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arXiv:2306.10855 · Physical Review Research

Noise-tolerant Grover's algorithm via success-probability prediction

Jian Leng, Fan Yang, Xiang‐Bin Wang

Published Jan 21, 2025• 4 citations
arXivHTMLPDF

Abstract

We present theoretical and experimental studies on efficient quantum search with noise. We propose a noise-tolerant method that significantly reduces the running time and exponentially improves the error threshold with number of qubits for Grover's search. Experiments are implemented on different quantum computing setups, with all results clearly confirming the advantage of our noise-tolerant method to the original Grover's search. In one setup, our method produces quantum advantages while the original Grover's search does not. In another setup with smaller noise, our method produces a larger quantum advantage than the original Grover's search does.

DOI
10.1103/physrevresearch.7.l012017

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Indian Journal of Pure & Applied Physics•Jan 1, 2023•4 citations
We present theoretical and experimental studies on efficient quantum search with noise. We propose a noise-tolerant method that significantly reduces the running time and exponentially improves the error threshold with number of qubits for Grover's search. Experiments are implemented on different quantum computing setups, with all results clearly confirming the advantage of our noise-tolerant method to the original Grover's search. In one setup, our method produces quantum advantages while the original Grover's search does not. In another setup with smaller noise, our method produces a larger quantum advantage than the original Grover's search does.
The Grover lower bound for the unstructured search problem can be surpassed when some information about the data structure is available. Here, we numerically observe that reinforcement can exponentially reduce the number of required evolution layers from D\sqrt{D}D​ to ln⁡D\ln DlnD in a DDD-dimensional system, by exploiting the information provided by the quantum state. Therefore, a reinforced quantum search is expected to exhibit a larger noise threshold compared to a standard search algorithm in a noisy environment. We use numerical simulations to characterize the level of noise tolerance via reinforcement in the presence of both coherent and incoherent noise, considering a system of NNN qubits and a single DDD-level (qudit) system. Our results show that reinforcement significantly enhances the algorithm's success probability and improves the scaling of the number of reinforced evolution layers with system size. These findings indicate that reinforcement offers a promising strategy for error mitigation, especially when a precise noise model is unavailable.
Grover's search algorithm is one of the most significant quantum algorithms, which can obtain quadratic speedup of the extensive search problems. Since Grover's search algorithm cannot be implemented on a real quantum computer at present, its quantum simulation is regarded as an effective method to study the search performance. When simulating the Grover's algorithm, the storage space required is exponential, which makes it difficult to simulate the high-qubit Grover's algorithm. To this end, we deeply study the storage problem of probability amplitude, which is the core of the Grover simulation algorithm. We propose a novel memory-efficient method via amplitudes compression, and validate the effectiveness of the method by theoretical analysis and simulation experimentation. The results demonstrate that our compressed simulation search algorithm can help to save nearly 87.5% of the storage space than the uncompressed one. Thus under the same hardware conditions, our method can dramatically reduce the required computing nodes, and at the same time, it can simulate at least 3 qubits more than the uncompressed one. Particularly, our memory-efficient simulation method can also be used to simulate other quantum algorithms to effectively reduce the storage costs required in simulation.
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.
The combination of quantum sensing with quantum computing to provide an enhancement over conventional quantum sensing has recently emerged as a promising potential application of quantum computing that could give advantages without needing large-scale or fault-tolerant hardware. In this work, we report an experimental demonstration of a recent theoretical proposal to repurpose Grover's search algorithm to improve the ability to detect signals with unknown frequency within a large detection bandwidth. Our experiments were based on a system comprising a single superconducting qubit coupled to a single superconducting cavity, highlighting the modest hardware requirements for realizing the protocol. We found that Grover-based sensing was able to outperform the natural non-Grover baseline for our experimental platform for detection bandwidths $>10 MHz,withanadvantagethatempiricallygrewsuperlinearlywiththebandwidthbeyondthatbreak−evenpoint.TheuseoftheGrover−basedprotocolreducedtheamountofsignalthatneededtobesensedtomakeanaccuratedetectiondecisionbymorethan1010~MHz, with an advantage that empirically grew superlinearly with the bandwidth beyond that break-even point. The use of the Grover-based protocol reduced the amount of signal that needed to be sensed to make an accurate detection decision by more than 1010 MHz,withanadvantagethatempiricallygrewsuperlinearlywiththebandwidthbeyondthatbreak−evenpoint.TheuseoftheGrover−basedprotocolreducedtheamountofsignalthatneededtobesensedtomakeanaccuratedetectiondecisionbymorethan10\times$ for choices of larger detection bandwidth and higher desired detection accuracy. Our results provide a proof-of-principle validation that Grover-based quantum computational sensing can be realized in near-term hardware and provide a metrological advantage well beyond break-even in spite of the additional protocol complexity.
Abstract Quantum computing can solve some classes of problems faster than classical computing. Among the greatest quantum algorithms to showcase this benefit is Grover's search algorithm, which has a quadratic speed-up for unstructured search problems. In this study, we present an implementation of Grover’s algorithm on a large-scale dataset comprising approximately 131,072 (217) names. We contrast its efficiency with the classical linear search based on time complexity, scalability, and the likelihood of success. The experiment was conducted using Qiskit on a quantum simulator, where several query scenarios were implemented to verify the algorithm's efficiency and accuracy. Our findings highlight the theoretical advantage of Grover’s algorithm in situations involving large data sets, while also discussing real-world limitations such as gate noise, qubit number, and circuit depth as we move towards actual quantum hardware. This study serves as a step toward evaluating the real-world relevance of quantum search algorithms and provides information on current challenges and future directions in quantum information retrieval.
For searching an item in unstructured databases, Grover's quantum search algorithm offers quadratic speedup overclassical search algorithms. This paper reports 2 to 5 quantum-bit (Qubit) implementations of Grover's search algorithmusing the phase-flip method for oracle function realization without any extra ancilla qubit. A comprehensive estimation andanalysis of the theoretical and physical accuracies of the algorithm have been presented. The impact of increasing qubits onaccuracy has been computed and analyzed. The metrics delineated for comparison are the number of qubits and gates, depthof the circuit, execution time, and theoretical/physical accuracy. The results revealed a greater disparity between theoreticaland physical accuracy using a higher number of qubits perceived to be caused by noisy qubits utilized in computations. Thenovelty of the work is the investigation of variations caused by the noise in the accuracy and execution time of Grover'ssearch algorithm. The results indicate that because of noise, the accuracy of 2- and 3- qubit implementations declined by14.49% and 33.86%, whereas the execution time increased by 50% and 80%; respectively.