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arXiv:2006.10037 · Physical Review A

Prospect of using Grover's search in the noisy-intermediate-scale quantum-computer era

Yulun Wang, Predrag Krstić

Published Oct 20, 2020• 30 citations
arXivHTMLPDF

Abstract

In order to understand the bounds of utilization of Grover's search algorithm for large unstructured data in the presence of quantum computer noise, we undertake a series of simulations by inflicting various types of noise, modeled by the IBM qiskit. We apply three forms of Grover's algorithm: (i) the standard one, with 4--10 qubits; (ii) a recently published modified Grover's algorithm, set to reduce the circuit depth; and (iii) the algorithms in (i) and (ii) with multicontrol Toffoli's gates modified by the addition of an ancilla qubit. Based on these simulations, we find the upper bound of noise for these cases, establish its dependence on the quantum depth of the circuit, and provide comparison among them. By extrapolation of the fitted thresholds, we predict what would be the typical gate error bounds when applying Grover's algorithms for the search of data in a data set as large as 32 000.

DOI
10.1103/physreva.102.042609

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In order to understand the bounds of utilization of Grover's search algorithm for large unstructured data in the presence of quantum computer noise, we undertake a series of simulations by inflicting various types of noise, modeled by the IBM qiskit. We apply three forms of Grover's algorithm: (i) the standard one, with 4--10 qubits; (ii) a recently published modified Grover's algorithm, set to reduce the circuit depth; and (iii) the algorithms in (i) and (ii) with multicontrol Toffoli's gates modified by the addition of an ancilla qubit. Based on these simulations, we find the upper bound of noise for these cases, establish its dependence on the quantum depth of the circuit, and provide comparison among them. By extrapolation of the fitted thresholds, we predict what would be the typical gate error bounds when applying Grover's algorithms for the search of data in a data set as large as 32 000.
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.
Target item searching in large-scale, unstructured text databases is a major computational task for traditional systems and usually requires algorithms whose time complexity is on the order ofO(N)O(N)O(N). Quantum computing presents a strong competitor by using Grover's algorithm, where theoretically the search complexity comes down toO(N)O(\sqrt{N})O(N​), making faster retrieval possible. This research considers the design and assessment of Grover's algorithm as it is used to find a target word in a paragraph. The process entails encoding a group of unique words into a quantum register and implementing a circuit that incorporates a bespoke oracle and a diffusion operator to amplify the probability amplitude of the target state. Performance was evaluated in two situations: an ideal noise-free simulation with Qiskit's AerSimulator and a real-world run on IBM's quantum hardware. Simulation results demonstrated always-high accuracy in identifying the target word. But tests on real quantum machines indicated that the reliability of the algorithm decreases with an increase in qubits. Though circuits of up to five qubits had tolerable accuracy, larger configurations were plagued by noise, gate errors, and decoherence effects. These results highlight both the potential of quantum search algorithms for text processing and the limitations of NISQ today.
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.
Unstructured searching, which is to find the marked element from a given unstructured data set, is a widely studied problem in computer science. It is well known that Grover algorithm provides a quadratic speedup to solve unstructured search problem compared with the classical algorithm. This algorithm has received a lot of attention due to the strong versatility. In this manuscript, we report experimental results of searching a unique target from 16 elements on five different quantum devices of IBM quantum Experience (IBMQ). We first implement the original Grover algorithm on these devices. However, the experiment probability of success of finding the correct target is almost the same as random choice. We then optimize the quantum circuit size of the search algorithm. The oracle operator and diffusion operator are two of the most costly operators in Grover algorithm. For the 16-element quantum search algorithm, both the oracle operator and diffusion operator consist of a triple controlled [Formula: see text] gate ([Formula: see text]) and some single-qubit gates. So we optimize the implementation of the [Formula: see text] gate according to the qubits layout of different quantum devices. On the ibmq_santiago, the experimental success rate of the 16-element quantum search algorithm is increased to [Formula: see text] by the optimization, which is better than all the published experiments implemented on IBMQ devices. For other IBMQ devices, the experimental success rate of 16-element quantum search also has been significantly improved. We then try to further reduce the size of the quantum circuit by modifying the Grover algorithm, with a tolerable loss of the theoretical success probability. On ibmq_quito, the experimental success rate is further improved from 25.23% to 27.56% after optimization. These experimental results show the importance of circuit optimization and algorithm optimization in the Noisy-Intermediate-Scale Quantum (NISQ) era.
Classical database join operations are a significant performance bottleneck in data-intensive applications, typically requiring quadratic time proportional to the size of the input. Quantum search algorithms, such as Grover’s algorithm, promise asymptotic speedups for unstructured search and can be adapted to accelerate equality-based joins. In this paper, we present a systematic simulation study of a Grover-based quantum join primitive and a hybrid classical-quantum join scheme, comparing them with a baseline classical nested-loop join. Parameterised Grover circuits have been implemented for marked-item search, together with resource estimation (qubit count, circuit depth, and gate counts), using the Qiskit Aer simulator. The classical join is modelled as a nested-loop equality join over two arrays, while the hybrid scheme uses a classical Bloom filter to reduce the candidate space, followed by a Grover search over the remaining items. To approximate near term hardware, we incorporate depolarizing gate noise and readout noise via Aer noise models and investigate two mitigation techniques: readout error calibration and zero noise extrapolation. Our simulations, conducted in a Python environment without GPU acceleration, demonstrate that the Grover based and hybrid joins exhibit the expected sub-quadratic scaling in runtime compared to the classical nested-loop join for problem sizes up to N = 215. We additionally observe that realistic noise significantly degrades the raw success probability of the quantum join, while combining readout mitigation with zero noise extrapolation partially restores accuracy. These results provide a resource-aware and noise-aware baseline for evaluating quantum-accelerated joins on future fault-tolerant or high-fidelity noisy intermediate-scale quantum (NISQ) devices.
Grover’s algorithm is a quantum search algorithm that makes a huge difference in finding an element of interest from unsorted and unstructured data. In the case of a classical search algorithm, testing O(N) elements within a dataset of size N is a significant number. Grover’s algorithm reduces this number to O(N)O(\sqrt N )O(N​) so the gain is obvious. This paper covers applied aspects of Grover’s algorithm, namely quantum circuit layout, efficiency of gates, fidelity of qubits, and the optimization of resources for searching unstructured data. Focus has been placed on quantum error correction: namely, planar surface code; resource costs involved have been quantified. The paper discusses the implications of quantum computing on data retrieval and how algorithms in quantum computing are crucial for solving issues presented by a changing environment of computation.