Quantum algorithm for linear systems of equations.
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Summary
This work exhibits a quantum algorithm for estimating x(-->)(dagger) Mx(-->) whose runtime is a polynomial of log(N) and kappa, and proves that any classical algorithm for this problem generically requires exponentially more time than this quantum algorithm.
- Type
- article
- Published
- 2008-11-19
- Cited by
- 3,297
- References
- 38
- Access
- Open access
- OpenAlex
- https://openalex.org/W1492999010
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:5187993
Keywords
Combinatorics, Physics, Quantum algorithm, Mathematical physics, Quantum
References
- The Mathematical Theory of Finite Element Methods
- A quantum algorithm to solve nonlinear differential equations
- Creating superpositions that correspond to efficiently integrable probability distributions
- Quantum Computation as Geometry
- Engineering functional quantum algorithms
- Limit on the Speed of Quantum Computation in Determining Parity
- Optimum phase-shift estimation and the quantum description of the phase difference.
- Introduction to the Theory of Computation
- Optimal quantum clocks
- Universal Quantum Simulators
- Approximating fractional time quantum evolution
- Quantum random access memory.
- Efficient Quantum Algorithms for Simulating Sparse Hamiltonians
- Introduction to dynamic systems: Theory, models and applications
- Adiabatic quantum state generation and statistical zero knowledge
- Space-Bounded Quantum Complexity
- An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
- On the Relationship Between Continuous- and Discrete-Time Quantum Walk
- A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
- Quantum algorithms revisited
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- Computational perspectives on Bell Inequalities and many-body quantum correlations
- Using Quantum Computing to Learn Physics
- Experimental realization of an interferometric quantum circuit to increase the computational depth
- Quantum Machine Learning: What Quantum Computing Means to Data Mining
- Reference Frames and Algorithms for Quantum Information Processing
- Preparing topological projected entangled pair states on a quantum computer
- Quipper: Concrete Resource Estimation in Quantum Algorithms
- Estimating the Resources for Quantum Computation with the QuRE Toolbox
- On the computational power of quantum computers
- Feedback control of superconducting quantum circuits
- Transport d'un électron unique dans des nanostructures
- Quantum algorithms for searching, resampling, and hidden shift problems
- Role of Computational Fluid Dynamics and Wind Tunnels in Aeronautics R and D
- Efficient algorithms in quantum query complexity
- Algorithms Bridging Quantum Computation and Chemistry
- Measurements of electric field noise and light-induced charging in cryogenic surface electrode ion traps
- Design of superconducting transmission line integrated surface-electrode ion-traps
- High-order quantum algorithm for solving linear differential equations
- Phase-Noise Limitations on Nonlinear-Optical Quantum Computing
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