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Register a new userImplementation of quantum search algorithm using classical Fourier optics
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Added by
Robert J. C. Spreeuw
Publication date
2001
fields
Physics
and research's language is
English
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We report on an experiment on Grovers quantum search algorithm showing that {em classical waves} can search a $N$-item database as efficiently as quantum mechanics can. The transverse beam profile of a short laser pulse is processed iteratively as the pulse bounces back and forth between two mirrors. We directly observe the sought item being found in $simsqrt{N}$ iterations, in the form of a growing intensity peak on this profile. Although the lack of quantum entanglement limits the {em size} of our database, our results show that entanglement is neither necessary for the algorithm itself, nor for its efficiency.
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We report the implementation of Grovers quantum search algorithm in the scalable system of trapped atomic ion quantum bits. Any one of four possible states of a two-qubit memory is marked, and following a single query of the search space, the marked element is successfully recovered with an average probability of 60(2)%. This exceeds the performance of any possible classical search algorithm, which can only succeed with a maximum average probability of 50%.
Grovers algorithm has achieved great success. But quantum search algorithms still are not complete algorithms because of Grovers Oracle. We concerned on this problem and present a new quantum search algorithm in adiabatic model without Oracle. We analyze the general difficulties in quantum search algorithms and show how to solve them in the present algorithm. As well this algorithm could deal with both single-solution and multi-solution searches without modification. We also implement this algorithm on NMR quantum computer. It is the first experiment which perform a real quantum database search rather than a marked-state search.
Grovers Search algorithm was a breakthrough at the time it was introduced, and its underlying procedure of amplitude amplification has been a building block of many other algorithms and patterns for extracting information encoded in quantum states. In this paper, we introduce an optimization of the inversion-by-the-mean step of the algorithm. This optimization serves two purposes: from a practical perspective, it can lead to a performance improvement; from a theoretical one, it leads to a novel interpretation of the actual nature of this step. This step is a reflection, which is realized by (a) cancelling the superposition of a general state to revert to the original all-zeros state, (b) flipping the sign of the amplitude of the all-zeros state, and finally (c) reverting back to the superposition state. Rather than canceling the superposition, our approach allows for going forward to another state that makes the reflection easier. We validate our approach on set and array search, and confirm our results experimentally on real quantum hardware.
We report the realization of a nuclear magnetic resonance computer with three quantum bits that simulates an adiabatic quantum optimization algorithm. Adiabatic quantum algorithms offer new insight into how quantum resources can be used to solve hard problems. This experiment uses a particularly well suited three quantum bit molecule and was made possible by introducing a technique that encodes general instances of the given optimization problem into an easily applicable Hamiltonian. Our results indicate an optimal run time of the adiabatic algorithm that agrees well with the prediction of a simple decoherence model.
Quantum computers will allow calculations beyond existing classical computers. However, current technology is still too noisy and imperfect to construct a universal digital quantum computer with quantum error correction. Inspired by the evolution of classical computation, an alternative paradigm merging the flexibility of digital quantum computation with the robustness of analog quantum simulation has emerged. This universal paradigm is known as digital-analog quantum computing. Here, we introduce an efficient digital-analog quantum algorithm to compute the quantum Fourier transform, a subroutine widely employed in several relevant quantum algorithms. We show that, under reasonable assumptions about noise models, the fidelity of the quantum Fourier transformation improves considerably using this approach when the number of qubits involved grows. This suggests that, in the Noisy Intermediate-Scale Quantum (NISQ) era, hybrid protocols combining digital and analog quantum computing could be a sensible approach to reach useful quantum supremacy.
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