Dynamical error reshaping for dual-rail erasure qubits

TL;DR

This work tackles the noise penalties that limit erasure-qubit performance in dual-rail superconducting cavities by deploying Space Curve Quantum Control (SCQC) to suppress ancilla-induced dephasing and ZZ crosstalk during erasure checks and two-qubit gates. By mapping gate dynamics to geometric space curves and enforcing first- and higher-order noise-cancellation conditions, the authors design robust, low-amplitude, broadband pulses, including a three-step joint-parity sequence and BARQ-based ancilla control. The resulting robust joint-parity gate and its TEXT-based derivation yield substantial fidelity gains, with erasure-check errors reduced by about two orders of magnitude and logical entangling gates by up to three orders, under realistic dephasing levels. The approach suggests further improvements with tunable dispersive coupling and provides a path to lower QEC overhead for erasure-biased qubits in current platforms.

Abstract

Erasure qubits -- qubits designed to have an error profile that is dominated by detectable leakage errors -- are a promising way to cut down the resources needed for quantum error correction. There have been several recent experiments demonstrating erasure qubits in superconducting quantum processors, most notably the dual-rail qubit defined by the one-photon subspace of two coupled cavities. An outstanding challenge is that the ancillary transmons needed to facilitate erasure checks and two-qubit gates introduce a substantial amount of noise, limiting the benefits of working with erasure-biased qubits. Here, we show how to suppress the adverse effects of transmon-induced noise while performing erasure checks or two-qubit gates. We present control schemes for these operations that suppress erasure check errors by two orders of magnitude and reduce the logical two-qubit gate infidelities by up to three orders of magnitude.

Figures (4)

• Figure 1: (a) Schematic of two DR qubits ($q_1$ and $q_2$) coupled by a beamsplitter. (b)--(c) Circuit diagrams for joint parity and $ZZ(\theta)_{\rm L}$ DCGs. Both diagrams refer to DR qubits, each comprised of two physical cavities $a$ and $b$, while $\ket{\textsl{g}}$ is the ground state of the ancilla qubit. (d) Gate infidelity vs dephasing noise in the ancilla qubit for the robust joint parity gate $U_{\rm JP}$ (blue-green) and logical entangling gate $ZZ(\pi/2)_{\rm L}$ (black-gray). $\xi$ is the dispersive coupling strength in step (ii) of our joint parity check sequence, while $\chi$ is the coupling in steps (i) and (iii). For comparison, the infidelity of the single-shot non-robust joint parity gate $\widetilde{U}_{\rm JP}$ (orange) is also shown.
• Figure 2: Gate design for steps (i) and (iii). (a) Control field $\Omega_2(t)$ on the transmon ancilla qubit for the $ZZ(\pi/2)$ gate obtained from the curvature and the torsion of the curve shown in the inset. (b) Gate infidelity $(\mathcal{I} = 1-\mathcal{F})$ vs dephasing noise strength $(\gamma/\chi)$ showing the robustness against quasi-static dephasing noise to leading-order for the $ZZ(\pi/2)$ gate (blue). For comparison, the infidelity of the non-robust square pulse with amplitude $\Omega/\chi = 5.5\pi$ is also shown (orange).
• Figure 3: Gate design for step (ii). (a)-(b) Control fields for the DR and ancilla qubit, respectively, for the $X_1\otimes Z_2$ gate. (c)-(d) Gate infidelity versus dephasing and crosstalk noise for the same gate. (a) Gaussian pulse of zero detuning that implements $X_1$. (b) Control fields obtained from the curve shown in the inset using BARQ that implements $Z_2$. (c) First-order robustness against $Z_2$ dephasing (blue) for several values of $ZZ$ crosstalk. (d) First-order robustness against $ZZ$ crosstalk (blue) for several values of $Z_2$ dephasing noise. For comparison, the infidelity of non-robust square pulses of constant amplitude $\Omega_1/\chi = 3\pi$ and $\Omega_2/\chi = 9\pi$ is also shown (orange).
• Figure S1: (a) Gate infidelity $(\mathcal{I} =1 -\mathcal{F})$ vs noise strength $(\xi)$ showing the robustness against $ZZ$ crosstalk to leading order for the $X_1\otimes X_2$ gate. The $X_1\otimes X_2$ operation is implemented by square pulses of amplitude $\Omega_1/\chi = \pi$ and $\Omega_2/\chi = 3\pi$. For comparison, the fidelity of non-robust square pulses is shown with dashed lines. For comparison, the fidelity of non-robust square pulses with amplitude $\Omega_1/\chi = \Omega_2/\chi = 3\pi$ is also shown (orange). (b) Circuit diagram for the joint parity dynamically corrected gate, where $a$ and $b$ are the two physical cavities, and $\ket{\textsl{g}}$ is the initial state of the ancilla qubit.