Mediated interactions beyond the nearest neighbor in an array of superconducting qubits

TL;DR

This paper develops a formalism to analyze and tune mediated interactions beyond nearest neighbors in superconducting transmon qubit arrays, enabling customizable coupling for quantum simulation and computation.

Contribution

It introduces a general theoretical framework and design strategies for controlling long-range mediated couplings in transmon arrays, extending beyond traditional nearest-neighbor interactions.

Findings

Coupling strength and range can be independently tuned via circuit design.

Simulations demonstrate feasible configurations for various interaction ranges.

Long-range interactions can be realized in realistic superconducting circuits.

Abstract

We consider mediated interactions in an array of floating transmons, where each qubit capacitor consists of two superconducting pads galvanically isolated from ground. Each such pair contributes two quantum degrees of freedom, one of which is used as a qubit, while the other remains fixed. However, these extraneous modes can generate coupling between the qubit modes that extends beyond the nearest neighbor. We present a general formalism describing the formation of this coupling and calculate it for a one-dimensional chain of transmons. We show that the strength of coupling and its range (that is, the exponential falloff) can be tuned independently via circuit design to realize a continuum from nearest-neighbor-only interactions to interactions that extend across the length of the chain. We present designs with capacitance and microwave simulations showing that various interaction configurations can be achieved in realistic circuits. Such coupling could be used in analog simulation of different quantum regimes or to increase connectivity in digital quantum systems. Thus mechanism must also be taken into account in other types of qubits with extraneous modes.