Scalable Circuits for Preparing Ground States on Digital Quantum
  Computers: The Schwinger Model Vacuum on 100 Qubits
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.
Roland C. Farrell Marc Illa Anthony N. Ciavarella Martin J. Savage