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

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 with use of classical computers, avoiding the challenging task of optimizing parameterized circuits on a quantum computer. SC-ADAPT-VQE is applied to the Schwinger model, and is 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 wave functions are found to become independent of the number of spatial sites, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:mi>L</a:mi></a:math>. This allows a controlled extrapolation of the circuits, determined with use of small or modest-sized systems, to arbitrarily large <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><d:mi>L</d:mi></d:math>. The circuits for the Schwinger model are determined on lattices up to <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><g:mi>L</g:mi><g:mo>=</g:mo><g:mn>14</g:mn></g:math> (28 qubits) with the Qiskit classical simulator, and are subsequently scaled up to prepare the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><j:mi>L</j:mi><j:mo>=</j:mo><j:mn>50</j:mn></j:math> (100 qubits) vacuum on IBM’s 127-superconducting-qubit quantum computers ibm_brisbane and ibm_cusco. After introduction of 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. Published by the American Physical Society 2024

Topics & Concepts