Experimental signatures of a $σ_zσ_x$ beam-splitter interaction between a Kerr-cat and transmon qubit

TL;DR

The paper addresses the challenge of ancilla-induced back-action in quantum error correction by introducing a Kerr-cat qubit as a noise-biased bosonic ancilla and demonstrating a beamsplitter interaction with a transmon that realizes an effective $\hat{\sigma}_z\hat{\sigma}_x$ coupling. The authors implement this interaction via a squeezing-driven Kerr-cat system and a beam-splitter drive, projecting onto the cat-qubit subspace and verifying phase-dependent dynamics consistent with theory. They show that the interaction rate $\Omega$ scales linearly with drive amplitude $\xi$ and with cat size $\alpha$, and that the third-order nonlinearity $\tilde{g}_3$ matches the design value, while also characterizing decoherence effects during interaction. This work establishes a practical route toward hybrid transmon-KCQ architectures for hardware-efficient syndrome extraction and advances toward fault-tolerant quantum processors using parity measurements.

Abstract

Quantum error correction (QEC) requires ancilla qubits to extract error syndromes from data qubits which store quantum information. However, ancilla errors can propagate back to the data qubits, introducing additional errors and limiting fault-tolerance. In superconducting quantum circuits, Kerr-cat qubits (KCQs), which exhibit strongly biased noise, have been proposed as ancillas to suppress this back-action and enhance QEC performance. Here, we experimentally demonstrate a beamsplitter interaction between a KCQ and a transmon, realizing an effective $σ_zσ_x$ coupling that can be employed for parity measurements in QEC protocols. We characterize the interaction across a range of cat sizes and drive amplitudes, confirming the expected scaling of the interaction rate. These results establish a step towards hybrid architectures that combine transmons as data qubits with noise-biased bosonic ancillas, enabling hardware-efficient syndrome extraction and advancing the development of fault-tolerant quantum processors.

Figures (8)

• Figure 1: (a) The Bloch sphere of the Kerr-cat with even/odd parity cat states on the $x$ axis, coherent states on the $z$ axis and parity-less cat states on the $y$ axis. (b) Cartoon of the transmon and Kerr-cat with their respective drives color coded according to panel (c). Frequency spectrum of the modes and drives.
• Figure 2: (a) Pulse sequence for measurement of beam-splitter interaction. (b) Bloch spheres that represent the final state (light blue arrows represent the initial state) of the KCQ and transmon for different interaction time and phase (colored stars). (c, d) Experimental and (e, f) simulated signatures of the beam-splitter interaction for varying interaction time and phase for $\xi = 2.6$. Colored stars in panel (c, d) correspond to the Bloch spheres in panel (b).
• Figure 3: (a) Oscillations of the transmon qubit $\braket{Z}$ observable versus interaction time and drive amplitude $\xi$ when starting from $\ket{\psi} = \ket{\mathcal{C}_\alpha^+}\ket{+Z}$, with $\alpha = 1.3$. (b) Data and fit at drive amplitude $\xi = 2.04$ (dashed line in (a)). (c) Beam-splitter rate versus drive amplitude $\xi$ for four cat sizes $\alpha$. (Inset) Third-order nonlinearity $\tilde{g}_3$ extracted from experiment (circles) and designed value (dashed red line).
• Figure 4: Two tone qubit spectroscopy of the SNAILmon in the Fock-basis with a CW pulse applied at $\omega_{bs}$ with varying amplitude in DAC units (D.U.).
• Figure 5: SNAILmon frequency versus flux (blue dots) plotted with a fit (blue line). The extracted nonlinearities $g_3$ (green), $g_4$ (orange) are calculated from the fit. Dashed line indicates the chosen operating flux of $0.33 \Phi_0$.