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.
Highlights
Analog quantum simulators have evolved in the last two decades from a theoretical concept to an experimental reality
The hardcore Bose–Hubbard model (HCB) is a strongly interacting system that displays some of the critical properties of interacting quantum systems, including the area-law to volume-law transition of the entanglement spectrum that has been extensively studied in many-body systems[22]
For the implementation of the HCB Hamiltonian, Eq (7), next-nearest neighbor couplings must be suppressed, which can be achieved in the limit where CG ≫ Csh, but the use of floating transmons opens the possibility of exploring models with non-local interactions in the future
Summary
Analog quantum simulators have evolved in the last two decades from a theoretical concept to an experimental reality (see e.g., refs 1–3). Such experiments have been performed for large numbers of Josephson junctions[29,30] We note that this regime can be avoided by choosing a different basis of states to describe the Hamiltonian, i.e., by switching the choice of which circuits and the coupling elements H^Ji;j. The rotating wave approximation is valid, and the coupling elements can move an excitation between sites but will not change the total number of excitations This regime is equivalent to models of bosonic particles, and we may describe the system with the Bose–Hubbard Hamiltonian, 1⁄4. We note that a subset of the particle-like regime, where Δω ~ J, can be used to simulate disordered systems This can be achieved either by intentionally varying the qubit frequency across the lattice, or by decreasing the hopping energy at a constant residual disorder. An experimental realization of a 2D version of Eq (7) can contribute significantly to our understanding of the eigenstates
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