Two-dimensional hard-core Bose–Hubbard model with superconducting qubits

Abstract

The pursuit of superconducting-based quantum computers has advanced the fabrication of and experimentation with custom lattices of qubits and resonators. Here, we describe a roadmap to use present experimental capabilities to simulate an interacting many-body system of bosons and measure quantities that are exponentially difficult to calculate numerically. We focus on the two-dimensional hard-core Bose–Hubbard model implemented as an array of floating transmon qubits. We describe a control scheme for such a lattice that can perform individual qubit readout and show how the scheme enables the preparation of a highly excited many-body state, in contrast with atomic implementations restricted to the ground state or thermal equilibrium. We discuss what observables could be accessed and how they could be used to better understand the properties of many-body systems, including the observation of the transition of eigenstate entanglement entropy scaling from area-law behavior to volume-law behavior.

Quantum transport and localization in 1d and 2d tight-binding lattices

“…|U | limit such that each lattice site can be occupied by at most a single particle, generally realizing the hard-core Bose-Hubbard model [25,26].…”

Parametrized Hamiltonian simulation using quantum optimal control

“…This is possible because capacitively coupled transmons in the dispersive regime have a Hamiltonian isomorphic to the BH Hamiltonian. However, parameter ranges for the simulation are limited due to hardware constraints and the device hardware used in these simulations do not support analog implementations of the EBH model, which is the sum of the typical BH model Hamiltonian with an additional extension term [26].…”

Quantum state tomography and purity measurement of a multiqubit system with random single-pulse rotations

“…system inspired by Ref. 4, where multiple resonant qubits are coupled to a single signal line via different-frequency resonators, so that individual dispersive readout is available but driving at the qubit frequency affects all qubits concurrently.…”

“…Modern quantum computing platforms have evolved rapidly in the last few years, achieving remarkably long coherence time and preparation and readout fidelity. While fully robust digital quantum computation is still some way away, near-term devices offer possibilities for new physical insights, including analog quantum simulators that can be used to study many body quantum systems [1][2][3][4]. A quantum simulator, however, is only as good as the information that one can extract from it.…”