The intriguing physical phenomena associated with exceptional points have established non-Hermitian physics as a frontier of modern research. Recent investigations have extended non-Hermitian physics into the fully quantum domain. However, existing studies predominantly concentrate on discrete-variable quantum systems, while non-Hermitian quantum effects in continuous-variable encoded systems remain largely unexplored. In this work, we investigate the exceptional structure for a driven-dissipative Kerr-cat qubit, realized with a Kerr nonlinear resonator. We find that the dissipation leads to a bidirectional jump between the two basis states of the cat qubit, which is in distinct contrast with the unidirectional jump associated with normal two-level systems. The competition between this jump and a single-photon drive gives arise to the emergence of third-order Liouvillian exceptional points (LEP3s), each corresponds to a crossing point of two lines of LEP2s. We further show that the LEP3 can exhibit the topological character of the Hamiltonian EP3s, which cannot be realized with a single qubit. Our work opens the possibility of realizing non-Hermitian phenomena with continuous-variable quantum systems.The intriguing physical phenomena associated with exceptional points have established non-Hermitian physics as a frontier of modern research. Recent investigations have extended non-Hermitian physics into the fully quantum domain. However, existing studies predominantly concentrate on discrete-variable quantum systems, while non-Hermitian quantum effects in continuous-variable encoded systems remain largely unexplored. In this work, we investigate the exceptional structure for a driven-dissipative Kerr-cat qubit, realized with a Kerr nonlinear resonator. We find that the dissipation leads to a bidirectional jump between the two basis states of the cat qubit, which is in distinct contrast with the unidirectional jump associated with normal two-level systems. The competition between this jump and a single-photon drive gives arise to the emergence of third-order Liouvillian exceptional points (LEP3s), each corresponds to a crossing point of two lines of LEP2s. We further show that the LEP3 can exhibit the topological character of the Hamiltonian EP3s, which cannot be realized with a single qubit. Our work opens the possibility of realizing non-Hermitian phenomena with continuous-variable quantum systems.

quant-pharXiv:2511.18482Science China Physics Mechanics and AstronomyNov 25, 20250 citations

Error-tolerant parity detector of cat-state qubits based on a topological quantum phase transition

Yi‐Hao Kang, Yu Wang, Qi-Ping Su +3 more

We propose a scheme for realizing parity measurement of cat-state qubits based on a topological quantum phase transition. The cat-state qubits, formed by the bosonic modes in the Kerr-nonlinear resonators with two-photon squeezing drives, couple with a superconducting qubit in the center. We demonstrate that the resonator-qubit couplings with proper strengths can induce a topological quantum phase transition when the cat-state qubits are initial in the even-parity states. The topological quantum phase transition provides an approach to distinguish the even-parity states from the odd-parity states by measuring a topological invariant, namely the Chern number. Due to the robustness of the Chern number, the scheme shows great tolerance for multiple types of disturbing factors, including the systematic errors of the control fields and the coupling strengths, the inter-resonator crosstalk, and decoherence. Therefore, the scheme may be useful to construct an error-tolerant parity detector of cat-state qubits.We propose a scheme for realizing parity measurement of cat-state qubits based on a topological quantum phase transition. The cat-state qubits, formed by the bosonic modes in the Kerr-nonlinear resonators with two-photon squeezing drives, couple with a superconducting qubit in the center. We demonstrate that the resonator-qubit couplings with proper strengths can induce a topological quantum phase transition when the cat-state qubits are initial in the even-parity states. The topological quantum phase transition provides an approach to distinguish the even-parity states from the odd-parity states by measuring a topological invariant, namely the Chern number. Due to the robustness of the Chern number, the scheme shows great tolerance for multiple types of disturbing factors, including the systematic errors of the control fields and the coupling strengths, the inter-resonator crosstalk, and decoherence. Therefore, the scheme may be useful to construct an error-tolerant parity detector of cat-state qubits.

Physical Review AJul 30, 20248 citations

Progress and challenges for topological qubits

S. Das Sarma

Bulletin of the American Physical SocietyMar 5, 20180 citations

Spin Kerr-cat qubits

Z. M. McIntyre, Daniel Loss

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 sweet spot near a clock transition in the spectrum of quadrupolar nuclei (having spin $I\geq 1$ ) to achieve a suppression of charge and magnetic 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 for sufficiently high asymmetry parameters. For nuclei in highly asymmetric electric-field gradients, the nuclear spin could therefore be initialized in the spin-Kerr-cat subspace using SU(2) rotations and measurement rather than full SU( $2I+1$ ) control. We calculate 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 second-scale $T_2^*$ times could be achieved with this encoding, with bitflips and leakage occurring on significantly longer timescales. We propose a two-qubit gate acting on spin Kerr-cat qubits and electron-spin qubits, enabled by adiabatically moving an electron on and off the donor potential. Based on numerical simulations, we estimate that with an enhancement of measured quadrupolar couplings by a factor of ${\approx} 2$ , a gate fidelity exceeding $99\%$ could be achieved for spin Kerr cats encoded in ${}^{123}\mathrm{Sb}$ , with a gate time under $100$ ns. By entangling the nuclear spin with an electron spin in this way, the spin Kerr-cat qubit could then be measured using a Pauli spin blockade readout of the electron.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 sweet spot near a clock transition in the spectrum of quadrupolar nuclei (having spin $I\geq 1$) to achieve a suppression of charge and magnetic 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 for sufficiently high asymmetry parameters. For nuclei in highly asymmetric electric-field gradients, the nuclear spin could therefore be initialized in the spin-Kerr-cat subspace using SU(2) rotations and measurement rather than full SU($2I+1$) control. We calculate 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 second-scale $T_2^*$ times could be achieved with this encoding, with bitflips and leakage occurring on significantly longer timescales. We propose a two-qubit gate acting on spin Kerr-cat qubits and electron-spin qubits, enabled by adiabatically moving an electron on and off the donor potential. Based on numerical simulations, we estimate that with an enhancement of measured quadrupolar couplings by a factor of ${\approx} 2$, a gate fidelity exceeding $99\%$ could be achieved for spin Kerr cats encoded in ${}^{123}\mathrm{Sb}$, with a gate time under $100$ ns. By entangling the nuclear spin with an electron spin in this way, the spin Kerr-cat qubit could then be measured using a Pauli spin blockade readout of the electron.

quant-pharXiv:2604.19687PRX QuantumApr 22, 20260 citations

I\geq 1

) to achieve a suppression of charge and magnetic 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 for sufficiently high asymmetry parameters. For nuclei in highly asymmetric electric-field gradients, the nuclear spin could therefore be initialized in the spin-Kerr-cat subspace using SU(2) rotations and measurement rather than full SU(

2I+1

) control. We calculate 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 second-scale

T_2^*

times could be achieved with this encoding, with bitflips and leakage occurring on significantly longer timescales. We propose a two-qubit gate acting on spin Kerr-cat qubits and electron-spin qubits, enabled by adiabatically moving an electron on and off the donor potential. Based on numerical simulations, we estimate that with an enhancement of measured quadrupolar couplings by a factor of

{\approx} 2

, a gate fidelity exceeding

99\%

could be achieved for spin Kerr cats encoded in

{}^{123}\mathrm{Sb}

, with a gate time under

100

ns. By entangling the nuclear spin with an electron spin in this way, the spin Kerr-cat qubit could then be measured using a Pauli spin blockade readout of the electron.