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arXiv:2604.19687 · PRX Quantum

Spin Kerr-cat qubits

Z. M. McIntyre, Daniel Loss

quant-phSubmitted Apr 21, 2026• Announced Apr 22, 2026• 0 citations
v1 · Apr 21, 2026v2 · Oct 20, 2026
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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.

DOI
10.1103/z3dj-95j6

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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≥1I\geq 1I≥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 Z2\mathbb{Z}_2Z2​-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/f1/f1/f noise, as well as relaxation of the qubit due to breaking of the Z2\mathbb{Z}_2Z2​ symmetry by charge-noise-induced fluctuations of the quadrupolar tensor. Using measured parameters for antimony (123Sb{}^{123}\mathrm{Sb}123Sb) donors in silicon, we estimate that a coherence time of T2∗=100T_2^*=100T2∗​=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 ≈4\approx 4≈4, a gate fidelity of 99%99\%99% could be achieved for spin Kerr-cat qubits encoded in 123Sb{}^{123}\mathrm{Sb}123Sb nuclear spins, neglecting errors that impact the electron while it is being shuttled and read out.
Bias-tailored quantum error correcting codes (QECCs) offer a higher error threshold than standard QECCs and have the potential to achieve lower logical errors with less space overhead. The spin-cat qubit, encoded in a large nuclear spin-FFF system, is a promising candidate for bias-tailored QECCs. Yet its feasibility is hindered by the difficulty of performing fast covariant SU(2) rotation with arbitrary rotation angles for nuclear spins and by a lack of noise characterization for gate operations in neutral atom platforms. Here we demonstrate single-qubit controls of 173Yb{}^{173}\mathrm{Yb}173Yb spin-cat qubits with nuclear spin I=5/2I=5/2I=5/2 in an optical tweezer array. We implement a covariant SU(2) rotation and non-linear rotations by optical beams and achieve an averaged single-Clifford gate fidelity of 0.961−5+50.961_{-5}^{+5}0.961−5+5​. The measurement of the coherence time and spin relaxation time shows that the idling error becomes increasingly biased toward dephasing errors as the magnitude of the encoded sublevel ∣mF∣|m_F|∣mF​∣ increases. Furthermore, we benchmark the noise bias of rank-preserving gates on spin-cat qubits, demonstrating a finite bias of 18−11+13218_{-11}^{+132}18−11+132​, in contrast to the case of the two-level system in 171Yb{}^{171}\mathrm{Yb}171Yb, which shows no bias within the experimental uncertainty. Our work demonstrates the feasibility of spin-cat qubits for realizing bias-tailored QECCs, paving the way for achieving hardware-efficient quantum error correction.
We propose a quadrupolar exchange-only spin qubit that is highly robust against charge noise and nuclear spin dephasing, the dominant decoherence mechanisms in quantum dots. The qubit consists of four electrons trapped in three quantum dots, and operates in a decoherence-free subspace to mitigate dephasing due to nuclear spins. To reduce sensitivity to charge noise, the qubit can be completely operated at an extended charge noise sweet spot that is first-order insensitive to electrical fluctuations. Because of on-site exchange mediated by the Coulomb interaction, the qubit energy splitting is electrically controllable and can amount to several GHz even in the "off" configuration, making it compatible with conventional microwave cavities.
Abstract Single electron spins bound to multi-phosphorus nuclear spin registers in silicon have demonstrated fast (0.8 ns) two-qubit SWAP\sqrt{\mathrm{SWAP}}SWAP​ SWAP gates and long spin relaxation times (~30 s). In these spin registers, when the donors are ionized, the nuclear spins remain weakly coupled to their environment, allowing exceptionally long coherence times. When the electron is present, the hyperfine interaction allows coupling of the spin and charge degrees of freedom for fast qubit operation and control. Here we demonstrate the use of the hyperfine interaction to enact electric dipole spin resonance to realize high-fidelity ( F=100−6+0F=10{0}_{-6}^{+0}F=100−6+0​ F = 10 0 − 6 + 0 %) initialization of all the nuclear spins within a four-qubit nuclear spin register. By controllably initializing the nuclear spins to ∣⇓⇓⇓⟩\left\vert \Downarrow \Downarrow \Downarrow \right\rangle∣⇓⇓⇓⟩ ⇓ ⇓ ⇓ , we achieve single-electron qubit gate fidelities of F = 99.78 ± 0.07% (Clifford gate fidelities of 99.58 ± 0.14%), above the fault-tolerant threshold for the surface code with a coherence time of $${T}_{2}^{\,* }=12\,\upmu {{{\rm{s}}}}$$ T 2 * = 12 μ s .
Nuclear spin qubits in silicon are well-isolated from their environment. Consequently, they have very long lifetimes and low sensitivity to noise, but this also suggests that control and measurement is challenging. We introduce electron pair interferometry (EPI), a protocol to overcome this challenge and maintain robustness to noise. EPI is implemented using an array of quantum dots with isoelectronic nuclear spin qubits located in the dots. A pair of electrons are initialized into a singlet ground state, split apart, and shuttled to the dots containing nuclear spin qubits. We show it is possible to coherently transfer the parity of the nuclei onto the measurable state of singlet/triplet-encoded electrons. Global nuclear magnetic resonance (NMR) can be used to change bases and implement dynamical decoupling (DD). Combined with selective hyperfine-induced ZπZ_πZπ​ rotations, our gate set is complete for universal quantum computation, tailored to Calderbank-Shor-Steane (CSS) quantum error correction, and robust to noise. We discuss very low sensitivity to charge noise and study the sensitivity to both DC and AC magnetic field inhomogeneity which depends strongly on their relative strengths.
A high degree of controllability and long coherence time make the nuclear spin of a phosphorus donor in isotopically purified silicon a promising candidate for a quantum bit. However, long-distance two-qubit coupling and fast, robust gates remain outstanding challenges for these systems. Here, following recent proposals for long-distance coupling via dipole-dipole interactions, we present a simple method to implement fast, high-fidelity arbitrary single- and two-qubit gates in the absence of charge noise. Moreover, we provide a method to make the single-qubit gates robust to moderate levels of charge noise to well within an error bound of ${10}^{\ensuremath{-}3}$.
Spin-12\frac{1}{2}21​ 119^{119}119Sn nuclei in a silicon semiconductor could make excellent qubits. Nuclear spins in silicon are known to have long coherence times. Tin is isoelectronic with silicon, so we expect electrons can easily shuttle from one Sn atom to another to propagate quantum information via a hyperfine interaction that we predict, from all-electron linearized augmented plane wave density functional theory calculations, to be roughly ten times larger than intrinsic 29^{29}29Si. A hyperfine-induced electro-nuclear controlled-phase (e-n-CPhase) gate operation, generated (up to local rotations) by merely holding an electron at a sweet-spot of maximum hyperfine strength for a specific duration of time, is predicted to be exceptionally resilient to charge/voltage noise. Diabatic spin flips are suppressed with a modest magnetic field (>15 >15~>15 mT for <10−6<10^{-6}<10−6 flip probabilities) and nuclear spin bath noise may be avoided via isotopic enrichment or mitigated using dynamical decoupling or through monitoring and compensation. Combined with magnetic resonance control, this operation enables universal quantum computation.