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Process in quantum computing
Quantum error correction (QEC) comprises a set of techniques used in quantum memory and quantum computing to protect quantum information from errors arising
Quantum_error_correction
Type of error correction in quantum computing
The five-qubit error correcting code, [[5,1,3]] code, or Laflamme–Miquel–Paz–Zurek code is the smallest quantum error correcting code that can protect
Five-qubit error correcting code
Five-qubit_error_correcting_code
Experimental technology level
decoherence, are not yet capable of continuous quantum error correction. This intermediate-scale is defined by the quantum volume, which is based on a moderate
Noisy intermediate-scale quantum computing
Noisy_intermediate-scale_quantum_computing
Code used in quantum error correction
In quantum computing, the Shor code or Shor nine qubit code is a foundational code in quantum error correction that protects quantum information against
Shor_code
Classification of quantum processors
incorporate quantum error correction to achieve arbitrarily low error rates (i.e. their logical error rate is much lower than their physical error rate). Full-FTQC
Fault tolerant quantum computing
Fault_tolerant_quantum_computing
Quantum error correction schemes can suppress the logical error rate arbitrarily low
through application of quantum error correction schemes, suppress the logical error rate to arbitrarily low levels. This shows that quantum computers can be
Threshold_theorem
Quantum error correction code
In quantum computing and quantum communication, a stabilizer code is a class of quantum codes for performing quantum error correction. The toric code,
Stabilizer_code
Types of quantum information
needed for the purposes of error-correction to produce an entity which behaves logically as a single qubit would in a quantum circuit or algorithm; this
Physical_and_logical_qubits
Proposed approach to a large-scale quantum computer based on Schrödinger cat states
against certain types of errors, particularly bit flips, making quantum error correction more efficient in superconducting circuits. The approach is being
Cat_qubit_quantum_computer
compared. Quantum error correction (QEC), is used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise
Glossary_of_quantum_computing
Set of quantum operations
quantum operations that map the set of n-fold Pauli group products into itself. It is most famously studied for its use in quantum error correction.
Clifford_group
Quantum computing chip
that Willow can reduce errors exponentially as the number of qubits is scaled, achieving below threshold quantum error correction. Second, that Willow completed
Willow_processor
Topological quantum error correcting 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. The first
Surface_code
Scheme for controlling errors in data over noisy communication channels
theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable
Error_correction_code
schemes for quantum error correction. Christopher Monroe and David J. Wineland at NIST (Boulder, Colorado) experimentally realize the first quantum logic gate
Timeline of quantum computing and communication
Timeline_of_quantum_computing_and_communication
Computer hardware technology that uses quantum mechanics
Recent milestones in quantum computing have increasingly focused on controlling decoherence through quantum error correction. In 2024, researchers demonstrated
Quantum_computing
Information held in the state of a quantum system
is used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is essential
Quantum_information
Aspect of quantum information science
This is mainly due to their ability to implement quantum error correction. Quantum error correction is important specifically for implementing QET protocols
Quantum_energy_teleportation
Computational benchmark
near-term quantum computers, since it does not require a quantum computer to perform any useful task or use high-quality quantum error correction, both of
Quantum_supremacy
Class of quantum error correcting codes
In quantum error correction, Calderbank–Shor–Steane (CSS) codes, named after their inventors, Robert Calderbank, Peter Shor and Andrew Steane, are a special
CSS_code
Highest rate quantum information can be sent through a noisy quantum channel
improve it. The quantum capacity theorem is important for the theory of quantum error correction, and more broadly for the theory of quantum computation.
Quantum_capacity
Quantum algorithm for integer factorization
computers and limited number of physical qubits available for quantum error correction, laboratory demonstrations of Shor's algorithm obtain correct results
Shor's_algorithm
Interdisciplinary theory behind quantum computing
(FTQC) era. Glossary of quantum computing Information theory Quantum mechanics Quantum computing Quantum error correction Quantum cryptography and its generalization
Quantum_information_science
German mathematical physicist
Berkeley. His research focuses on quantum information theory, in particular quantum error correction and quantum complexity theory. He is known for his
Nikolas_Breuckmann
Quantum Computing company in Boston, Massachusetts
Nvidia-trained transformer models for quantum error correction (QEC). Unrelated to the aforementioned Quantum Benchmarking Initiative, on October 23
QuEra_Computing_Inc.
Code for quantum correction
The Steane code is a tool in quantum error correction introduced by Andrew Steane in 1996. It is a CSS code (Calderbank-Shor-Steane), using the classical
Steane_code
American physicist (born 1950)
macroscopic quantum tunneling in superconducting circuits. In 2023, the Yale group, including Girvin, demonstrated real-time quantum error correction beyond
Steven_Girvin
Property of computational resources needed
"Quantum Magic in Quantum Electrodynamics". arXiv:2503.03098 [quant-ph]. Magic state distillation Gottesman–Knill theorem Quantum error correction Holographic
Magic_(quantum_information)
Means of studying the interaction of light and matter
resonators has opened new avenues for quantum simulation, quantum error correction, and hybrid quantum systems. The strong, controllable coupling between artificial
Circuit quantum electrodynamics
Circuit_quantum_electrodynamics
Marko; Monroe, Christopher (2020). "Fault-Tolerant Operation of a Quantum Error-Correction Code". arXiv:2009.11482 [quant-ph]. "The Power of Co-Design, Hermanni
List_of_quantum_processors
Type of quantum computer
states in quantum error correction. Topological quantum computers are equivalent in computational power to other standard models of quantum computation
Topological_quantum_computer
Fermion that is its own antiparticle
and process quantum information within a quantum computation. Though the codes typically have no Hamiltonian to provide suppression of errors, fault-tolerance
Majorana_fermion
Procedure in quantum information science
essential concept of quantum error correction. From the parity measurement, an appropriate unitary operation can be applied to correct the error without knowing
Parity_measurement
Loss of quantum coherence
most powerful tools for combating quantum decoherence is Quantum error correction (QEC). QEC schemes encode quantum information redundantly across multiple
Quantum_decoherence
Cloud quantum computing platform
first demonstration of quantum error correction circuit using flag qubits on IBM quantum hardware was reported. "IBM Quantum Devices". 2024-05-15. "Transitioning
IBM_Quantum_Platform
Interdisciplinary research area
S2CID 44098998. Bacon, Dave (2013-09-12). "Experimental quantum error correction". Quantum Error Correction. Cambridge University Press. pp. 509–518. doi:10
Quantum_machine_learning
Networks connecting quantum processors
addition to quantum error correction, classical error correction can be employed by quantum networks in special cases such as quantum key distribution. In
Quantum_network
Proposed quantum computer implementation
Langer, C.; Ozeri, R.; Wineland, D.J. (2004). "Realization of quantum error correction". Nature. 432 (7017): 602–605. Bibcode:2004Natur.432..602C. doi:10
Trapped-ion_quantum_computer
Quantum analog of Bayes' theorem
including quantum retrodiction, quantum error correction, and entanglement wedge reconstruction for black hole physics. Suppose we have a quantum state which
Petz_recovery_map
Quantum computing implementation
quantum computing includes device-level improvement, developing error correction methods, and demonstrating quantum advantage by comparing a quantum processor's
Superconducting quantum computing
Superconducting_quantum_computing
Process of "purifying" entangled quantum states
DiVincenzo, Smolin and Wootters established the connection to quantum error-correction in a ground-breaking paper published in August 1996, also in the
Entanglement_distillation
Theorem in quantum computing
states: "No quantum error correcting code can have a continuous symmetry which acts transversely on physical qubits". In other words, no quantum error correcting
Eastin–Knill_theorem
Basic unit of quantum information
state. Quantum error correction can be used to maintain the purity of qubits. Various kinds of physical operations can be performed on qubits. Quantum logic
Qubit
Quantum error correcting code
(link) Poulin, David (2005). "Stabilizer Formalism for Operator Quantum Error Correction". Phys. Rev. Lett. 95 (23) 230504. American Physical Society.
Bacon–Shor_code
Dutch physicist (born 1969)
areas in quantum information theory, including entanglement detection, quantum error correction, fault-tolerant quantum computing and quantum memories
Barbara_Terhal
Quantum error correcting code
(GKP) code is a quantum error correcting code that encodes logical qubits into the continuous degrees of freedom of a quantum system. It is named
Gottesman–Kitaev–Preskill code
Gottesman–Kitaev–Preskill_code
Israeli mathematician and computer scientist
are stated as follows: Conjecture 1 (No quantum error correction). The process for creating a quantum error-correcting code will necessarily lead to
Gil_Kalai
Algorithm in quantum information theory
vivo magnetic resonance spectroscopy. Quantum error correction is a quantum algorithm for protection from errors. The algorithm operates on the relevant
Algorithmic_cooling
Quantum-mechanical version of computer memory
of quantum error correction, the storage of qubits is limited by the internal coherence time of the physical qubits holding the information. "Quantum memory"
Quantum_memory
Quantum computing company
is a quantum computing company based in Paris and Boston. The company is known for its cat qubit quantum architecture and its work in quantum error correction
Alice_&_Bob_(company)
American engineer and physicist
entanglement in quantum error correction and for producing a quantum error correction code from an arbitrary classical error correction code. "Fellows"
Todd_Brun
British theoretical physicist (born 1953)
of the first quantum algorithms, the theory of quantum logic gates and quantum computational networks, the first quantum error-correction scheme, and several
David_Deutsch
Foundational object in quantum communication theory
"Noiseless Subsystems and the Structure of the Commutant in Quantum Error Correction". Quantum Information Processing. 2 (5): 381–419. arXiv:quant-ph/0402056
Quantum_channel
System of rules to convert information into another form or representation
writing Cipher Code (semiotics) Cultural code Equipment codes Quantum error correction Semiotics Universal language Secret Warfare: Battle of Codes and
Code
16-element matrix group
formalism, a widely-used framework for constructing and describing quantum error correction codes using sets of commuting Pauli operators. Stabilizer codes
Pauli_group
Unit of quantum information
PMC 11333499. PMID 39160166. Brock, Benjamin; al., et (14 May 2025). "Quantum error correction of qudits beyond break-even" (PDF). Nature. 641 (8063): 612–618
Qutrit
American quantum information scientist
computation, quantum analogs of Shannon's theorem, and methods for quantum error correction and noise reduction. Lloyd was born on August 2, 1960. Lloyd's
Seth_Lloyd
Unit of information in a quantum computer
states Qupit – Qudit with prime number dimensions (commonly used in quantum error correction) Qudit teleportation is the transfer of qudit information from
Qudit
spans quantum information theory (including communication trade-offs, quantum rate-distortion), network quantum information, quantum error correction, quantum
Mark_Wilde
Interaction of a quantum system with a classical observer
Einstein's thought experiments Holevo's theorem Quantum error correction Quantum limit Quantum logic Quantum Zeno effect Schrödinger's cat SIC-POVM Hellwig
Measurement in quantum mechanics
Measurement_in_quantum_mechanics
Cryptography secured against quantum computers
Post-quantum cryptography (PQC), sometimes referred to as quantum-proof, quantum-safe, or quantum-resistant, is the development of cryptographic algorithms
Post-quantum_cryptography
Change of basis applied in quantum computing
In quantum computing, the quantum Fourier transform (QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier
Quantum_Fourier_transform
Method in quantum communication
ebits so that the global stabilizer is Abelian and thus forms a valid quantum error-correcting code. We review the construction of an entanglement-assisted
Entanglement-assisted stabilizer formalism
Entanglement-assisted_stabilizer_formalism
German scientist
progress toward quantum error correction". The Keyword. 22 February 2023. Acharya, Rajeev; et al. (2023). "Suppressing quantum errors by scaling a surface
Hartmut_Neven
Computational complexity class of problems
bounded-error quantum polynomial time (BQP) is the class of decision problems solvable by a quantum computer in polynomial time, with an error probability
BQP
American physicist
known for his work regarding quantum error correction, in particular the invention of the stabilizer formalism for quantum error-correcting codes, Gottesman–Kitaev–Preskill
Daniel_Gottesman
Theorem of quantum circuits
types of quantum algorithms use only Clifford gates, including the standard algorithms for entanglement distillation and quantum error correction. From a
Gottesman–Knill_theorem
Definition of quantum circuits
S2CID 8391036. Gottesman, Daniel (1997-05-28). Stabilizer Codes and Quantum Error Correction (PhD thesis). Caltech. arXiv:quant-ph/9705052. Bibcode:1997PhDT
Clifford_gate
Criteria for a usable quantum computer
is of particular importance when you consider quantum error correction, a procedure to perform quantum processes that are robust against certain types
DiVincenzo's_criteria
Research facility in the United States
annealers by combining quantum error correction with energy penalties that suppress decoherence into a single quantum annealing correction method. The QCC was
USC-Lockheed Martin Quantum Computing Center
USC-Lockheed_Martin_Quantum_Computing_Center
Quantum information paradigm
such as quantum teleportation, quantum error correction, and superdense coding, rely on entanglement. However, entanglement is a fragile quantum property
Quantum_illumination
Quantum instruction set architecture
in A Practical Quantum Instruction Set Architecture. Many quantum algorithms (including quantum teleportation, quantum error correction, simulation, and
Quil (instruction set architecture)
Quil_(instruction_set_architecture)
Basic circuit in quantum computing
application of gates typically introduces errors, and the quantum states' fidelities decrease over time. If error correction is used, the usable gates are further
Quantum_logic_gate
Set of mathematical concepts in quantum gravity
technically, quantum geometry refers to the shape of a spacetime manifold as experienced by D-branes, which includes quantum corrections to the metric
Quantum_geometry
Term in quantum mechanics
fidelity and quantum error correction". arXiv:quant-ph/9606012. C. A. Fuchs and J. van de Graaf, "Cryptographic Distinguishability Measures for Quantum Mechanical
Fidelity_of_quantum_states
Quantum physics of light and matter in a cavity
Cavity Quantum Electrodynamics (cavity QED) is the study of the interaction between light confined in a reflective cavity and atoms or other particles
Cavity quantum electrodynamics
Cavity_quantum_electrodynamics
Method of quantum computing
computing Quantum optics Quantum error correction Quantum Turing machine Adiabatic quantum computation Hamiltonian quantum computation Fowler, Austin
One-way_quantum_computer
Canadian theoretical physicist (1960–2025)
of quantum mechanics, the development of methods to protect quantum information against noise through quantum control and quantum error correction for
Raymond_Laflamme
include quantum error correction, adiabatic quantum computation, quantum phase transitions, coherent control, photonics, and quantum electronics. First
Center for Quantum Information Science & Technology
Center_for_Quantum_Information_Science_&_Technology
Quantum algorithm for counting solutions to search problems
The Quantum counting algorithm is a quantum algorithm for efficiently counting the number of solutions for a given search problem. The algorithm is based
Quantum_counting_algorithm
Metric for a quantum computer's capabilities
Quantum volume is a metric that measures the capabilities and error rates of a quantum computer. It expresses the maximum size of square quantum circuits
Quantum_volume
Computational complexity of quantum algorithms
problems that can be efficiently solved by a quantum computer with bounded error is called BQP ("bounded error, quantum, polynomial time"). More formally, BQP
Quantum_complexity_theory
Quantum Computing Division/Software
Microsoft Azure Quantum is a public cloud-based quantum computing platform developed by Microsoft, that offers quantum hardware, software, and solutions
Microsoft_Azure_Quantum
Form of quantum computing
Hamiltonian quantum computation is a form of quantum computing. Unlike methods of quantum computation such as the adiabatic, measurement-based and circuit
Hamiltonian quantum computation
Hamiltonian_quantum_computation
intermediate-scale quantum era? Can quantum computers reach fault tolerance? Is it possible to have enough qubit scalability to implement quantum error correction? What
List of unsolved problems in physics
List_of_unsolved_problems_in_physics
Zimbabwean-American consultant, researcher and writer
Can AI Reverse the Productivity Slowdown.” He contributed to the quantum error correction work, led by Hartmut Neven, which was recognized as the Physics
James_Manyika
Quantum-informatics technique
The term quantum state discrimination collectively refers to quantum-informatics techniques, with the help of which, by performing a small number of measurements
Quantum_state_discrimination
Cryptography based on quantum mechanical phenomena
implementation of quantum repeaters. Quantum repeaters have the ability to resolve quantum communication errors in an efficient way. Quantum repeaters, which
Quantum_cryptography
adaptive quantum logic and error correction mechanisms. The protocol employs three novel quantum logics — Quantum Adaptive Hadamard (QAH), Quantum Conditional
List of quantum key distribution protocols
List_of_quantum_key_distribution_protocols
American physicist (born 1967)
entanglement distillation, for quantum error-correction and the faithful transmission of quantum information through noisy quantum channels, as well as for entanglement-assisted
John_A._Smolin
Originally defined for surface code quantum error correction, the technique was later extended to other codes such as quantum low density parity check (QLDPC)
Lattice_surgery
Optimization algorithms using quantum computing
Quantum optimization algorithms are quantum algorithms that are used to solve optimization problems. Mathematical optimization deals with finding the
Quantum optimization algorithms
Quantum_optimization_algorithms
Model of quantum computation
A quantum Turing machine (QTM) or universal quantum computer is an abstract machine used to model the effects of a quantum computer. It provides a simple
Quantum_Turing_machine
Phenomenon resulting from the superposition of two waves
addition to the classical wave model for understanding optical interference, quantum matter waves also demonstrate interference. The above can be demonstrated
Wave_interference
Paradigm of quantum computer
quantum computation scheme involving only ancilla resources, quantum teleportations and error corrections. It uses another way of efficient quantum computation
Linear optical quantum computing
Linear_optical_quantum_computing
Textbook by scientists Michael Nielsen and Isaac Chuang
Chapter 8: Quantum Noise and Quantum Operations Chapter 9: Distance Measures for Quantum Information Chapter 10: Quantum Error-Correction Chapter 11:
Quantum Computation and Quantum Information
Quantum_Computation_and_Quantum_Information
Quantum algorithm for eigenvalue estimation
In quantum computing, the quantum phase estimation algorithm is a quantum algorithm to estimate the phase corresponding to an eigenvalue of a given unitary
Quantum phase estimation algorithm
Quantum_phase_estimation_algorithm
Type of quantum computer built out of Rydberg atoms
neutral atom quantum computer is a type of quantum computer built using Rydberg atoms; this type has many commonalities with trapped-ion quantum computers
Neutral_atom_quantum_computer
Quantum algorithm
In quantum computing, the variational quantum eigensolver (VQE) is a quantum algorithm for quantum chemistry, quantum simulations and optimization problems
Variational quantum eigensolver
Variational_quantum_eigensolver
Physical phenomenon
Quantum teleportation is a technique for transferring quantum information from a sender at one location to a receiver some distance away. While teleportation
Quantum_teleportation
QUANTUM ERROR-CORRECTION
QUANTUM ERROR-CORRECTION
Girl/Female
Biblical
Fourth.
Male
English
Scottish surname transferred to forename use, from a place name possibly ERROL means "to wander."Â
Boy/Male
Danish, Finnish, French, German, Latin, Shakespearean, Swedish
Born Fifth
Biblical
fourth
Boy/Male
Anglo Saxon
Terror.
Boy/Male
Hindu, Indian
Calm
Boy/Male
Christian & English(British/American/Australian)
Wanderering Noble
Boy/Male
Anglo Saxon
Terror.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi
Error-less
Boy/Male
Anglo Saxon
Terror.
Boy/Male
American, Anglo, British, Christian, Danish, English, German, Jamaican, Latin, Scottish
To Wander; Nobleman; Leader; Earl; Wanderer
Girl/Female
Australian, British, English, Gaelic, Irish
Terror; Lovers
Boy/Male
Arabic, Hindu, Indian, Muslim, Tamil
Terror; Kings; Royal
Boy/Male
Latin Biblical
Born fourth.
Boy/Male
Hindu
King of terror
Boy/Male
Tamil
King of terror
Boy/Male
Anglo Saxon
Terror.
Girl/Female
Hindu, Indian
Without Error
Boy/Male
English American German Latin Scottish
Army commander. Army, weald power. Also can be a, meaning nobleman. Famous bearer: Australian...
Female
Arthurian
, error for Nineve (q.v.).
QUANTUM ERROR-CORRECTION
QUANTUM ERROR-CORRECTION
Male
Irish
Irish Gaelic form of English Raymond, RÉAMANN means "wise protector."
Boy/Male
Hindu, Indian, Traditional
Blessed by Lord Vishnu
Male
Hindi/Indian
(मानदीप) Variant spelling of Hindi Mandeep, MANDIP means "light of the mind."
Boy/Male
Hindu, Indian
Honest and Dignified
Girl/Female
Muslim/Islamic
A daughter of Ajlan; She was a narrator of Hadith
Boy/Male
Sikh
Happiness
Boy/Male
Gujarati, Indian
Lord Shiva
Biblical
my name; my desolations
Boy/Male
American, Australian, German
A Modern Invented Name; An Elongated Version of Mark; Of Mars; The God of War
Girl/Female
Indian
Cute Smile
QUANTUM ERROR-CORRECTION
QUANTUM ERROR-CORRECTION
QUANTUM ERROR-CORRECTION
QUANTUM ERROR-CORRECTION
QUANTUM ERROR-CORRECTION
n.
Exemption from error.
n.
Quantity; amount.
n.
A homogeneous algebraic function of two or more variables, in general containing only positive integral powers of the variables, and called quadric, cubic, quartic, etc., according as it is of the second, third, fourth, fifth, or a higher degree. These are further called binary, ternary, quaternary, etc., according as they contain two, three, four, or more variables; thus, the quantic / is a binary cubic.
n.
A quantic of the second degree. See Quantic.
n.
A definite portion of a manifoldness, limited by a mark or by a boundary.
n.
A departing or deviation from the truth; falsity; false notion; wrong opinion; mistake; misapprehension.
n.
The difference between the approximate result and the true result; -- used particularly in the rule of double position.
n.
Misguidance; error.
n.
A wandering or deviation from the right course or standard; irregularity; mistake; inaccuracy; something made wrong or left wrong; as, an error in writing or in printing; a clerical error.
n.
Mistake; error; fault.
n.
The difference between the observed value of a quantity and that which is taken or computed to be the true value; -- sometimes called residual error.
n.
A mistake in the proceedings of a court of record in matters of law or of fact.
n.
A quantic of the fourth degree. See Quantic.
pl.
of Quantum
n.
The difference between an observed value and the true value of a quantity.
n.
Liability to error.
n.
A wandering; a roving or irregular course.
n.
A moral offense; violation of duty; a sin or transgression; iniquity; fault.
n.
A fault of a player of the side in the field which results in failure to put out a player on the other side, or gives him an unearned base.
n.
A quantic of the fifth degree. See Quantic.