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

Abstract

A quantum circuit to simulate time evolution of wave functions under an S2 operator is provided, and integrated it to the quantum phase estimation circuit to calculate the spin quantum number S of arbitrary wave functions on quantum computers.

Quantum Circuit Learning with Error Backpropagation Algorithm and Experimental Implementation

“…From this point of view, the quantum advantage is a more realistic goal, and it aims to find the concrete and beneficial applications of the NISQ devices. Within the scope of quantum advantage, the application of quantum computers can be expanded far beyond computing speed racing to the usage in various fields, such as representing wavefunctions in quantum chemistry [10][11][12][13][14] or working as a quantum kernel to represent enhanced high-dimensional features in the field of machine learning [15][16][17][18].…”

A probabilistic spin annihilation method for quantum chemical calculations on quantum computers

“…[26][27][28] An approach for the calculation of the spin quantum number S of arbitrary wave functions on quantum computers has also appeared recently. 29 These approaches enable us to compute the wave functions of desired spin states and to check whether quantum simulations terminate with the desired spin state or not. Now, the simple and fundamental question arises: can we purify the spin contaminated wave functions obtained from quantum simulations by eliminating unwanted spin components?…”

“…In this setting, we can compute the eigenvalue of the S 2 operator, S(S + 1), of the wave function being used. 29 Note that H and S 2 have simultaneous eigenfunctions because H and S 2 commute. An additional quantum gate Z Z defined in eqn (4) is introduced to efficiently calculate the spin quantum number of odd-electron systems.…”

“…By utilising the Z Z gate, the time evolution of the wave function of a particular spin state can be cancelled, which enables us to discriminate the spin-doublet state (S = 1/2) from the spinquartet (S = 3/2) state in the one-qubit QPE. 29 To achieve the PSA on a quantum computer, a quantum circuit depicted in Fig. 1 is constructed.…”

“…1 were carried out by using the python program developed with OpenFermion 41 and Cirq 42 libraries. In the time evolution of the wave function under the S 2 operator, we used a generalised spin coordinate mapping (GSCM) proposed before 29 in conjunction with the secondorder Trotter decomposition as given in eqn (10) and N = 2. The GSCM was designed to perform spin operations on quantum computers equipped with a smaller number of quantum gates than conventional approaches like Jordan-Wigner transformation (JWT) 1,43 and Bravyi-Kitaev transformation (BKT).…”