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Computational complexity of quantum algorithms
Quantum complexity theory is the subfield of computational complexity theory that deals with complexity classes defined using quantum computers, a computational
Quantum_complexity_theory
Interdisciplinary theory behind quantum computing
Quantum information science is an interdisciplinary field that combines the principles of quantum mechanics, information theory, and computer science
Quantum_information_science
Computational benchmark
generated by the quantum experiment. For this conclusion to be valid, only very mild assumptions in the theory of computational complexity have to be invoked
Quantum_supremacy
Computational complexity class of problems
In computational complexity theory, bounded-error quantum polynomial time (BQP) is the class of decision problems solvable by a quantum computer in polynomial
BQP
Computer hardware technology that uses quantum mechanics
Ethan; Vazirani, Umesh (1993). "Quantum complexity theory". Proceedings of the twenty-fifth annual ACM symposium on Theory of computing – STOC '93. San Diego
Quantum_computing
Amount of resources to perform an algorithm
Quantum complexity theory has been developed to study the complexity classes of problems solved using quantum computers. It is used in post-quantum cryptography
Computational_complexity
Inherent difficulty of computational problems
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource
Computational complexity theory
Computational_complexity_theory
Class of problems in computer science
In complexity theory, PP, or PPT is the class of decision problems solvable by a probabilistic Turing machine in polynomial time with an error probability
PP_(complexity)
Complexity class
computational complexity theory, the class QIP (which stands for Quantum Interactive Proof) is the quantum computing analogue of the classical complexity class
QIP_(complexity)
American computer scientist (born 1981)
at Austin. His primary areas of research are computational complexity theory and quantum computing. Aaronson grew up in the United States, though he
Scott_Aaronson
Index of articles associated with the same name
proof Quantum complexity theory#Quantum query complexity, the number of queries needed to solve a problem using a quantum algorithm Query complexity in the
Query_complexity
Interpretation of quantum mechanics
collapse is explained by the mechanism of quantum decoherence. Decoherence approaches to interpreting quantum theory have been widely explored and developed
Many-worlds_interpretation
Quantum algorithm
problem Simon's problem Ethan Bernstein and Umesh Vazirani (1997). "Quantum Complexity Theory". SIAM Journal on Computing. 26 (5): 1411–1473. doi:10.1137/S0097539796300921
Bernstein–Vazirani_algorithm
Algorithm to be run on quantum computers
Yard, J. (2008). "The Jones polynomial: quantum algorithms and applications in quantum complexity theory". Quantum Information and Computation. 8 (1): 147–180
Quantum_algorithm
Fringe hypothesis
the universe. He claimed that both quantum theory and relativity pointed to this deeper theory, a quantum field theory. This more fundamental level was
Quantum_mind
Quantum Merlin Arthur
QMA, as an abbreviation for Quantum Merlin Arthur, refers to a complexity class in computational complexity theory. It is the set of all formal languages
QMA
Hamiltonian complexity or quantum Hamiltonian complexity is a topic which deals with problems in quantum complexity theory and condensed matter physics
Hamiltonian_complexity
Model of quantum computation
equal to the classical complexity class PP. Quantum simulator § Solving physics problems Andrew Yao (1993). Quantum circuit complexity. 34th Annual Symposium
Quantum_Turing_machine
Experimental technology level
transformative potential. Quantum complexity theory Quantum noise List of companies involved in quantum computing or communication List of quantum processors Timeline
Noisy intermediate-scale quantum computing
Noisy_intermediate-scale_quantum_computing
Computer science
computational complexity theory, exact quantum polynomial time (EQP or sometimes QP) is the class of decision problems that can be solved by a quantum computer
Exact_quantum_polynomial_time
German mathematical physicist
information theory, in particular quantum error correction and quantum complexity theory. He is known for his work (together with Anurag Anshu and Chinmay
Nikolas_Breuckmann
Theorem in computational complexity theory
computational complexity theory, the PCP theorem (also known as the PCP characterization theorem) states that every decision problem in the NP complexity class
PCP_theorem
Encoding an n-bit string in m qubits
are fundamental in the study of quantum communication complexity, quantum entanglement, and the foundations of quantum mechanics, particularly in the context
Quantum_random_access_code
Complexity of sending information in a distributed algorithm
of communication. Note that, unlike in computational complexity theory, communication complexity is not concerned with the amount of computation performed
Communication_complexity
Indian–American academic (born 1959)
the field of quantum computing. His 1993 paper with his student Ethan Bernstein on quantum complexity theory defined a model of quantum Turing machines
Umesh_Vazirani
(1995). An Introduction to Quantum Field Theory. Reading: Addison-Wesley. Schwartz, Matthew (2014). Quantum Field Theory and the Standard Model. Cambridge
List of textbooks on classical mechanics and quantum mechanics
List_of_textbooks_on_classical_mechanics_and_quantum_mechanics
Interpretation of quantum mechanics
is an interpretation of quantum mechanics that takes an agent's actions and experiences as the central concerns of the theory. It is the most prominent
QBism
Set of mathematical concepts in quantum gravity
Planck length. Each theory of quantum gravity uses the term "quantum geometry" in a slightly different fashion. String theory uses quantum geometry to describe
Quantum_geometry
List of quantum computing algorithms
of quantum processors List of quantum software Quantum circuit Quantum complexity theory Quantum information science Quantum programming Quantum supremacy
List_of_quantum_algorithms
Interdisciplinary research area
sometimes called quantum-enhanced machine learning. QML algorithms use qubits and quantum operations to try to improve the space and time complexity of classical
Quantum_machine_learning
Method of quantum computing via entanglement
the context of quantum position verification, and has since been related to a number of other subjects including computational complexity, aspects of classical
Non-local_quantum_computation
Latvian computer scientist
is a Latvian computer scientist active in the fields of quantum information theory and quantum computing. Ambainis has held past positions at the Institute
Andris_Ambainis
Type of quantum computer
A topological quantum computer is a type of quantum computer. It utilizes anyons, a type of quasiparticle that occurs in two-dimensional systems. The
Topological_quantum_computer
complexity class contained in PP defined via GapP functions. The class often arises in the context of quantum computing. AWPP contains the complexity
AWPP
Deviations from local realism
limit of objects. Thus, quantum theory is local in the strict sense defined by special relativity and, as such, the term "quantum nonlocality" is sometimes
Quantum_nonlocality
Search problem in quantum mechanics
and a binary vector. 2D HLF can be solved exactly by a constant-depth quantum circuit restricted to a 2-dimensional grid of qubits using bounded fan-in
Hidden linear function problem
Hidden_linear_function_problem
Mathematical problem in von Neumann algebra theory
Ji, Natarajan, Vidick, Wright, and Yuen announced a result in quantum complexity theory that implies a negative answer to Connes' embedding problem. However
Connes_embedding_problem
In computational complexity theory, a language B (or a complexity class B) is said to be low for a complexity class A (with some reasonable relativized
Low_(complexity)
Hypothetical physical concept
strong nuclear and weak nuclear forces which were combined in the quantum field theory to implement the Standard Model of physics, a unification of all
Theory_of_everything
Complexity class
computational complexity theory, PostBQP is a complexity class consisting of all of the computational problems solvable in polynomial time on a quantum Turing
PostBQP
attempts at creating a quantum information theory, showing that Shannon information theory cannot directly be generalized to the quantum case, but rather that
Timeline of quantum computing and communication
Timeline_of_quantum_computing_and_communication
Foundational object in quantum communication theory
In quantum information theory, a quantum channel is a communication channel that can transmit quantum information, as well as classical information. An
Quantum_channel
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
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
Quantum search 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
Grover's_algorithm
Information held in the state of a quantum system
ISBN 978-3-642-11914-9. Benatti, Fabio (2009). "Quantum Information Theory". Dynamics, Information and Complexity in Quantum Systems. Theoretical and Mathematical
Quantum_information
Cloud quantum computing platform
IBM Quantum Platform (previously known as IBM Quantum Experience) is an online platform allowing public and premium access to cloud-based quantum computing
IBM_Quantum_Platform
Type of quantum circuit construction
Quantum gate teleportation is a quantum circuit construction where a gate is applied to target qubits by first applying the gate to an entangled state
Quantum_gate_teleportation
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
Concept in quantum information theory
In quantum information theory, quantum state purification refers to the process of representing a mixed state as a pure quantum state of higher-dimensional
Quantum_state_purification
Proposed quantum computer implementation
A trapped-ion quantum computer (TIQC) is one proposed approach to a large-scale quantum computer. Ions, or charged atomic particles, can be confined and
Trapped-ion_quantum_computer
This list contains quantum processors, also known as quantum processing units (QPUs). Some devices listed below have only been announced at press conferences
List_of_quantum_processors
Simulators of quantum mechanical systems
in different complexity classes, which is why quantum Turing machines are useful for simulating quantum systems. This is known as quantum supremacy, the
Quantum_simulator
Force resulting from the quantisation of a field
In quantum field theory, the Casimir effect (or Casimir force) is a physical force acting on the macroscopic boundaries of a confined space which arises
Casimir_effect
The claw finding problem is a classical problem in complexity theory, with several applications in cryptography. In short, given two functions f, g, viewed
Claw_finding_problem
Sorting algorithms for quantum computers
Thus, for this task, quantum computers are no better than classical ones, and should be disregarded when it comes to time complexity. However, in space-bounded
Quantum_sort
Basic unit of quantum information
In quantum computing, a qubit (/ˈkjuːbɪt/) or quantum bit is a basic unit of quantum information, the quantum version of the classic binary bit. A qubit
Qubit
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
Basic circuit in quantum computing
In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit
Quantum_logic_gate
Property of computational resources needed
In quantum information theory, magic is a property that quantifies the computational resources needed to describe quantum states beyond stabilizer states
Magic_(quantum_information)
Description of a quantum-mechanical system
function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after
Schrödinger_equation
Cryptography based on quantum mechanical phenomena
Quantum cryptography is the exploiting of quantum-mechanical properties such as quantum entanglement, measurement disturbance, no-cloning theorem, and
Quantum_cryptography
Quantum algorithm for integer factorization
polynomial complexity circuit on an ideal quantum computer. Thus, it might be feasible to defeat RSA by constructing a large enough quantum computer. This
Shor's_algorithm
Branch of physics seeking to explain chaotic dynamical systems in terms of quantum theory
Quantum chaos is a branch of physics focused on how chaotic classical dynamical systems can be described in terms of quantum theory. The primary question
Quantum_chaos
Dutch physicist (born 1969)
low-depth quantum circuits or stoquastic Hamiltonians, perturbative gadgets for quantum simulation and quantum complexity theory. She also developed quantum protocols
Barbara_Terhal
Sub-field of quantum physics and optics
demonstration of quantum entanglement, quantum teleportation, and quantum logic gates. The latter are of much interest in quantum information theory, a subject
Quantum_optics
Set of problems in computational complexity theory
In computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly
Complexity_class
Proposed design of bank notes
A quantum money scheme is a quantum cryptographic protocol that creates and verifies banknotes that are resistant to forgery. It is based on the principle
Quantum_money
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
Problem in communication complexity theory
lower bound on the communication complexity of gap-hamming-distance". Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11. p. 51
Gap-Hamming_problem
Brazilian physicist
European Quantum Information Young Investigator Award for "his highly appraised achievements in entanglement theory, quantum complexity theory, and quantum many-body
Fernando_Brandão
Highest rate quantum information can be sent through a noisy quantum channel
In the theory of quantum communication, the quantum capacity is the highest rate at which quantum information can be communicated over many independent
Quantum_capacity
Type of quantum computer
The Kane quantum computer is a proposal for a scalable quantum computer proposed by Bruce Kane in 1998, who was then at the University of New South Wales
Kane_quantum_computer
Quantum computing applied to natural language processing
Quantum natural language processing (QNLP) is the application of quantum computing to natural language processing (NLP). It computes word embeddings as
Quantum natural language processing
Quantum_natural_language_processing
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
Formulation of quantum mechanics
descriptions of the same quantum system. Another advantage is that it is in practice easier to guess the correct form of the Lagrangian of a theory, which naturally
Path-integral_formulation
Physics phenomenon
deterministic complexity of Edmonds' Problem and quantum entanglement". Proceedings of the thirty-fifth annual ACM symposium on Theory of computing. p
Quantum_entanglement
Type of quantum information processing
Adiabatic quantum computing has been shown to be polynomially equivalent to conventional quantum computing in the circuit model. The time complexity for an
Adiabatic_quantum_computation
performing them on quantum devices. In the section of the book on quantum algorithms, chapter 7 includes material on quantum complexity theory and the Deutch
Quantum Computing: A Gentle Introduction
Quantum_Computing:_A_Gentle_Introduction
Secure communication method
Quantum key distribution (QKD) is a secure communication method that implements a cryptographic protocol based on the laws of quantum mechanics, specifically
Quantum_key_distribution
Theorem in physics
in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the
Bell's_theorem
Subfield of computer science and mathematics
computational complexity, parallel and distributed computation, probabilistic computation, quantum computation, automata theory, information theory, cryptography
Theoretical_computer_science
Paradigm of quantum computer
Linear optical quantum computing or linear optics quantum computation (LOQC), also photonic quantum computing (PQC), is a paradigm of quantum computation
Linear optical quantum computing
Linear_optical_quantum_computing
Proposed semiconductor implementation of quantum computers
The spin qubit quantum computer is a quantum computer based on controlling the spin of charge carriers (electrons and electron holes) in semiconductor
Spin_qubit_quantum_computer
Property of states in quantum mechanics
In physics, in the area of quantum information theory and quantum computation, quantum steering is a special kind of nonlocal correlation, which is intermediate
Quantum_steering
Quantum Mechanics in Neural Networks
ideas on quantum neural computation were published independently in 1995 by Subhash Kak and Ron Chrisley, engaging with the theory of quantum mind, which
Quantum_neural_network
Square matrix whose off-diagonal entries are nonpositive
and P-matrices are nonsingular M-matrices. In the context of quantum complexity theory, these are referred to as stoquastic operators. As per the definition
Z-matrix_(mathematics)
Conjecture in quantum gravity
In quantum gravity and quantum complexity theory, the complexity equals action duality (CA-duality) is the conjecture that the gravitational action of
CA-duality
Quantum error correction schemes can suppress the logical error rate arbitrarily low
In quantum computing, the threshold theorem (or quantum fault-tolerance theorem) states that a quantum computer with a physical error rate below a certain
Threshold_theorem
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
Estimate of time taken for running an algorithm
the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly
Time_complexity
Concept in probability theory
well-defined. See also PostBQP, a complexity class defined with postselection. Using postselection it seems quantum Turing machines are much more powerful:
Postselection
Type of code in quantum computing
code typically has a high complexity although those for modern codes do have lower complexity. Quantum convolutional coding theory offers a different paradigm
Quantum_convolutional_code
Theorem in quantum information science
identical copy of an arbitrary unknown quantum state, a statement which has profound implications in the field of quantum computing among others. The theorem
No-cloning_theorem
Subfield of econophysics which applies quantum theory to finance
Quantum finance is an interdisciplinary research field that applies theories and methods developed by quantum physicists and economists to finance. It
Quantum_finance
Computer programming for quantum computers
Quantum programming refers to the process of designing and implementing algorithms that operate on quantum systems, typically using quantum circuits composed
Quantum_programming
Continuous (non-quantized) quantities in quantum information science
to that computer. The classical complexity of many continuous problems is known. Therefore, when the quantum complexity of these problems is obtained,
Continuous-variable quantum information
Continuous-variable_quantum_information
Field of mathematics and science based on non-linear systems and initial conditions
Chaos Theory and Some Assumptions About the Future of the European Union". Chaos, complexity and leadership 2018 explorations of chaotic and complexity theory
Chaos_theory
Networks connecting quantum processors
Quantum networks form an important element of quantum computing and quantum communication systems. Quantum networks facilitate the transmission of information
Quantum_network
Quantum physics-based metaheuristic for optimization problems
Quantum annealing (QA) is an optimization process for finding the global minimum of a given objective function over a given set of candidate solutions
Quantum_annealing
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