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The time-dependent Hartree-Fock (TDHF) method is an approach to simulate themean field dynamics of electrons within the assumption that the electrons moveindependently in their self-consistent average field and within the space ofsingle Slater determinants. One of the major advantages of performing timedynamics within Hartree-Fock theory is the free fermionic nature of theproblem, which makes TDHF classically simulatable in polynomial time. Here, wepresent a hybrid TDHF implementation for quantum computers. This quantumcircuit grows with time; but with our recent work on circuit compression viathe Yang-Baxter equation (YBE), the resulting circuit is constant depth. Thisstudy provides a new way to simulate TDHF with the aid of a quantum device aswell as provides a new direction for the application of YBE symmetry in quantumchemistry simulations.

Hybrid algorithm for the time-dependent Hartree-Fock method using the Yang-Baxter equation on quantum computers