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arXiv:1509.04858

Multi-Qubit Dynamical Quantum Search Algorithm with Dissipation

Ali H. Homid, Mahmoud Abdel‐Aty, A.‐S. F. Obada

Published Sep 16, 2015• 0 citations
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Abstract

We invoke an efficient search algorithms as a key challenge in multi-qubit quantum systems. An original algorithm called dynamical quantum search algorithm from which Grover algorithm is obtained at a specified time is presented. This algorithm is distinguished by accuracy in obtaining high probability of finding any marked state in a shorter time than Grover algorithm time. The algorithm performance can be improved with respect to the different values of the controlled phase. A new technique is used to generate the dynamical quantum gates in the presence of dissipation effect that helps in implementing the current algorithm.

DOI
10.48550/arxiv.1509.04858

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We invoke an efficient search algorithms as a key challenge in multi-qubit quantum systems. An original algorithm called dynamical quantum search algorithm from which Grover algorithm is obtained at a specified time is presented. This algorithm is distinguished by accuracy in obtaining high probability of finding any marked state in a shorter time than Grover algorithm time. The algorithm performance can be improved with respect to the different values of the controlled phase. A new technique is used to generate the dynamical quantum gates in the presence of dissipation effect that helps in implementing the current algorithm.
Abstract A new technique was developed to generate the dynamical quantum gates, depend on the ferromagnetism and antiferromagnetism phenomena in the superconducting flux qubits system at the same interaction time. According to the dynamical controls techniques of such gates, we invoke and synthesize a new algorithm called the dynamical quantum search algorithm. The Grover algorithm was obtained at a specified time for the current algorithm. This algorithm was distinguished by accuracy in obtaining high probability of finding any marked state in a shorter time compared with Grover algorithm time. The algorithm performance was improved with respect to different values of the dynamical controls.
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Following experimental work [Nature, 473, 194 (2011)10.1038/nature10012], we propose a new physical scheme for perfect implementation of a quantum search algorithm in the presence of qubits dissipation. It is shown that the Grover algorithm is obtained as a special case of the suggested quantum search algorithm. We have generated the quantum gates to realize the required steps for implementing the algorithm. Experimental evidence has been discussed in which, during a critical portion of quantum annealing, the qubits become entangled, and entanglement persists even as these systems reach equilibrium with a thermal environment. Our results provide an encouraging sign that quantum annealing is a viable technology for large-scale quantum computing. It is shown that the protocol can be successfully implemented within the present experimental limits.
We explore the possibility of an N -qubit ( N > 3) Grover search in cavity QED, based on a fast operation of an N -qubit controlled phase-flip with atoms in resonance with the cavity mode. We demonstrate both analytically and numerically that our scheme can be achieved efficiently to find a marked state with high fidelity and high success probability. As an example, a ten-qubit Grover search is simulated specifically under the discussion of experimental feasibility and challenge. We argue that our scheme is applicable to the case involving an arbitrary number of qubits. As cavity decay is involved in our quantum trajectory treatment, we can analytically understand the implementation of a Grover search subject to dissipation, which will be very helpful for relevant experiments.
Grover's quantum search algorithm is analyzed for the case in which the initial state is an arbitrary pure quantum state $|\ensuremath{\varphi}〉$ of n qubits. It is shown that the optimal time to perform the measurement is independent of $|\ensuremath{\varphi}〉,$ namely, it is identical to the optimal time in the original algorithm in which $|\ensuremath{\varphi}〉=|0〉,$ with the same number of marked states, r. The probability of success Ps{P}_{\mathrm{s}}Ps​ is obtained in terms of the amplitudes of the state $|\ensuremath{\varphi}〉$ and is shown to be independent of r. A class of states, which includes fixed points and cycles of the Grover iteration operator, is identified. The relevance of these results in the context of using the success probability as an entanglement measure is discussed. In particular, the Groverian entanglement measure, previously limited to a single marked state, is generalized to the case of several marked states.
Quantum computing has noteworthy speedup over classical computing by taking advantage of quantum parallelism, i.e., the superposition of states. In particular, quantum search is widely used in various computationally hard problems. Grover's search algorithm finds the target element in an unsorted database with quadratic speedup than classical search and has been proved to be optimal in terms of the number of queries to the database. The challenge, however, is that Grover's search algorithm leads to high numbers of quantum gates, which make it infeasible for the Noise-Intermediate-Scale-Quantum (NISQ) computers. In this paper, we propose a novel hardware efficient quantum search algorithm to overcome this challenge. Our key idea is to replace the global diffusion operation with low-cost local diffusions. Our analysis shows that our algorithm has similar oracle complexity to the original Grover's search algorithm while significantly reduces the circuit depth and gate count. The circuit cost reduction leads to a remarkable improvement in the system success rates, paving the way for quantum search on NISQ machines.