Scaling of variational quantum circuit depth for condensed matter systems

Abstract

We benchmark the accuracy of a variational quantum eigensolver based on a finite-depth quantum circuit encoding ground state of local Hamiltonians. We show that in gapped phases, the accuracy improves exponentially with the depth of the circuit. When trying to encode the ground state of conformally invariant Hamiltonians, we observe two regimes. A finite-depth regime, where the accuracy improves slowly with the number of layers, and a finite-size regime where it improves again exponentially. The cross-over between the two regimes happens at a critical number of layers whose value increases linearly with the size of the system. We discuss the implication of these observations in the context of comparing different variational ansatz and their effectiveness in describing critical ground states.

Variational Quantum Eigensolver for SU($N$) Fermions

“…It is only after the parameterized quantum circuit has enough depth to reach the target entanglement entropy, that the VQE can start to approximate the target observable with high precision, as previously shown in Ref. [47]. We observe that correctly taking the ground-state entanglement into account is very important to capture the physics of the system.…”

Qibo: a framework for quantum simulation with hardware acceleration

“…Qibo provides a pre-coded implementation of the AAVQE for finding the ground state of the transverse field Ising Hamiltonian defined in equation (5) and can be executed for any number of qubits, variational circuit layers and number of adiabatic steps specified by the user. Particularly, the example may be used to explore how the accuracy of the VQE ansatz scales with the underlying circuit depth, as presented in [74].…”

Qibo: a framework for quantum simulation with hardware acceleration

“…( 5) and can be executed for any number of qubits, variational circuit layers and number of adiabatic steps specified by the user. Particularly, the example may be used to explore how the accuracy of the VQE ansatz scales with the underlying circuit depth, as presented in [71].…”