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Quantum algorithm for solving systems of linear equations
The Harrow–Hassidim–Lloyd (HHL) algorithm is a quantum algorithm for obtaining certain limited information about the solution to a system of linear equations
HHL_algorithm
Topics referred to by the same term
HHL could refer to: Hafthohlladung, a German anti-tank mine of World War II Handelshochschule Leipzig, now the HHL Leipzig Graduate School of Management
HHL
Algorithm to be run on quantum computers
system for algorithm discovery and optimization Quantum machine learning Quantum optimization algorithms Quantum sort Primality test HHL algorithm Nielsen
Quantum_algorithm
American computer scientist (born 2000)
known classical algorithms. The best known quantum algorithm for matrix completion runs in polylogarithmic time by using the HHL algorithm as a subroutine
Ewin_Tang
Computer hardware technology that uses quantum mechanics
practical end-to-end advantage on current devices. For example, the HHL Algorithm, named after its discoverers Harrow, Hassidim, and Lloyd, is believed
Quantum_computing
Optimization algorithms using quantum computing
least-squares fitting algorithm makes use of a version of Harrow, Hassidim, and Lloyd's quantum algorithm for linear systems of equations (HHL), and outputs the
Quantum optimization algorithms
Quantum_optimization_algorithms
American quantum information scientist
introduced the HHL algorithm for solving systems of linear equations, and later several quantum machine learning algorithms based on it. These algorithms were widely
Seth_Lloyd
Quantum algorithm framework
S2CID 1118993. Quantum algorithm HHL algorithm Quantum machine learning Digital signal processing Implementation of the QSVT algorithm for matrix inversion
Quantum singular value transformation
Quantum_singular_value_transformation
Deterministic quantum algorithm
The Deutsch–Jozsa algorithm is a deterministic quantum algorithm proposed by David Deutsch and Richard Jozsa in 1992 with improvements by Richard Cleve
Deutsch–Jozsa_algorithm
American quantum information theorist (born 1980)
and Seth Lloyd introduced the HHL algorithm. The algorithm was widely thought to give quantum machine learning algorithms with exponential speedups over
Aram_Harrow
query algorithms Hamiltonian simulation: simulates the time evolution of quantum systems governed by a Hamiltonian HHL algorithm: quantum algorithm for
List_of_algorithms
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
Computational complexity class of problems
the Jones polynomial at certain roots of unity Harrow-Hassidim-Lloyd (HHL) algorithm Hidden subgroup problem Polynomial hierarchy (PH) Quantum complexity
BQP
Quantum algorithm for integer factorization
Shor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor
Shor's_algorithm
Quantum algorithm
The Bernstein–Vazirani algorithm, which solves the Bernstein–Vazirani problem, is a quantum algorithm invented by Ethan Bernstein and Umesh Vazirani in
Bernstein–Vazirani_algorithm
Problem in computer science
computer. The quantum algorithm solving Simon's problem, usually called Simon's algorithm, served as the inspiration for Shor's algorithm. Both problems are
Simon's_problem
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
List of quantum computing algorithms
algorithms, including algorithms, algorithmic techniques, computational models, and problem frameworks used in quantum computing. A quantum algorithm
List_of_quantum_algorithms
Applications of machine learning to quantum physics
computing Quantum machine learning Quantum annealing Quantum neural network HHL Algorithm Comparison of machine learning software Torlai, Giacomo; Mazzola, Guglielmo;
Machine_learning_in_physics
Very general problem in computer science
especially important in the theory of quantum computing because Shor's algorithms for factoring and finding discrete logarithms in quantum computing are
Hidden_subgroup_problem
Research University in Kolkata, India
sixteen-year bottleneck in quantum computing. Their pioneering Ψ-HHL algorithm optimizes the classic HHL framework, which was previously hindered by high "condition
The Chatterjee Group Centres for Research and Education in Science and Technology
The_Chatterjee_Group_Centres_for_Research_and_Education_in_Science_and_Technology
Cryptography secured against quantum computers
quantum-resistant, is the development of cryptographic algorithms (usually public-key algorithms) that are currently thought, but not proven, to be secure
Post-quantum_cryptography
is demonstrated. Graphene quantum dot spin qubits are proposed. The HHL algorithm for solving linear equations is published. Graphene quantum dot qubits
Timeline of quantum computing and communication
Timeline_of_quantum_computing_and_communication
Quantum computing algorithm
Clifford gates are also universal. The first magic state distillation algorithm, invented by Sergey Bravyi and Alexei Kitaev, is as follows. Input: Prepare
Magic_state_distillation
Change of basis applied in quantum computing
many quantum algorithms, notably Shor's algorithm for factoring and computing the discrete logarithm, the quantum phase estimation algorithm for estimating
Quantum_Fourier_transform
Quantum algorithm
In quantum computing, the Brassard–Høyer–Tapp (BHT) algorithm is a quantum algorithm that solves the collision problem. In this problem, one is given n
BHT_algorithm
Quantum algorithm
eigensolver (VQE) is a quantum algorithm for quantum chemistry, quantum simulations and optimization problems. It is a hybrid algorithm that uses both classical
Variational quantum eigensolver
Variational_quantum_eigensolver
Quantum algorithm for counting solutions to search problems
Quantum counting algorithm is a quantum algorithm for efficiently counting the number of solutions for a given search problem. The algorithm is based on the
Quantum_counting_algorithm
Quantum physics-based metaheuristic for optimization problems
Apolloni, N. Cesa Bianchi and D. De Falco as a quantum-inspired classical algorithm. It was formulated in its present form by T. Kadowaki and H. Nishimori
Quantum_annealing
Quantum algorithm
search (sometimes regarded as QFS, similar to DFS and BFS) is a quantum algorithm for finding a marked node in a graph. The concept of a quantum walk is
Quantum_walk_search
Algorithm in quantum information theory
Algorithmic cooling is an algorithmic method for transferring heat (or entropy) from some qubits to others or outside the system and into the environment
Algorithmic_cooling
Search problem in quantum mechanics
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Hidden linear function problem
Hidden_linear_function_problem
Interdisciplinary research area
Many QML algorithms in this category are based on variations of the quantum algorithm for linear systems of equations (colloquially called HHL, after the
Quantum_machine_learning
Sorting algorithms for quantum computers
A quantum sort is any sorting algorithm that runs on a quantum computer. Any comparison-based quantum sorting algorithm would take at least Ω ( n log
Quantum_sort
Computational benchmark
has a superpolynomial speedup over the best known or possible classical algorithm for that task. Examples of proposals to demonstrate quantum supremacy
Quantum_supremacy
Experimental technology level
approximate optimization algorithm (QAOA), which use NISQ devices but offload some calculations to classical processors. These algorithms have been successful
Noisy intermediate-scale quantum computing
Noisy_intermediate-scale_quantum_computing
Quantum computing protocol
a Shadow generation algorithm. When predicting the properties of ρ {\displaystyle \rho } , a Median-of-means estimation algorithm is used to deal with
Classical_shadow
Quantum computing technique
generalizes the idea behind Grover's search algorithm, and gives rise to a family of quantum algorithms. It was discovered by Gilles Brassard and Peter
Amplitude_amplification
quantum systems and compute molecular spectra (building on approaches like HHL). Machine Learning (potential): While not yet fully demonstrated, Qrisp's
Qrisp
Theorem in physics
J.; Spekkens, Robert W. (2015-03-03). "The lesson of causal discovery algorithms for quantum correlations: causal explanations of Bell-inequality violations
Bell's_theorem
Code used in quantum error correction
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Shor_code
Computational complexity of quantum algorithms
time. Asymptotic computational complexities of both quantum algorithms and classical algorithms are often expressed with asymptotic notation. Some common
Quantum_complexity_theory
Interdisciplinary theory behind quantum computing
engineering. It involves developing theoretical frameworks, designing quantum algorithms, constructing quantum hardware, and implementing quantum communication
Quantum_information_science
Theorem in quantum information theory
{\displaystyle U} to operator norm error. Furthermore, there is an efficient algorithm to find such a sequence. More generally, the theorem also holds in SU(d)
Solovay–Kitaev_theorem
Basic circuit in quantum computing
although they can also be whole algorithms (e.g. the Quantum Fourier transform) – But this is only true if such algorithms contains no measurement operations
Quantum_logic_gate
Secure communication method
encryption algorithm to encrypt (and decrypt) a message, which can then be transmitted over a standard communication channel. The algorithm most commonly
Quantum_key_distribution
Polyalphabetic encryption system
EWZ EXY FFP FGO FHN FIM FJL FKK FVZ FWY FXX GGN GHM GIL GJK GUZ GVY GWX HHL HIK HJJ HTZ HUY HVX HWW IIJ ISZ ITY IUX IVW JRZ JSY JTX JUW JVV KQZ KRY KSX
Beaufort_cipher
Quantum mechanics idea
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Entanglement_swapping
Model of quantum computation
captures all of the power of quantum computation—that is, any quantum algorithm can be expressed formally as a particular quantum Turing machine. However
Quantum_Turing_machine
Open-source software development kit
(quantum applications or algorithmic routines) on the IBM Quantum Platform to invoke as needed. This turns custom quantum algorithms into services, enabling
Qiskit
Quantum key distribution protocol - B92
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
B92_protocol
Complexity class
Turing machine with postselection and bounded error (in the sense that the algorithm is correct at least 2/3 of the time on all inputs). Postselection is not
PostBQP
Property of computational resources needed
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Magic_(quantum_information)
Quantum cryptographic method
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Six-state_protocol
Type of quantum information processing
computing in the circuit model. The time complexity for an adiabatic algorithm is the time taken to complete the adiabatic evolution which is dependent
Adiabatic_quantum_computation
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
Crucial concept of quantum information
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Incompatibility of quantum measurements
Incompatibility_of_quantum_measurements
Quantum computing applied to natural language processing
processes. The first quantum algorithm for natural language processing used the DisCoCat framework and Grover's algorithm to show a quadratic quantum speedup
Quantum natural language processing
Quantum_natural_language_processing
Restricted model of non-universal quantum computation
classical polynomial-time algorithm for the exact boson sampling problem highly unlikely. The best proposed classical algorithm for exact boson sampling
Boson_sampling
Definition of quantum circuits
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Clifford_gate
Quantum key distribution protocol
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
BB84
Quantum Mechanics in Neural Networks
the desired output algorithm's behavior. The quantum network thus 'learns' an algorithm. The first quantum associative memory algorithm was introduced by
Quantum_neural_network
Quantum error correcting code
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Bacon–Shor_code
Quantum error correcting code
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Gottesman–Kitaev–Preskill code
Gottesman–Kitaev–Preskill_code
Networks connecting quantum processors
NV centers can be utilized at room temperatures. Small scale quantum algorithms and quantum error correction has already been demonstrated in this system
Quantum_network
Cloud quantum computing platform
are freely accessible by the public. This service can be used to run algorithms and experiments, and explore tutorials and simulations around what might
IBM_Quantum_Platform
Technique for comparing quantum states
Wiebe, Nathan; Kapoor, Anish; Svore, Krysta M. (1 March 2015). "Quantum Algorithms for Nearest-Neighbor Methods for Supervised and Unsupervised Learning"
Swap_test
Information held in the state of a quantum system
quantum algorithms can be used to perform computations faster than in any known classical algorithm. The most famous example of this is Shor's algorithm that
Quantum_information
Topological quantum error correcting code
upper limits and are useless unless efficient algorithms are found to achieve them. The most well-used algorithm is minimum weight perfect matching. When applied
Surface_code
Property of states in quantum mechanics
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Quantum_steering
Remote quantum processors for computation
internet. Cloud access enables users to develop, test, and execute quantum algorithms without the need for direct interaction with specialized hardware, facilitating
Cloud-based_quantum_computing
Type of quantum computer built out of Rydberg atoms
B.; Noel, T.; Saffman, M. (April 2022). "Multi-qubit entanglement and algorithms on a neutral-atom quantum computer". Nature. 604 (7906): 457–462. arXiv:2112
Neutral_atom_quantum_computer
Description of a quantum-mechanical system
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Schrödinger_equation
Unit of quantum information
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Qutrit
Type of error correction in quantum computing
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Five-qubit error correcting code
Five-qubit_error_correcting_code
Structure that repeats in time; a novel type or phase of non-equilibrium matter
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Time_crystal
Quantum-informatics technique
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Quantum_state_discrimination
Quantum logic gate
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Cirac–Zoller controlled-NOT gate
Cirac–Zoller_controlled-NOT_gate
Planned quantum technology campus in Chicago
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Illinois Quantum and Microelectronics Park
Illinois_Quantum_and_Microelectronics_Park
Superconducting qubit implementation
qubits that have had the most success are ion traps and NMR, with Shor's algorithm even being implemented using NMR. However, it is hard to see these two
Charge_qubit
decision problem is a member of BQP if there exists a quantum algorithm (an algorithm that runs on a quantum computer) that solves the decision problem
Glossary_of_quantum_computing
Quantum channel
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Amplitude_damping_channel
Computation complexity problem
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Hidden_matching_problem
Protocol in quantum cryptography
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Decoy_state
Principle in quantum information theory
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
No-communication_theorem
Concept in quantum information theory
theorem. Purification is used in algorithms such as entanglement distillation, magic state distillation and algorithmic cooling. Let H S {\displaystyle
Quantum_state_purification
Metric for a quantum computer's capabilities
< N, the quantum volume goes down if more qubits are added. To run an algorithm that only requires n < N qubits on an N-qubit machine, it could be beneficial
Quantum_volume
Computer science
This is in contrast to bounded-error quantum computing, where quantum algorithms are expected to run in polynomial time, but may not always do so. In the
Exact_quantum_polynomial_time
Open-source framework for quantum computers
# m1=11010 OpenFermion is a library that compiles quantum simulation algorithms to Cirq. TensorFlow Quantum is an extension of TensorFlow that allows
Cirq
Physical phenomenon
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Quantum_teleportation
Intermediate representation for quantum instructions
is a programming language designed for describing quantum circuits and algorithms for execution on quantum computers. It is designed to be an intermediate
OpenQASM
Theorem of quantum circuits
understood[citation needed]. The Gottesman-Knill theorem proves that all quantum algorithms whose speed up relies on entanglement that can be achieved with CNOT and
Gottesman–Knill_theorem
Basic unit of quantum information
Youpeng; Yan, Fei; Sun, Xiaoming; Yu, Dapeng (2022-11-14). "Scalable algorithm simplification using quantum AND logic". Nature Physics. 19 (1). Springer
Qubit
Model of computation
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
One_clean_qubit
Point defect in diamonds
also be initialized as qubits and enable the implementation of quantum algorithms and networks. It has also been explored for applications in quantum computing
Nitrogen-vacancy_center
Types of quantum information
a physical or abstract qubit that performs as specified in a quantum algorithm or quantum circuit subject to unitary transformations, has a long enough
Physical_and_logical_qubits
Type of quantum computer
Nonetheless, certain algorithms may be a more natural fit to the topological quantum computer model. For example, algorithms for evaluating the Jones
Topological_quantum_computer
Process in quantum computing
Various strategies exist for encoding and decoding, including classical algorithms that map measured error syndromes to their corresponding recovery operations
Quantum_error_correction
Form of quantum computing
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
Hamiltonian quantum computation
Hamiltonian_quantum_computation
Class of quantum error correcting codes
sharing Quantum algorithms Algorithmic cooling Amplitude amplification Bernstein–Vazirani BHT Boson sampling Deutsch–Jozsa Grover's HHL Hidden subgroup
CSS_code
HHL ALGORITHM
HHL ALGORITHM
Surname or Lastname
English
English : variant spelling of Keel.Perhaps an Americanized spelling of German Kehl or Kühl (see Kuhl).
Surname or Lastname
English
English : variant spelling of Beal.Americanized spelling of German Biehl or Bühl (see Buehl).
Girl/Female
Norse
Goddess of the underworld.
Girl/Female
Anglo, Arabic, Australian
Wife of Prophet Jacob and Mother of Prophet Joseph
Surname or Lastname
English and Scottish
English and Scottish : of uncertain origin; in part it may be a shortened form of McCall.Probably also an Americanized spelling of Ahl or Al.
Surname or Lastname
English and Irish
English and Irish : variant spelling of Keeley.Americanized spelling of German Kühle, variant of Kühl (see Kuhl).
Boy/Male
English American German Norse Shakespearean Teutonic
A nickname for Henry 'Rules his household.
Boy/Male
American, Anglo, Australian, British, Christian, Danish, English, German, Norse, Scandinavian, Teutonic
Rules his Household; A Nickname for Henry; Estate Ruler; Army Ruler; Home Ruler
Female
Hungarian
Hungarian form of Hebrew Rachel, RÃHEL means "ewe."
Boy/Male
Muslim/Islamic
Name of an Ahl As-Suffah
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : habitational name from any of various minor places in northern England so named from Old English hol ‘hollow’, ‘sunken’ + rod ‘clearing’ (see Rhodes).
Surname or Lastname
English (Lancashire)
English (Lancashire) : habitational name from a place near Accrington named Brocklehurst, from Old English brocc-hol ‘badger’s sett’ + hyrst ‘wooded hill’.
Male
English
Pet form of English Henry, HAL means "home-ruler."
Boy/Male
Christian & English(British/American/Australian)
Variant of Henry
Surname or Lastname
English (northern)
English (northern) : habitational name from any of various places, for example in West Yorkshire, so called from Old English hol ‘hollow’, ‘sunken’ + Old Norse gata ‘road’.
Boy/Male
Shakespearean
King Henry IV, 1 & 2' King. Also Hal, king's son and Prince of Wales, who becomes Henry V....
Surname or Lastname
English
English : variant spelling of Allman.Swedish : variant spelling of Ahlman.German : variant spelling of Ahl(e)mann (see Ahlman).Jewish (Ashkenazic) : variant spelling of Almen ‘widower’.
Girl/Female
French
Little Hal.
Boy/Male
Biblical
Pain, infirmity.
Biblical
pain; infirmity
HHL ALGORITHM
HHL ALGORITHM
Boy/Male
Shakespearean
The Life of Timon of Athens'.
Surname or Lastname
English
English : from Old French balon ‘bundle’, ‘roll’, ‘pack’, hence a nickname for a small, rotund man or possibly a metonymic occupational name for a carrier of goods and merchandise.French (Bâlon) : generally regarded as a habitational name from Baalons in the Ardennes, it may however simply be from balon ‘ball’, ‘roll’ (see 1) or a derivative of Bal.
Boy/Male
Arabic, Muslim
An Accomplished Person; A Scholar
Boy/Male
Tamil
From the meadow farm
Girl/Female
American, Australian, British, English, Greek
Manifestation of God; Appearance
Girl/Female
Indian
Eye
Boy/Male
Tamil
A part of divine
Girl/Female
Spanish Italian
Boy/Male
Muslim/Islamic
Light of the religion
Boy/Male
Tamil
Nirmit | நிரà¯à®®à®¿à®¤Â
Created
HHL ALGORITHM
HHL ALGORITHM
HHL ALGORITHM
HHL ALGORITHM
HHL ALGORITHM
n.
The art of calculating with any species of notation; as, the algorithms of fractions, proportions, surds, etc.
a.
Whole.
n.
Alt. of Algorithm
n.
The art of calculating by nine figures and zero.