Abstract
AbstractAn adaptive variational quantum imaginary time evolution (AVQITE) approach is introduced that yields efficient representations of ground states for interacting Hamiltonians on near‐term quantum computers. It is based on McLachlan's variational principle applied to imaginary time evolution of variational wave functions. The variational parameters evolve deterministically according to equations of motions that minimize the difference to the exact imaginary time evolution, which is quantified by the McLachlan distance. Rather than working with a fixed variational ansatz, where the McLachlan distance is constrained by the quality of the ansatz, the AVQITE method iteratively expands the ansatz along the dynamical path to keep the McLachlan distance below a chosen threshold. This ensures the state is able to follow the quantum imaginary time evolution path in the system Hilbert space rather than in a restricted variational manifold set by a predefined fixed ansatz. AVQITE is used to prepare ground states of H4, H2O, and BeH2 molecules, where it yields compact variational ansätze and ground state energies within chemical accuracy. Polynomial scaling of circuit depth with system size is shown through a set of AVQITE calculations of quantum spin models. Finally, quantum Lanczos calculations are demonstrated alongside AVQITE without additional quantum resource costs.
Highlights
Quantum computers promise to solve certain types of classically difficult problems more efficiently, with quantum simulation as an important example [1]
For an N -qubit system with Hamiltonian Hcomposed of NH Pauli strings, and a parameterized ansatz |Ψ[θ] of Nθ parameters with an operator pool of dimension Np, the upper bound for the number of distinct measurement circuits Nm for adaptive variational quantum imaginary time evolution (AVQITE) calculations is given by NH + NH2 + Nθ(Nθ − 1)/2 + NpNθ, where NpNθ comes from the operator selection step
They demonstrate the general applicability of AVQITE to finding accurate and compact variational ansatze for interacting many-electron models
Summary
Quantum computers promise to solve certain types of classically difficult problems more efficiently, with quantum simulation as an important example [1]. The VQITE method has the advantage of maintaining a fixed circuit depth along the imaginary-time path, but its accuracy is limited by the fidelity of the variational ansatz in representing the ground state. We develop an adaptive VQITE (AVQITE) method to perform quantum imaginary time evolution for efficient, high-fidelity ground-state preparation for interacting quantum systems. AVQITE bridges the QITE and VQITE approaches by evolving a quantum state in the system’s Hilbert space towards the ground state, similar to QITE, yet with a circuit that grows sublinearly and saturates with imaginary time, leading to a final compact variational ansatz. We envision AVQITE, with its compact variational circuits and avoidance of explicit high-dimensional optimization, as a viable way to efficiently prepare ground states of interacting fermion systems (e.g., molecules) on NISQ devices
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