Variational Quantum Simulation for Quantum Chemistry

Abstract

Variational quantum‐classical hybrid algorithms are emerging as important tools for simulating quantum chemistry with quantum devices. These algorithms can be applied to evaluate various molecular properties, including potential energy surfaces. Here in, recent progresses on the development of the so‐called variational quantum eigensolver (VQE) are surveyed. The eigensolver aims at reducing the consumption of quantum resources as much as possible. The key feature of VQE is that variation quantum states are optimized by a feedback process, where the measurement of the Hamiltonian is implemented term by term. This approach avoids the need of encoding all of the information about the molecular Hamiltonian in a quantum circuit. The VQE method is also compatible with classical methods in quantum chemistry, such as unitary coupled‐cluster ansatz. Furthermore, basic elements of VQE are covered, such as qubit encoding, mapping rules of the fermionic operators, ansatz preparation, together with several techniques for improving the performance, including constraining, and error mitigation.

Unitary-coupled restricted Boltzmann machine ansatz for quantum simulations

“…In particular, VQE has been experimentally demonstrated on several leading platforms of quantum computations 3,[5][6][7][8] . These encouraging experimental outcomes strengthen our anticipation that quantum simulations [9][10][11][12][13] should be among the first set of applications to benefit from quantum computations. Nevertheless, it is also becoming increasingly clear that further developments [14][15][16][17][18][19] are required to improve VQE and similar HQC algorithms if the goal is to establish an unambiguous quantum advantage for problems of realistic interests.…”

Computational chemistry on quantum computers

“…Sophisticated methods have been used to reduce the cost of quantum chemistry simulations [11][12][13], such as hybrid quantum classical (HQC) algorithms [14,15]. Here we focus on one of these HQC algorithms, the variational quantum eigensolver (VQE) [16]. In this algorithm, the computation is split into several quantum sub-tasks.…”

Quantum chemistry on quantum computers: quantum simulations of the time evolution of wave functions under theS2operator and determination of the spin quantum numberS

“…19,20 The VQE has attracted attention as the computation model in noisy intermediatescale quantum (NISQ) 32 devices, because coherence times required for the simulations are much lower than the QPEbased approaches. [19][20][21][22][23][24][25][26] Despite the rapid progress in the methodologies to calculate molecular energies on quantum computers, approaches to calculate physical quantities other than energies have been less documented. In fact, to our knowledge, there is no theoretical proposal to determine spin quantum numbers of arbitrary wave functions on quantum computers.…”