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Quantum multi-programming for Grover’s search

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Quantum multi-programming is a method utilizing contemporary noisy intermediate-scale quantum computers by executing multiple quantum circuits concurrently. Despite early research on it, the research remains on quantum gates or small-size quantum algorithms without correlation. In this paper, we propose a quantum multi-programming (QMP) algorithm for Grover’s search. Our algorithm decomposes Grover’s algorithm by the partial diffusion operator and executes the decomposed circuits in parallel by QMP. We proved that this new algorithm increases the rotation angle of the Grover operator which, as a result, increases the success probability. The new algorithm is implemented on IBM quantum computers and compared with the canonical Grover’s algorithm and other variations of Grover’s algorithms. The empirical tests validate that our new algorithm outperforms other variations of Grover’s algorithms as well as the canonical Grover’s algorithm.

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All code and data generated or analyzed during this study are available at the GitHub repository,


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We would like to thank the Brookhaven National Laboratory operated IBM-Q Hub. This research used quantum computing resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC05-00OR22725. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231 using NERSC award DDR-ERCAP0022229. We acknowledge the access to IonQ and Honeywell Quantum Solution through the Microsoft Azure Quantum grant No. 35984. Microsoft Azure Quantum funded access to quantum computers and simulators from IonQ through the Azure Quantum Credits program. The work of Vladimir Korepin was supported by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Co-design Center for Quantum Advantage (C2QA) under Contract No. DE-SC0012704.

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Correspondence to Kwangmin Yu.

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Appendix A Partial measurement

figure e

Appendix B Qubit mapping layout and circuit depth

In this section, the layout of IBM quantum computers and qubit mappings is visualized. Each sub-figure is results of qiskit.visualization.plot_circuit_layout() function calls in Qiskit, and the numbers in the black circles represent the logical qubits of the QMP circuit before the transpiling.

See Figs. 8, 9, 10.

Fig. 8
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Circuit mapping layouts for G2D3M3 on IBMQ_Brooklyn

Fig. 9
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Circuit mapping layouts for G2D3M3 on IBM_Washington

Fig. 10
figure 10

Circuit mapping layouts for G3D2M2 on IBM_Washington

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Park, G., Zhang, K., Yu, K. et al. Quantum multi-programming for Grover’s search. Quantum Inf Process 22, 54 (2023).

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