Time Evolution of Uniform Sequential Circuits

Abstract

Simulating time evolution of generic quantum many-body systems using classical numerical approaches has an exponentially growing cost either with evolution time or with the system size. In this work, we present a polynomially scaling hybrid quantum-classical algorithm for time evolving a one-dimensional uniform system in the thermodynamic limit. This algorithm uses a layered uniform sequential quantum circuit as a variational ansatz to represent infinite translation-invariant quantum states. We show numerically that this ansatz requires a number of parameters polynomial in the simulation time for a given accuracy. Furthermore, this favourable scaling of the ansatz is maintained during our variational evolution algorithm. All steps of the hybrid optimization are designed with near-term digital quantum computers in mind. After benchmarking the evolution algorithm on a classical computer, we demonstrate the measurement of observables of this uniform state using a finite number of qubits on a cloud-based quantum processing unit. With more efficient tensor contraction schemes, this algorithm may also offer improvements as a classical numerical algorithm.

19 pages, 14 figures

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• Riemannian quantum circuit optimization for Hamiltonian simulation
• Scalable simulation of non-equilibrium quantum dynamics via classically optimised unitary circuits
• Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries
• Sequential quantum simulation of spin chains with a single circuit QED device
• Quantum tensor network algorithms for evaluation of spectral functions on quantum computers
• Sequential Generation of Two-dimensional Super-area-law States with Local Parent Hamiltonian