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Quantum algorithm for linear systems of equations.
- A. Harrow, Avinatan Hassidim, S. Lloyd
- Computer Science, MathematicsPhysical review letters
- 19 November 2008
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.
Universal Quantum Simulators
- S. Lloyd
- 23 August 1996
Feynman's 1982 conjecture, that quantum computers can be programmed to simulate any local quantum system, is shown to be correct.
Gaussian quantum information
This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination.
Ultimate physical limits to computation
- S. Lloyd
- Physics, EducationNature
- 13 August 1999
The physical limits of computation as determined by the speed of light c, the quantum scale ℏ and the gravitational constant G are explored.
Quantum random access memory.
An architecture that exponentially reduces the requirements for a memory call: O(logN) switches need be thrown instead of the N used in conventional RAM designs, which yields a more robust QRAM algorithm, as it in general requires entanglement among exponentially less gates, and leads to an exponential decrease in the power needed for addressing.
Quantum-Enhanced Measurements: Beating the Standard Quantum Limit
This work has shown that conventional bounds to the precision of measurements such as the shot noise limit or the standard quantum limit are not as fundamental as the Heisenberg limits and can be beaten using quantum strategies that employ “quantum tricks” such as squeezing and entanglement.
Advances in quantum metrology
The statistical error in any estimation can be reduced by repeating the measurement and averaging the results. The central limit theorem implies that the reduction is proportional to the square root…
Enhanced Sensitivity of Photodetection via Quantum Illumination
- S. Lloyd
- 12 September 2008
It is shown that for photodetection, quantum illumination with m bits of entanglement can in principle increase the effective signal-to-noise ratio by a factor of 2m, an exponential improvement over unentangled illumination.
Quantum Algorithm Providing Exponential Speed Increase for Finding Eigenvalues and Eigenvectors
A new polynomial time quantum algorithm is described that uses the quantum fast Fourier transform to find eigenvalues and eigenvectors of a local Hamiltonian and that can be applied in cases for which all known classical algorithms require exponential time.
Adiabatic quantum computation is equivalent to standard quantum computation
- D. Aharonov, W. V. Dam, J. Kempe, Zeph Landau, S. Lloyd, O. Regev
- Physics, Computer Science45th Annual IEEE Symposium on Foundations of…
- 18 May 2004
The model of adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its exact computational power has been unknown, so this result implies that the adiABatic computation model and the standard quantum circuit model are polynomially equivalent.