Enhanced response at exceptional points in multi-qubit systems for sensing

TL;DR

This paper explores high-order exceptional points in multi-qubit systems with parity-time symmetry, revealing the maximum order of energy response and proposing a Floquet scheme for implementing multi-body interactions for enhanced sensing.

Contribution

It analytically determines the maximum order of exceptional points in multi-qubit systems and introduces a Floquet scheme to realize multi-body interactions for sensing applications.

Findings

Maximum exceptional point order is n+1 in n-qubit systems.

Achieving higher-order response requires nontrivial multi-body interactions.

Proposed Floquet scheme enables implementation in trapped ions or superconducting qubits.

Abstract

Exceptional points featuring enhanced energy response to perturbation hold significant potential in detection and measurement of weak signals. Of particular interest is the existence and property of high-order exceptional points in quantum systems, owing to the capability to provide high-order response to perturbations. We investigate the exceptional points in a system of $n$ identical qubits possessing parity-time-reversal symmetry. We prove that owing to an incomplete coalescence of eigenstates, the highest possible order of exceptional point is $n+1$, which is also the upper bound of the order of energy response to perturbation. More interestingly, by considering an Ising-type interaction, we analytically prove that to achieve an $(m+1)$-th order response for any $m \le n$, the system must acquire a nontrivial $m$-body interaction. Finally, we propose a Floquet driving scheme to implement an effective multi-body Ising-type interaction, which can be realized in trapped ions or superconducting qubits.