Spin Kerr-cat qubits

TL;DR

The paper introduces the spin Kerr-cat qubit encoding using quadrupolar nuclei, which suppresses noise and could achieve coherence times of up to 100 seconds, enabling high-fidelity two-qubit gates.

Contribution

It proposes a novel noise-robust qubit encoding based on spin cat states in quadrupolar nuclei, with estimated long coherence times and high-fidelity gate operations.

Findings

Estimated coherence time of 100 seconds for the spin Kerr-cat qubit.

Proposed two-qubit gate with 99% fidelity under enhanced quadrupolar splittings.

Noise suppression achieved through first-order dephasing reduction in the encoding.

Abstract

The use of noise-robust qubit encodings provides a way of extending the lifetime of quantum information at the hardware level. In this work, we introduce the spin Kerr-cat encoding, which leverages a clock transition in the spectrum of quadrupolar nuclei (having spin length $I\geq 1$) to achieve a first-order suppression of noise leading to qubit dephasing. The basis states of the spin Kerr-cat qubit are given by the two lowest levels of a $\mathbb{Z}_2$-symmetric nuclear-spin Hamiltonian and are well approximated by spin cat states. We compute the dephasing time of the spin Kerr-cat qubit under a model of $1/f$ noise, as well as relaxation of the qubit due to breaking of the $\mathbb{Z}_2$ symmetry by charge-noise-induced fluctuations of the quadrupolar tensor. Using measured parameters for antimony (${}^{123}\mathrm{Sb}$) donors in silicon, we estimate that a coherence time of $T_2^*=100$ s could be achieved with this encoding. We propose a two-qubit gate mediated by hopping electrons and estimate that with an enhancement of measured quadrupolar splittings by a factor of $\approx 4$, a gate fidelity of $99\%$ could be achieved for spin Kerr-cat qubits encoded in ${}^{123}\mathrm{Sb}$ nuclear spins, neglecting errors that impact the electron while it is being shuttled and read out.