Scalable Circuits for Preparing Ground States on Digital Quantum Computers: The Schwinger Model Vacuum on 100 Qubits

TL;DR

This paper introduces SC-ADAPT-VQE, a scalable quantum algorithm for preparing ground states of large, translationally-invariant systems, demonstrated by preparing the Schwinger model vacuum on up to 100 qubits using IBM quantum computers.

Contribution

The paper presents a new scalable quantum circuit construction method, SC-ADAPT-VQE, that leverages decay of correlations to efficiently prepare ground states on large systems.

Findings

Successfully prepared the Schwinger model vacuum on 100 qubits.

Circuits exhibit exponential convergence and size-independence in structure.

Quantum results agree well with classical simulations after error mitigation.

Abstract

The vacuum of the lattice Schwinger model is prepared on up to 100 qubits of IBM's Eagle-processor quantum computers. A new algorithm to prepare the ground state of a gapped translationally-invariant system on a quantum computer is presented, which we call Scalable Circuits ADAPT-VQE (SC-ADAPT-VQE). This algorithm uses the exponential decay of correlations between distant regions of the ground state, together with ADAPT-VQE, to construct quantum circuits for state preparation that can be scaled to arbitrarily large systems. These scalable circuits can be determined using classical computers, avoiding the challenging task of optimizing parameterized circuits on a quantum computer. SC-ADAPT-VQE is applied to the Schwinger model, and shown to be systematically improvable, with an accuracy that converges exponentially with circuit depth. Both the structure of the circuits and the deviations of prepared wavefunctions are found to become independent of the number of spatial sites, $L$. This allows for a controlled extrapolation of the circuits, determined using small or modest-sized systems, to arbitrarily large $L$. The circuits for the Schwinger model are determined on lattices up to $L=14$ (28 qubits) with the qiskit classical simulator, and subsequently scaled up to prepare the $L=50$ (100 qubits) vacuum on IBM's 127 superconducting-qubit quantum computers ibm_brisbane and ibm_cusco. After introducing an improved error-mitigation technique, which we call Operator Decoherence Renormalization, the chiral condensate and charge-charge correlators obtained from the quantum computers are found to be in good agreement with classical Matrix Product State simulations.