Stabilizing a Bosonic Qubit using Colored Dissipation

Abstract

Biased-noise qubits are a promising candidate for realizing hardware efficient fault-tolerant quantum computing. One promising biased-noise qubit is the Kerr cat qubit, which has recently been demonstrated experimentally. Despite various unique advantages of Kerr cat qubits, we explain how the noise bias of Kerr cat qubits is severely limited by heating-induced leakage in their current implementations. Then, we show that by adding frequency-selective single-photon loss to Kerr cat qubits we can counteract the leakage and thus recover much of their noise bias. We refer to such Kerr cat qubits combined with frequency-selective single-photon loss as colored Kerr cat qubits as they are protected by a colored dissipation. In particular, we show how a suitably engineered lossy environment can suppress the leakage and bit-flip errors of a Kerr cat qubit while not introducing any additional phase-flip errors. Since our scheme only requires single-photon loss, it can be readily implemented by using passive and linear elements. Moreover, our frequency-selectivity technique can be generally applied to energy-gap protected qubits whose computational basis states are given by near degenerate ground states of a Hamiltonian with a non-zero energy gap between the ground and excited state manifolds.

Combined Dissipative and Hamiltonian Confinement of Cat Qubits

“…Although each spacing can be suppressed exponentially with the mean number of photons |α| 2 , this suppression only kicks in at higher |α| 2 for higher excited states. As discussed in [29] and further argued in this paper, this fact has major consequences on the effective bit-flip suppression for such a confinement.…”

“…Higher values of n would contribute with significant δ n , even at shorter times and larger α. However, they contribute to smaller terms since λ n decreases exponentially with n [29]. The study of [29] shows that at very large values of |α| 2 (well above the average photon numbers considered here) one can hope to retrieve an approximate exponential suppression given by p X ∝ exp(−0.94|α| 2 ) which is still less significant than the prefactor exp(−2|α| 2 ) achieved for dissipative cat qubits and with all values of |α| 2 .…”

“…However, in the absence of dissipative stabilization of the cat qubit manifold, leakage induced by perturbations different from quasi-static Hamiltonians such as thermal excitation or photon dephasing, is not countered. As shown in [29] and further argued in this paper, this leakage can in turn lead to significant bit-flip errors that suppress the noise bias and therefore block the way towards hardware-efficient fault-tolerance. Recently, the authors of [29] have proposed a promising approach to remedy this problem and to ensure the suppression of bit-flips.…”

“…As shown in [29] and further argued in this paper, this leakage can in turn lead to significant bit-flip errors that suppress the noise bias and therefore block the way towards hardware-efficient fault-tolerance. Recently, the authors of [29] have proposed a promising approach to remedy this problem and to ensure the suppression of bit-flips. This approach consists in the addition of a colored relaxation to compensate for the leakage out of the cat manifold.…”

Ancilla-Error-Transparent Controlled Beam Splitter Gate

“…Two-photon dissipation commutes with the photon number parity operator and hence does not cause dephasing errors. Recently a 'colored cat qubit' [72] that is stabilized by single-photon dissipation has been proposed, but we have not included this possibility in our simulations.…”