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arXiv:2102.01783 · Quantum Information Processing

Implementation of efficient quantum search algorithms on NISQ computers

Kun Zhang, Pooja Rao, Kwangmin Yu, Hyunkyung Lim, V. E. Korepin

Published Jul 1, 2021• 44 citations
arXivHTMLPDF
DOI
10.1007/s11128-021-03165-2

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Abstract Quantum search algorithm (also known as Grover's algorithm) lays the foundation for many other quantum algorithms. Although it is very simple, its implementation is limited on noisy intermediate-scale quantum (NISQ) processors. Grover's algorithm was designed without considering the physical resources, such as depth, in the real implementations. Therefore, Grover's algorithm can be improved for NISQ devices. In this paper, we demonstrate how to implement quantum search algorithms better on NISQ devices. We present detailed benchmarks of the five-qubit quantum search algorithm on different quantum processors, including IBMQ, IonQ, and Honeywell quantum devices. We report the highest success probability of the five-qubit search algorithm compared to previous works. Our results show that designing the error-aware quantum search algorithms is possible, which can maximally harness the power of NISQ computers.
Canonical quantum algorithms often achieve low execution fidelities on current Noisy Intermediate-Scale Quantum (NISQ) hardware. The standard implementation of Grover's search algorithm, designed for theoretical generality, produces deep, gate-heavy circuits that are susceptible to noise. This paper challenges the "one-size-fits-all" design paradigm by using Grammatical Evolution (GE) to automatically discover hardware-efficient, state-specific quantum circuits. We demonstrate this approach by evolving bespoke circuits for all eight 3-qubit computational basis states and executing them on a 133-qubit IBM Heron quantum processor. To our knowledge, this is the first hardware-validated application of GE for this task. The results indicate significant performance gains: evolved circuits achieve hardware-executed fidelities up to 96.9% (vs. 66.3% baseline) while reducing circuit depth by 82.5–96.6% and gate count by 77.4–94.6% compared to canonical implementations. These findings suggest that automated symbolic search is a viable approach to designing algorithms that can execute on today's NISQ devices.
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.