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Physical Review A

Quantum search protocol for an atomic array

Marlan O. Scully, Muhammad Suhail Zubairy

Published Jul 5, 2001• 11 citations
Publisher

Abstract

Quantum computers can, in principle, exceed the speed of ordinary computers by taking advantage of quantum coherence and entanglement. It is possible to find a ``needle in a haystack'' of $N\ensuremath{-}1$ straws in only $\sqrt{N}$ searches by utilizing coherent superposition states. In the present paper we show how modern quantum optics may provide a simple and practicable quantum search procedure, which may also yield insights into quantum search algorithms in general.

DOI
10.1103/physreva.64.022304

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Mark W. Coffey

A very recent proposal for performing quantum search without entanglement by optical means is briefly discussed. Since the search of a simple, completely unstructured list or its equivalent is involved, it appears that exponential resources are required. Therefore the proposed search of a Rydberg-atom array is not practicable for quantum computing.

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Quantum computers can, in principle, exceed the speed of ordinary computers by taking advantage of quantum coherence and entanglement. It is possible to find a ``needle in a haystack'' of N\ensuremath−1N\ensuremath{-}1N\ensuremath−1 straws in only N\sqrt{N}N​ searches by utilizing coherent superposition states. In the present paper we show how modern quantum optics may provide a simple and practicable quantum search procedure, which may also yield insights into quantum search algorithms in general.
Quantum mechanics can speed up a range of search applications over unsorted data. For example, imagine a phone directory containing NNN names arranged in completely random order. To find someone's phone number with a probability of 50%, any classical algorithm (whether deterministic or probabilistic) will need to access the database a minimum of 0.5N0.5N0.5N times. Quantum mechanical systems can be in a superposition of states and simultaneously examine multiple names. By properly adjusting the phases of various operations, successful computations reinforce each other while others interfere randomly. As a result, the desired phone number can be obtained in only O(N)O(\sqrt{N})O(N​) accesses to the database.
In this paper we propose a practical framework to utilize quantum computers in the future. To the best of our knowledge, this is the first paper to show a concrete usage of quantum computation in general programming. In our framework, we can utilize a quantum computer as a coprocessor to speed-up some parts of a program that runs on a classical computer. To do so, we propose several new ideas and techniques, such as a practical method to design a large quantum circuits for search problems and an efficient quantum comparator.
Any computation is necessarily a physical process. The current drive towards increasing speed and miniaturization of computers lead modern technology towards the subatomic domain - quantum computing, where strange quantum behavior takes over from familiar classical notions. The quantum computers have the ability to solve problems with varied computational complexities and more importantly hard problems. A problem is said to be hard, if the best possible algorithm requires exponential resources. This exponential quantum parallelism is the basis for the quantum speedup of many algorithms, and has made the construction of fast algorithms for quantum computers possible. Various proposals exist for modeling and devising procedures on computational problems related to factoring, searching, quantum counting, generalization of quantum algorithms etc. (Shor, 1994). In this paper, we have discussed the importance of algorithms such as order-finding, factoring and quantum searching which require exorbitant resources for their solution which otherwise is impossible on a classical computer
Abstract Quantum superposition is a powerful computational tool to have at one’s disposal – in fact, a phrase along the lines quantum computers evaluate a function for every possible input in superposition and hence achieve a massive speed-up appears in virtually every popular and media article on the subject. The reality is, however, a little more complicated. In this chapter, we look at what is probably the closest quantum algorithm to the naive idea of ‘evaluating for every possibility at once’, namely Lov Grover’s quantum search algorithm. Grover’s algorithm is one of the oldest and most important quantum algorithms and offers a quadratic advantage over the best possible classical algorithm for the problem of searching an unstructured database. Notably, a quadratic quantum advantage is the best one can hope for in certain problems that exhibit a lack of structure, which is proven by considering the performance of the best possible quantum algorithm tackling the OR problem.
The quantum Fourier transform (QFT);Similarities and differences of coherent optical FFT to the QFT. Grover’s search algorithm implemented with a coherent optical correlator. Quantum algorithms requiring bit entanglement -Shor’s algorithm for large number factorisation. Spatial Light Modulator (SLM) pixels placed in a binary superposition state. Addressed with an “interaction free” measurement. Allows exponential increase in processing power. Quantum search algorithm for a decryption problem based on superposition state of coherent wavefront.