Quantum search on noisy intermediate-scale quantum devices

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.

Quantum optimization algorithm for solving elliptic boundary value problems on D-Wave quantum annealing device

“…The solution of the linear system, that is Equation (7), solved using a classical algorithm on a classical computer is…”

“…Thus, it is important to design quantum computing algorithms that work around the limitations of the current NISQ devices, and recent studies addressed how to deal with the quantum noise and make quantum algorithms robust on NISQ computers. [2][3][4][5][6][7][8] HHL algorithm, 9 a monumental quantum algorithm for solving linear systems on the gate model quantum computers, was invented in 2008 and a variety of advanced variations were developed [10][11][12] as well as the finite element method based on HHL. 13 However, HHL and its variations have a lot of limitations such as quantum states of the solution, the need for quantum RAM, limitations of matrix A, and so on.…”

Quantum multi-programming for maximum likelihood amplitude estimation

“…6 Additionally, Variational Quantum Algorithms (VQAs), such as Quantum Approximate Optimization Algorithm (QAOA), 7,8 Variation Quantum Eigensolver (VQE), 9 and Quantum Neural Networks, [10][11][12][13] have drawn attention as a promising candidate to achieve quantum advantage on NISQ devices. A different approach for NISQ devices is improving the traditional quantum algorithms such as Quantum Amplitude Estimation (QAE) [14][15][16][17][18][19][20] and Grover's search [21][22][23][24] to work on NISQ devices efficiently.…”

Practical quantum approximate optimization algorithms on IBM quantum processors

“…In this vein, various quantum error mitigation methods 2 are developed and applied [3][4][5] to Hamiltonian simulations, as well as utilizing pulse level optimization. 6 Additionally, quantum noise-resilient algorithms, such as Quantum Amplitude Estimation (QAE) [7][8][9][10][11][12][13] and Grover's search, [14][15][16][17] were developed to run the traditional quantum algorithms on noisy quantum computers. On the other hand, Variational Quantum Algorithms (VQAs), such as Quantum Approximate Optimization Algorithm (QAOA), 18,19 Variation Quantum Eigensolver (VQE), 20 and Quantum Machine Learning, [21][22][23][24][25] have drawn attention as a promising candidate to achieve quantum advantage on NISQ devices.…”