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Physical Review A

Comment on “quantum search protocol for an atomic array”

Mark W. Coffey

Published Oct 25, 2002• 1 citation
Publisher

Abstract

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.

DOI
10.1103/physreva.66.046301

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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.
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 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.
Grover's quantum search algorithm has recently been implemented without entanglement, by replacing multiple particles with a single particle having exponentially many states. We recall that all physical resources must be accounted for to quantify algorithm complexity, and that this scheme typically incurs exponential costs in some other resource(s). In particular, we demonstrate that a recent experimental realization requires exponentially increasing precision. There is, however, a quantum algorithm which searches a "sophisticated" database (not unlike a Web search engine) with a single query, but which we show does not require entanglement even for multiparticle implementations.
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
Quantum information processing based on Rydberg atoms emerged as a promising direction two decades ago. Recent experimental and theoretical progresses have shined exciting light on this avenue. In this concise review, we will briefly introduce the basics of Rydberg atoms and their recent applications in associated areas of neutral atom quantum computation and simulation. We shall also include related discussions on quantum optics with Rydberg atomic ensembles, which are increasingly used to explore quantum computation and quantum simulation with photons.
We discuss the energetic cost of superadiabatic models of quantum computation. Specifically, we investigate the energy-time complementarity in general transitionless controlled evolutions and in shortcuts to the adiabatic quantum search over an unstructured list. We show that the additional energy resources required by superadiabaticity for arbitrary controlled evolutions can be minimized by using probabilistic dynamics, so that the optimal success probability is fixed by the choice of the evolution time. In the case of analog quantum search, we show that the superadiabatic approach induces a non-oracular counter-diabatic Hamiltonian, with the same energy-time complexity as equivalent adiabatic implementations.