The Variational Quantum Eigensolver (VQE) is an algorithm that may enable the near-term application of intermediate-scale quantum computers to solve quantum chemistry and optimization problems. The variational nature of such a quantum-classical hybrid algorithm allows one to construct the trial wave function of quantum simulation by inherent interactions in available hardware [1]. Meanwhile, techniques in Nuclear Magnetic Resonance (NMR) have been revisited recently to propose the substitution of pulsed entangling gates in quantum algorithms with continuous-time evolution of the system Hamiltonian [2,3,4]. Here we propose a novel scheme to prepare the trial wave function for quantum-classical hybrid algorithms by free evolution of native couplings and spin echoes. We discuss how this NMR-inspired method fits naturally to the implementation of near-term algorithms.

As a concrete example, we report a quantum chemistry simulation using the VQE on a 2-qubit superconducting device [5] in which we use fixed frequency qubits and build the algorithm using the native 2-qubit interaction resulting from a static capacitive coupling. The quantum circuit of the VQE is constructed by varying the timings of echo pulses to manipulate the native ZZ coupling. This method allows us to implement a VQE algorithm without needing repeated 2-qubit-gate tune-up and enables the simple and understandable implementation of error mitigation [6,7].

[1] A. Kandala, et al., Nature, 549 242-246 (2017).
[2] A. Parra-Rodriguez, et al., Phys. Rev. A 101, 022305 (2020).
[3] G. Bhole, et al., Phys. Rev. Applied. 13, 034002 (2020).
[4] T. Tsunoda et al., Phys. Rev. A 102, 032405 (2020).
[5] J. Rahamim, et al., Appl. Phys. Lett. 110, 222602 (2017).
[6] K. Temme, et al., Phys. Rev. Lett. 119, 180509 (2017).
[7] Y. Li, et al., Phys. Rev. X 7, 021050 (2017).

Keywords: Superconducting qubits, Near-term quantum algorithms, Nuclear Magnetic Resonance technique