experiment

### Einstein–Podolsky–Rosen paradox

The Einstein–Podolsky–Rosen (EPR) paradox is a thought experiment proposed by physicists Albert Einstein, Boris Podolsky and Nathan Rosen, which argues that the description of physical reality provided by quantum mechanics is incomplete.

Topics: instance of: thought experiment, subclass of: physical paradox, named after: Albert Einstein, named after: Boris Podolsky

Sources:
- https://en.wikipedia.org/wiki/Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox

### Reversible computing

Reversible computing is any model of computation where every step of the process is time-reversible.

Topics: subclass of: computing

Sources:
- https://en.wikipedia.org/wiki/Reversible_computing

### Unitary matrix

In linear algebra, an invertible complex square matrix U is unitary if its matrix inverse U−1 equals its conjugate transpose U*, that is, if

Topics: subclass of: normal matrix, subclass of: element

Sources:
- https://en.wikipedia.org/wiki/Unitary_matrix

### Toffoli gate

In logic circuits, the Toffoli gate, also known as the CCNOT gate ("controlled-controlled-not"), invented by Tommaso Toffoli in 1980 is a CNOT gate with two control bits and one target bit.

Topics: subclass of: logic gate, named after: Tommaso Toffoli

Sources:
- https://en.wikipedia.org/wiki/Toffoli_gate

### Controlled NOT gate

In computer science, the controlled NOT gate, controlled-X gate, controlled-bit-flip gate, Feynman gate or controlled Pauli-X is a quantum logic gate that is an essential component in the construction of a gate-based quantum computer.

Topics: instance of: Clifford gate

Sources:
- https://en.wikipedia.org/wiki/Controlled_NOT_gate

### Quantum logic gate

In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate is a basic quantum circuit operating on a small number of qubits.

Topics: subclass of: quantum circuit, part of: quantum computer

Sources:
- https://en.wikipedia.org/wiki/Quantum_logic_gate

### No-cloning theorem

In physics, the no-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state, a statement which has profound implications in the field of quantum computing among others.

Topics: instance of: no-go theorem, part of: list of theorems

Sources:
- https://en.wikipedia.org/wiki/No-cloning_theorem

### Superposition principle

The superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually.

Topics: instance of: linear combination, instance of: mathematical property

Sources:
- https://en.wikipedia.org/wiki/Superposition_principle

### Qubit

In quantum computing, a qubit or quantum bit is a basic unit of quantum information, the quantum version of the classic binary bit.

Topics: instance of: unit of information, subclass of: quantity, named after: bit

Sources:
- https://en.wikipedia.org/wiki/Qubit

### Quantum decoherence

Quantum decoherence is the loss of quantum coherence.

Topics: subclass of: quantum effect

Sources:
- https://en.wikipedia.org/wiki/Quantum_decoherence

### Linear combination

In mathematics, a linear combination or superposition is an expression constructed from a set of terms by multiplying each term by a constant and adding the results.

Topics: subclass of: mathematical expression

Sources:
- https://en.wikipedia.org/wiki/Linear_combination

### Quantum computing

A quantum computer is a computer that represents and processes information using quantum states.

Sources:
- https://en.wikipedia.org/wiki/Quantum_computing

## Relationships

- Quantum teleportation — related_to → William Wootters: Co-author of the 1993 paper establishing the quantum teleportation prot...
- Quantum teleportation — related_to → No-communication theorem: Fundamental constraint preventing quantum teleportation from enabling f...
- Quantum teleportation — related_to → Quantum network: Systematic application of teleportation for distributed quantum computi...
- Quantum teleportation — related_to → Quantum logic gate: Basic operational unit used to perform the Bell state measurement in te...
- Quantum teleportation — related_to → Einstein–Podolsky–Rosen paradox: Conceptual foundation for the entanglement required for quantum telepor...
- Quantum teleportation — related_to → Quantum state: The physical entity being transferred during the teleportation process
- Quantum teleportation — related_to → Charles H. Bennett (physicist): Lead researcher who co-authored the seminal 1993 paper on quantum telep...
- Quantum teleportation — related_to → Quantum tomography: Method used to verify the fidelity of the teleported quantum state
- Quantum teleportation — related_to → Quantum information: The physical quantity being transferred in the teleportation protocol
- Quantum teleportation — related_to → Bell test: Experimental verification of the entanglement used in teleportation
- Quantum teleportation — related_to → Entanglement swapping: Protocol that extends teleportation to connect distant entangled partic...
- Quantum teleportation — related_to → Bell state: Specific entangled state used as the resource for teleportation
- Quantum teleportation — related_to → Quantum entanglement: Essential resource required to perform quantum teleportation
- Bell's theorem — related_to → Kochen–Specker theorem: Complementary no-go theorem
- Bell's theorem — related_to → Hidden-variable theory: Class of theories excluded by the theorem
- Bell's theorem — related_to → Quantum contextuality: Related fundamental quantum property
- Bell's theorem — related_to → CHSH inequality: Experimental generalization of Bell's theorem
- Bell's theorem — related_to → Local hidden-variable theory: Concept refuted by Bell's theorem
- Bell's theorem — related_to → Quantum nonlocality: Physical phenomenon implied by the theorem
- Bell's theorem — related_to → Aspect's experiment: Definitive experimental verification
- Bell's theorem — related_to → Einstein–Podolsky–Rosen paradox: Precursor to Bell's theorem
- Bell's theorem — related_to → Bell state: Specific entangled state used in tests
- Bell's theorem — related_to → Quantum entanglement: Physical state required for the theorem
- Bell's theorem — related_to → Bell test: Experimental application of the theorem
- Bell's theorem — related_to → John Stewart Bell: Author of the theorem
- Bloch sphere — related_to → Poincaré sphere: optical analog to the Bloch sphere
- Bloch sphere — related_to → Spherical coordinate system: mathematical framework for mapping states to the sphere
- Bloch sphere — related_to → Pauli matrices: basis for the coordinates of the Bloch vector
- Bloch sphere — related_to → Felix Bloch: namesake and developer of the geometrical representation
- Bloch sphere — related_to → Quantum logic gate: acts as a rotation on the Bloch sphere
- Bloch sphere — related_to → Density matrix: represented by points within the interior of the sphere
- Bloch sphere — related_to → Quantum state: defines the points on the surface of the sphere
- Bloch sphere — related_to → Quantum state space: the domain visualized by the Bloch sphere
- Bloch sphere — related_to → Unitary transformation: corresponds to rotations on the Bloch sphere
- Bloch sphere — related_to → Quantum superposition: visualized as a vector pointing away from the poles
- Bloch sphere — related_to → Qubit: the fundamental system represented by the Bloch sphere
- Quantum tunnelling — related_to → WKB approximation: provides a semi-classical method for estimating tunnelling transmission...
- Quantum tunnelling — related_to → Field electron emission: relies on quantum tunnelling to extract electrons from metal surfaces
- Quantum tunnelling — related_to → Josephson effect: demonstrates quantum tunnelling of Cooper pairs in superconductors
- Quantum tunnelling — related_to → Alpha decay: serves as a natural example of quantum tunnelling in nuclear physics
- Quantum tunnelling — related_to → Scanning tunneling microscope: utilizes quantum tunnelling as its primary operating mechanism
- Quantum tunnelling — related_to → Rectangular potential barrier: defines the physical constraint that quantum tunnelling overcomes
- Quantum tunnelling — related_to → Schrödinger equation: provides the mathematical framework to calculate tunnelling probabiliti...
- Quantum tunnelling — related_to → Wave function: describes the probability amplitude that allows for barrier penetration
- Quantum tunnelling — related_to → Superconducting quantum computing: employs Josephson junctions which rely on quantum tunnelling
- Google Quantum AI — related_to → Superconducting quantum computing: foundational hardware technology used by Google Quantum AI
- Google Quantum AI — related_to → John M. Martinis: former lead researcher at Google Quantum AI
- Google Quantum AI — related_to → Willow processor: successor to the Sycamore quantum processor
- Google Quantum AI — related_to → Surface code: primary error-correction architecture explored by Google Quantum AI
- Google Quantum AI — related_to → Quantum supremacy: demonstrated by Google Quantum AI using the Sycamore processor
- Google Quantum AI — related_to → Cross-entropy benchmarking: verification technique utilized by Google Quantum AI
- Google Quantum AI — related_to → Noisy intermediate-scale quantum computing: the current operational era for Google Quantum AI
- Google Quantum AI — related_to → Quantum error correction: core research objective for Google Quantum AI
- Google Quantum AI — related_to → Sycamore (processor): flagship quantum processor developed by Google Quantum AI
- Bell state — related_to → Hadamard transform: Quantum gate used to create superposition in Bell state construction
- Bell state — related_to → John Stewart Bell: Physicist who formulated the theorem underlying Bell states
- Bell state — related_to → Quantum key distribution: Application of Bell states in secure communication
- Bell state — related_to → Controlled NOT gate: Quantum logic gate used to generate Bell states
- Bell state — related_to → Density matrix: Mathematical tool for representing mixed Bell states
- Bell state — related_to → Qubit: Fundamental unit of information composing Bell states
- Bell state — related_to → Einstein–Podolsky–Rosen paradox: Thought experiment that led to the definition of Bell states
- Bell state — related_to → Greenberger–Horne–Zeilinger state: Multipartite generalization of Bell states
- Bell state — related_to → Entanglement swapping: Process that generates entanglement using Bell state measurements
- Bell state — related_to → Bell test: Experimental verification of Bell state properties
- Bell state — related_to → Quantum entanglement: Physical phenomenon exemplified by Bell states
- Quantum teleportation — related_to → Gilles Brassard: co-author of the original teleportation protocol
- Quantum teleportation — related_to → No-cloning theorem: fundamental constraint on quantum information transfer
- Quantum teleportation — related_to → Quantum circuit: model for implementing teleportation protocols
- Quantum entanglement — related_to → Quantum nonlocality: physical consequence of quantum entanglement
- Quantum entanglement — related_to → Entropy of entanglement: measure of the degree of entanglement in a quantum system
- Quantum entanglement — related_to → Bell test: empirical validation of quantum entanglement
- Quantum entanglement — related_to → Schmidt decomposition: method for quantifying entanglement in bipartite systems
- Quantum entanglement — related_to → Density matrix: mathematical tool for describing entangled states
- Quantum entanglement — related_to → Einstein–Podolsky–Rosen paradox: conceptual foundation for the study of quantum entanglement
- Quantum entanglement — related_to → Quantum cryptography: application utilizing entanglement for secure communication
- Quantum entanglement — related_to → Greenberger–Horne–Zeilinger state: multipartite generalization of entangled states
- Quantum entanglement — related_to → Monogamy of entanglement: fundamental constraint on entanglement distribution
- Hilbert space — related_to → Compact operator: Class of operators with discrete spectral properties
- Hilbert space — related_to → Hilbert projection theorem: Existence of orthogonal projections onto closed subspaces
- Hilbert space — related_to → Parseval's identity: Equality condition for orthonormal expansions
- Hilbert space — related_to → Bessel's inequality: Constraint on coefficients in orthonormal expansions
- Hilbert space — related_to → Parallelogram law: Geometric condition for inner product existence
- Hilbert space — related_to → Banach space: Broader class of complete normed vector spaces
- Hilbert space — related_to → Cauchy sequence: Fundamental criterion for completeness
- Hilbert space — related_to → Complete metric space: Topological requirement for Hilbert space
- Hilbert space — related_to → David Hilbert: Namesake and foundational contributor
- Hilbert space — related_to → Spectral theorem: Decomposition of self-adjoint operators
- Hilbert space — related_to → Self-adjoint operator: Operators with real eigenvalues and orthogonal eigenvectors
- Hilbert space — related_to → Riesz representation theorem: Duality between vectors and continuous linear functionals
- Hilbert space — related_to → Orthonormal basis: Basis for representing vectors in Hilbert space
- Grover's algorithm — related_to → Black box: represents the input mechanism for the search process
- Grover's algorithm — related_to → Shor's algorithm: serves as the primary counterpart in quantum algorithm history
- Grover's algorithm — related_to → Query complexity: measures the efficiency of the algorithm
- Grover's algorithm — related_to → Quantum algorithm: classifies the algorithm within the field of quantum computing
- Grover's algorithm — related_to → Oracle machine: models the black box interaction in the algorithm
- Grover's algorithm — related_to → Amplitude amplification: provides the general framework for the algorithm's operation
- Grover's algorithm — related_to → Lov Grover: invented the algorithm in 1996
- Hilbert space — related_to → Lp space: Common example of a Hilbert space
- Hilbert space — related_to → Quantum entanglement: Phenomenon described by tensor products of Hilbert spaces
- Hilbert space — related_to → Unitary transformation: Operator preserving the Hilbert space structure
- Hilbert space — related_to → Density matrix: Operator acting on a Hilbert space
- Hilbert space — related_to → Wave function: Element of a Hilbert space
- Hilbert space — related_to → Quantum state: Physical representation within a Hilbert space
- Von Neumann entropy — related_to → John von Neumann: eponymous creator
- Von Neumann entropy — related_to → Logarithm of a matrix: computational requirement for entropy
- Von Neumann entropy — related_to → Thermodynamic equilibrium: application in statistical mechanics
- Von Neumann entropy — related_to → Trace (linear algebra): mathematical foundation for calculation
- Von Neumann entropy — related_to → Entropy (information theory): classical information theory counterpart
- Von Neumann entropy — related_to → Quantum entanglement: measure of subsystem uncertainty
- Von Neumann entropy — related_to → Quantum information: fundamental metric in the field
- Von Neumann entropy — related_to → Quantum state: physical system described by entropy
- Von Neumann entropy — related_to → Density matrix: mathematical object required for definition
- Fault tolerant quantum computing — related_to → Magic state distillation: required technique to achieve universal fault-tolerant computation
- Fault tolerant quantum computing — related_to → Fault tolerance: fundamental property required for reliable quantum computation
- Fault tolerant quantum computing — related_to → Clifford gate: essential class of operations for fault-tolerant circuits
- Fault tolerant quantum computing — related_to → Quantum decoherence: the primary obstacle to fault-tolerant operation
- Fault tolerant quantum computing — related_to → Noisy intermediate-scale quantum computing: the precursor era to fault-tolerant computing
- Fault tolerant quantum computing — related_to → Stabilizer code: the mathematical framework for most fault-tolerant codes
- Fault tolerant quantum computing — related_to → Surface code: a specific implementation strategy for fault tolerance
- Fault tolerant quantum computing — related_to → Physical and logical qubits: distinguishes between raw hardware and error-corrected information
- Fault tolerant quantum computing — related_to → Threshold theorem: provides the theoretical guarantee for fault-tolerant computing
- Fault tolerant quantum computing — related_to → Quantum error correction: the foundational technology for fault-tolerant quantum computing
- Qudit — related_to → Unitary transformation: describes the evolution of qudit states
- Qudit — related_to → Quantum information science: provides the theoretical foundation for qudit utility
- Qudit — related_to → Qutrit: serves as the simplest non-trivial qudit
- Qudit — related_to → Generalizations of Pauli matrices: provides the basis for qudit operators
- Qudit — related_to → Quantum state space: defines the mathematical structure of qudit states
- Qudit — related_to → Quantum error correction: requires specialized codes for qudit systems
- Qudit — related_to → Superdense coding: can be generalized using qudits
- Qudit — related_to → Quantum logic gate: implements operations on qudit states
- Qudit — related_to → Measurement in quantum mechanics: collapses the qudit state into a single outcome
- Qudit — related_to → Quantum decoherence: affects the stability of qudit information
- Qudit — related_to → Hilbert space: provides the geometric space for qudit vectors
- Qudit — related_to → Quantum superposition: enables the multi-state nature of qudits
- Qudit — related_to → Quantum state: defines the physical manifestation of a qudit
- Qudit — related_to → Qubit: represents the binary case of the qudit generalization
- Grover's algorithm — related_to → Quantum computing: Broad field of application
- Grover's algorithm — related_to → BQP: Complexity class membership
- Shor's algorithm — related_to → Post-quantum cryptography: field developed in response to Shor's algorithm
- Shor's algorithm — related_to → Modular exponentiation: computational step within the algorithm
- Shor's algorithm — related_to → BQP: complexity class containing Shor's algorithm
- Shor's algorithm — related_to → Peter Shor: inventor of the algorithm
- Shor's algorithm — related_to → Quantum Fourier transform: mathematical core of Shor's algorithm
- Shor's algorithm — related_to → RSA cryptosystem: cryptographic system vulnerable to Shor's algorithm
- Shor's algorithm — related_to → Integer factorization: computational problem solved by Shor's algorithm
- Shor's algorithm — related_to → Computational complexity theory: theoretical framework for evaluating the algorithm
- Shor's algorithm — related_to → Quantum circuit: implementation model for the algorithm
- Shor's algorithm — related_to → Quantum algorithm: general category of the source
- Quantum cryptography — related_to → Post-quantum cryptography: alternative approach to cryptographic security against quantum computers
- Quantum cryptography — related_to → One-time pad: theoretically unbreakable encryption method enabled by quantum keys
- Quantum cryptography — related_to → BB84: foundational protocol for quantum key distribution
- Quantum cryptography — related_to → Measurement in quantum mechanics: mechanism for detecting eavesdropping attempts
- Quantum cryptography — related_to → Quantum network: infrastructure for distributing quantum cryptographic keys
- Quantum cryptography — related_to → Quantum superposition: basis for encoding information in quantum states
- Quantum cryptography — related_to → No-cloning theorem: theoretical barrier preventing eavesdropping without detection
- Quantum cryptography — related_to → Quantum key distribution: primary application of quantum cryptography
- Quantum error correction — related_to → Steane code: is a seven-qubit CSS code used for error correction
- Quantum error correction — related_to → Physical and logical qubits: is the unit of information protected by QEC
- Quantum error correction — related_to → Stabilizer code: provides the mathematical framework for most practical QEC codes
- Quantum error correction — related_to → Shor code: represents the first discovered quantum error-correcting code
- Quantum error correction — related_to → Surface code: serves as a leading topological quantum error correction code
- Quantum error correction — related_to → Threshold theorem: defines the feasibility of fault-tolerant quantum computation
- Quantum error correction — related_to → Quantum circuit: is the structure where error correction is implemented
- Quantum error correction — related_to → Quantum state: is the entity being preserved by error correction
- Quantum error correction — related_to → Noisy intermediate-scale quantum computing: represents the current era lacking full error correction
- Quantum error correction — related_to → Quantum decoherence: is the primary source of noise requiring correction
- Quantum information — related_to → Quantum channel: physical medium for quantum information
- Quantum information — related_to → Quantum tomography: method for reconstructing quantum information
- Quantum information — related_to → Quantum discord: measure of non-classical correlations
- Quantum information — related_to → Quantum cryptography: application of quantum information principles
- Quantum information — related_to → Superdense coding: protocol for efficient quantum communication
- Quantum information — related_to → Holevo's theorem: upper limit on classical information retrieval
- Quantum information — related_to → Quantum capacity: fundamental limit on information transmission
- Quantum information — related_to → Quantum error correction: method for protecting quantum information
- Quantum information — related_to → Density matrix: mathematical representation of quantum information
- Quantum information — related_to → Qubit: basic unit of quantum information
- Quantum information — related_to → No-cloning theorem: fundamental constraint on quantum information
- Quantum information — related_to → Quantum entanglement: resource for quantum information processing
- Quantum supremacy — related_to → Quantum simulator: Benchmark for measuring quantum advantage
- Quantum supremacy — related_to → John Preskill: Coined the term quantum supremacy
- Quantum supremacy — related_to → Noisy intermediate-scale quantum computing: Era of hardware where quantum supremacy is pursued
- Quantum supremacy — related_to → Cross-entropy benchmarking: Benchmark problem used to prove quantum supremacy
- Quantum supremacy — related_to → Computational complexity theory: Theoretical foundation for defining quantum advantage
- Quantum supremacy — related_to → Sycamore (processor): First experimental demonstration of quantum supremacy
- Quantum supremacy — related_to → Quantum error correction: Necessary technology for future quantum supremacy
- Quantum supremacy — related_to → Quantum decoherence: Primary obstacle to achieving quantum supremacy
- Quantum supremacy — related_to → Quantum algorithm: Tools used to achieve quantum supremacy
- Quantum supremacy — related_to → Quantum circuit: Model used to execute quantum supremacy experiments
- Quantum supremacy — related_to → Quantum computing: Field of study defining the goal of quantum supremacy
- Quantum superposition — related_to → Quantum state: vector representation of a superposition
- Quantum superposition — related_to → Copenhagen interpretation: framework for interpreting the collapse of superposition
- Quantum superposition — related_to → Double-slit experiment: classic demonstration of quantum superposition
- Quantum superposition — related_to → Wave function: mathematical representation of a quantum state
- Quantum superposition — related_to → Wave interference: physical manifestation of quantum superposition
- Quantum superposition — related_to → Wave–particle duality: conceptual foundation for quantum superposition
- Quantum superposition — related_to → Schrödinger equation: defines the mathematical framework for quantum superposition
- Quantum superposition — related_to → Quantum decoherence: process that destroys quantum superposition
- Quantum superposition — related_to → Hilbert space: mathematical space where superposition occurs
- Quantum superposition — related_to → Qubit: fundamental unit that utilizes superposition
- Quantum superposition — related_to → Measurement in quantum mechanics: terminates the superposition of a quantum state
- Quantum superposition — related_to → Quantum entanglement: relies on superposition to describe multi-particle states
- Quantum teleportation — related_to → Quantum key distribution: a related quantum communication technique
- Quantum teleportation — related_to → Classical information channel: required for the completion of the teleportation process
- Quantum teleportation — related_to → Bell's theorem: the theoretical foundation for the entanglement used in teleportation
- Quantum teleportation — related_to → Qubit: the basic unit of information transferred in teleportation
- Quantum circuit — related_to → Clifford gate: forms a subset of gates that are efficiently simulatable
- Quantum circuit — related_to → Circuit complexity: measures the computational resources required by a quantum circuit
- Quantum circuit — related_to → Measurement in quantum mechanics: acts as the final stage of a quantum circuit
- Quantum circuit — related_to → Quantum algorithm: defines the computational logic implemented by quantum circuits
- Quantum circuit — related_to → Quantum logic gate: serves as the fundamental building block of quantum circuits
- Quantum circuit — related_to → Hilbert space: defines the mathematical space where circuit operations occur
- Quantum circuit — related_to → Toffoli gate: is a universal reversible gate used in quantum circuits
- Quantum circuit — related_to → Reversible computing: provides the theoretical framework for quantum circuit operations
- Quantum circuit — related_to → No-cloning theorem: imposes fundamental constraints on quantum circuit design
- Quantum circuit — related_to → Qubit: is the fundamental unit of information processed by circuits
- Quantum circuit — related_to → Unitary matrix: mathematically represents the operation of a quantum circuit
- Quantum entanglement — related_to → Aspect's experiment: Empirical confirmation of entanglement
- Quantum entanglement — related_to → No-cloning theorem: Constraint on entangled state manipulation
- Quantum entanglement — related_to → Qubit: Fundamental unit for entangled systems
- Quantum entanglement — related_to → Quantum decoherence: Mechanism for loss of entanglement
- Quantum logic gate — related_to → Reversible computing: computational paradigm underlying quantum logic gates
- Quantum logic gate — related_to → No-cloning theorem: fundamental constraint on quantum logic gate operations
- Quantum logic gate — related_to → Toffoli gate: universal three-qubit quantum logic gate
- Quantum logic gate — related_to → Unitary matrix: mathematical representation of quantum logic gates
- Quantum logic gate — related_to → Controlled NOT gate: essential two-qubit entangling quantum logic gate
- Quantum logic gate — related_to → Quantum computing: field of study utilizing quantum logic gates
- Quantum logic gate — related_to → Linear combination: mathematical basis for quantum gate state transformation
- Quantum logic gate — related_to → Quantum entanglement: phenomenon generated by multi-qubit quantum logic gates
- Quantum logic gate — related_to → Qubit: basic unit of information operated on by quantum gates
- Qubit — related_to → Hilbert space: mathematical framework for qubit state vectors
- Qubit — related_to → No-cloning theorem: physical constraint on qubit manipulation
- Qubit — related_to → Quantum error correction: method for protecting qubits from decoherence
- Qubit — related_to → Superposition principle: fundamental quantum mechanical principle enabling qubit states
- Qubit — related_to → Linear combination: mathematical basis for qubit superposition
- Qubit — related_to → Quantum decoherence: process causing loss of qubit information
- Quantum computing — related_to → Quantum decoherence: primary technical challenge
- Quantum computing — related_to → Shor's algorithm: defining quantum algorithm
- Quantum computing — related_to → Quantum entanglement: computational resource
- Quantum computing — related_to → Linear combination: enabling physical principle
- Quantum computing — related_to → Qubit: fundamental unit of information