We propose a scheme to generate spin cat states, i.e., superpositions of maximally separated quasiclassical states on a single high-dimensional nuclear spin in a solid-state device. We exploit a strong quadrupolar nonlinearity to drive the nucleus significantly faster than usual gate sequences, achieving collapses and revivals two orders of magnitude faster than the dephasing timescale. Furthermore, these states are engineered without entanglement with an ancilla, hence, are robust against error propagation. With our multitone control, we can realize arbitrary high-spin rotations within an experimentally feasible regime, as well as transform a spin coherent state to a spin cat state using only phase modulation, opening the possibility of storing and manipulating high-fidelity cat states. Published by the American Physical Society 2024
Spin cat states are superpositions of two or more coherent spin states (CSSs) that are distinctly separated over the Bloch sphere. Additionally, the nuclei with angular momenta greater than 1/2 possess a quadrupolar charge distribution. At the intersection of these two phenomena, we devise a simple scheme for generating various types of nuclear-spin cat states. The native biaxial electric quadrupole interaction that is readily available in strained solid-state systems plays a key role here. However, the fact that built-in strain cannot be switched off poses a challenge for the stabilization of target cat states once they are prepared. We remedy this by abruptly diverting via a single rotation pulse the state evolution to the neighborhood of the fixed points of the underlying classical Hamiltonian flow. Optimal process parameters are obtained as a function of electric field gradient biaxiality and nuclear-spin angular momentum. The overall procedure is seen to be robust under 5% deviations from optimal values. We show that higher-level cat states with four superposed CSS can also be formed using three rotation pulses. Finally, for open systems subject to decoherence we extract the scaling of cat-state fidelity damping with respect to the spin quantum number. This reveals rates greater than the dephasing of individual CSSs. Yet, our results affirm that these cat states can preserve their fidelities for practically useful durations under the currently attainable decoherence levels.
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≥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
Z2-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
Z2 symmetry by charge-noise-induced fluctuations of the quadrupolar tensor. Using measured parameters for antimony (
123Sb) donors in silicon, we estimate that second-scale
T2∗ 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
≈2, a gate fidelity exceeding
99% could be achieved for spin Kerr cats encoded in
123Sb, 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.
Abstract Quantum superpositions of macroscopically distinct classical states—so-called Schrödinger cat states—are a resource for quantum metrology, quantum communication and quantum computation. In particular, the superpositions of two opposite-phase coherent states in an oscillator encode a qubit protected against phase-flip errors1, 2. However, several challenges have to be overcome for this concept to become a practical way to encode and manipulate error-protected quantum information. The protection must be maintained by stabilizing these highly excited states and, at the same time, the system has to be compatible with fast gates on the encoded qubit and a quantum non-demolition readout of the encoded information. Here we experimentally demonstrate a method for the generation and stabilization of Schrödinger cat states based on the interplay between Kerr nonlinearity and single-mode squeezing1, 3 in a superconducting microwave resonator4. We show an increase in the transverse relaxation time of the stabilized, error-protected qubit of more than one order of magnitude compared with the single-photon Fock-state encoding. We perform all single-qubit gate operations on timescales more than sixty times faster than the shortest coherence time and demonstrate single-shot readout of the protected qubit under stabilization. Our results showcase the combination of fast quantum control and robustness against errors, which is intrinsic to stabilized macroscopic states, as well as the potential of these states as resources in quantum information processing5–8.
High-dimensional quantum systems are a valuable resource for quantum information processing. They can be used to encode error-correctable logical qubits, which has been demonstrated using continuous-variable states in microwave cavities or the motional modes of trapped ions. For example, high-dimensional systems can be used to realise `Schrödinger cat' states, superpositions of widely displaced coherent states that can also be used to illustrate quantum effects at large scales. Recent proposals have suggested encoding qubits in high-spin atomic nuclei, finite-dimensional systems that can host hardware-efficient versions of continuous-variable codes. Here we demonstrate the creation and manipulation of Schrodinger cat states using the spin-7/2 nucleus of an antimony atom embedded in a silicon nanoelectronic device. We use a multi-frequency control scheme to produce spin rotations that preserve the symmetry of the qudit, and constitute logical Pauli operations for qubits encoded in the Schrodinger cat states. Our work demonstrates the ability to prepare and control nonclassical resource states, a prerequisite for applications in quantum information processing and quantum error correction using our scalable, manufacturable semiconductor platform.
The Kerr-cat qubit is a bosonic qubit in which multiphoton Schrödinger cat states are stabilized by applying a two-photon drive to an oscillator with a Kerr nonlinearity. The suppressed bit-flip rate with increasing cat size makes this qubit a promising candidate to implement quantum error correction codes tailored for noise-biased qubits. However, achieving strong light-matter interactions necessary for stabilizing and controlling this qubit has traditionally required strong microwave drives that heat the qubit and degrade its performance. In contrast, increasing the coupling to the drive port removes the need for strong drives at the expense of large Purcell decay. By integrating an effective band-block filter on chip, we overcome this trade-off and realize a Kerr-cat qubit in a scalable 2D superconducting circuit with high coherence. This filter provides 30 dB of isolation at the qubit frequency with negligible attenuation at the frequencies required for stabilization and readout. We experimentally demonstrate quantum nondemolition readout fidelity of 99.6% for a cat with eight photons. Also, to have high-fidelity universal control over this qubit, we combine fast Rabi oscillations with a new demonstration of the X ( π / 2 ) gate through phase modulation of the stabilization drive. Finally, the lifetime in this architecture is examined as a function of the cat size of up to ten photons in the oscillator, achieving a bit-flip time higher than 1 ms and only a linear increase in the phase-flip rate, in good agreement with the theoretical analysis of the circuit. Our qubit shows promise as a building block for fault-tolerant quantum processors with a small footprint. Published by the American Physical Society 2024
We present a set of and pulses that realize paradigmatic operations such as the transfer of the ground state population into the excited state and arbitrary X/Y rotations on the Bloch sphere. These pulses are based on the phase modulation of the control field. We provide an experimental proof-of-concept of these operations by using a transmon qubit, demonstrating resilience against deviations in the drive amplitude of more than ≈20% , and/or detuning from the qubit transition frequency in the order of 10MHz . This modulation scheme is straightforward to implement in practice and can be deployed to any other qubit-based experimental platform. Published by the American Physical Society 2024