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Combining Hamiltonian and Dissipation Engineering in Superconducting Circuits to Realize Noise-Biased Qubits

Francesco Adinolfi

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Quantum error correction (QEC) is essential for practical quantum computation, but conventional approaches require large numbers of physical qubits per logical qubit, imposing severe hardware overhead. Noise-biased qubits, in which one error type dominates over the others, offer a route to reducing this overhead by enabling tailored QEC codes that exploit the error asymmetry. This work demonstrates, through two separate experiments, that combining Hamiltonian and dissipation engineering provides a versatile framework for enhancing the noise-bias of superconducting qubits. In the first experiment, we focus on the Kerr-cat qubit (KCQ), a noise-biased qubit encoded in the degenerate eigenstates of a two-photon driven Kerr oscillator, and study leakage outside the KCQ manifold, a key limitation of this system. We apply microwave pulses to selectively address the leakage states and to perform the first direct measurement of their population. We find a leakage population exceeding 9 %, consistent with substantial quantum heating and twelve times larger than the thermal excited-state population of the undriven oscillator. To reduce it, we introduce frequency-selective engineered single-photon dissipation. We show that this suppresses the leakage and extends the bit-flip time to 3.6 ms, while leaving the phase-flip time unchanged and reaching a qubit noise bias of 1400. In the second experiment, we introduce the gain-engineered transmon: a qubit encoded in the |g⟩ and |f⟩ levels of a standard transmon, in which a frequency-selective engineered single-photon-gain channel on the |e⟩ ↔ |f⟩ transition autonomously corrects single-photon loss errors. We demonstrate a factor-of-17 enhancement of the relaxation time, at the cost of only a 2.1 reduction in echo coherence time, while maintaining single-qubit gate errors below 0.5 %. Numerical simulations further show that the gain-engineered transmon can serve as a noisebiased ancilla for fault-tolerant error detection, suppressing both the ancilla detection infidelity and the error backaction below those of a standard |g⟩ ↔ |e⟩ ancilla qubit. These results establish the combination of Hamiltonian and dissipation engineering as a practical strategy for protecting quantum information. Because our architectures build on standard superconducting circuits, they integrate easily into existing platforms. We envision that steady improvements to noise-biased qubits, such as those developed in this thesis, could allow them to replace the transmon as the building block of superconducting quantum processors, lowering the hardware overhead of fault-tolerant quantum computation. Beyond quantum information processing, the driven nonlinear oscillators discussed in this thesis may serve as analog simulators of complex quantum dynamics, and as platforms for studying fundamental effects in driven-dissipative systems.

DOI
10.3929/ethz-c-000806886

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Quantum error correction (QEC) is essential for practical quantum computation, but conventional approaches require large numbers of physical qubits per logical qubit, imposing severe hardware overhead. Noise-biased qubits, in which one error type dominates over the others, offer a route to reducing this overhead by enabling tailored QEC codes that exploit the error asymmetry. This work demonstrates, through two separate experiments, that combining Hamiltonian and dissipation engineering provides a versatile framework for enhancing the noise-bias of superconducting qubits. In the first experiment, we focus on the Kerr-cat qubit (KCQ), a noise-biased qubit encoded in the degenerate eigenstates of a two-photon driven Kerr oscillator, and study leakage outside the KCQ manifold, a key limitation of this system. We apply microwave pulses to selectively address the leakage states and to perform the first direct measurement of their population. We find a leakage population exceeding 9 %, consistent with substantial quantum heating and twelve times larger than the thermal excited-state population of the undriven oscillator. To reduce it, we introduce frequency-selective engineered single-photon dissipation. We show that this suppresses the leakage and extends the bit-flip time to 3.6 ms, while leaving the phase-flip time unchanged and reaching a qubit noise bias of 1400. In the second experiment, we introduce the gain-engineered transmon: a qubit encoded in the |g⟩ and |f⟩ levels of a standard transmon, in which a frequency-selective engineered single-photon-gain channel on the |e⟩ ↔ |f⟩ transition autonomously corrects single-photon loss errors. We demonstrate a factor-of-17 enhancement of the relaxation time, at the cost of only a 2.1 reduction in echo coherence time, while maintaining single-qubit gate errors below 0.5 %. Numerical simulations further show that the gain-engineered transmon can serve as a noisebiased ancilla for fault-tolerant error detection, suppressing both the ancilla detection infidelity and the error backaction below those of a standard |g⟩ ↔ |e⟩ ancilla qubit. These results establish the combination of Hamiltonian and dissipation engineering as a practical strategy for protecting quantum information. Because our architectures build on standard superconducting circuits, they integrate easily into existing platforms. We envision that steady improvements to noise-biased qubits, such as those developed in this thesis, could allow them to replace the transmon as the building block of superconducting quantum processors, lowering the hardware overhead of fault-tolerant quantum computation. Beyond quantum information processing, the driven nonlinear oscillators discussed in this thesis may serve as analog simulators of complex quantum dynamics, and as platforms for studying fundamental effects in driven-dissipative systems.
The interaction between a qubit and its environment can be engineered such that one error channel dominates over all others, resulting in noise bias. This property enables error correction codes to focus on the dominant error type, thereby significantly reducing the number of physical systems required for fault-tolerant quantum computation. However, engineering noise bias typically introduces complexity at the physical system level, which decreases its usefulness by limiting scalability. Here, we introduce and experimentally realize a noise-biased qubit in a standard transmon-readout resonator circuit, one of the most common superconducting architectures, by only adding a single microwave tone. We encode the qubit in the transmon ∣g⟩|\mathrm{g}\rangle∣g⟩- and ∣f⟩|\mathrm{f}\rangle∣f⟩-states, and engineer a frequency-selective gain channel that counteracts single-photon loss errors between the computational states. We demonstrate an order-of-magnitude enhancement in relaxation time compared to the ∣g⟩−∣e⟩|\mathrm{g}\rangle-|\mathrm{e}\rangle∣g⟩−∣e⟩ encoding, conceding only a factor-of-two decrease in the echo-coherence time. Furthermore, we show that this qubit is compatible with fast, high-fidelity operations. Our results open a path towards using this system as a simple building-block for hardware-efficient quantum error detection and correction schemes.
Quantum computing crucially relies on maintaining quantum coherence for the duration of a calculation. Bosonic quantum error correction protects this coherence by encoding qubits into superpositions of noise-resilient oscillator states. In the case of the Kerr-cat qubit (KCQ), these states derive their stability from being the quasi-degenerate ground states of an engineered Hamiltonian in a driven nonlinear oscillator. KCQs are experimentally compatible with on-chip architectures and high-fidelity operations, making them promising candidates for a scalable bosonic quantum processor. However, their bit-flip time must increase further to fully leverage these advantages. Here, we present direct evidence that the bit-flip time in a KCQ is limited by leakage out of the qubit manifold and experimentally mitigate this process. We coherently control the leakage population and measure it to be > 9%, twelve times higher than in the undriven system. We then cool this population back into the KCQ manifold with engineered dissipation, identify conditions under which this suppresses bit-flips, and demonstrate increased bit-flip times up to 3.6 milliseconds. By employing both Hamiltonian confinement and engineered dissipation, our experiment combines two paradigms for Schrödinger-cat qubit stabilization. Our results elucidate the interplay between these stabilization processes and indicate a path towards fully realizing the potential of these qubits for quantum error correction.
Noise-biased qubits have bit-flip errors that are exponentially suppressed relative to phase-flip errors, and offer a promising route toward fault-tolerant quantum computing. However, this bias can be compromised during gate operations with non-biased control qubits. To address this limitation, we propose a "0-n" Fock qubit architecture that maintains the noise bias by encoding information in the ground state and n-th excited state of a nonlinear multi-level system, such as a transmon. This encoding is achieved via a dissipative stabilization that acts as decay and gain for lower and upper intermediate levels, respectively. We first analytically demonstrate that bit-flip errors are exponentially suppressed with the number of levels. Then, we present a practical implementation using a multi-mode lossy filter to achieve the frequency-selective dissipation. Finally, we numerically demonstrate that bit-flip probabilities approaching 10−810^{-8}10−8 are achievable for controlled-X gates on cat qubits using the 0-n qubit as an ancilla with n≥9n \geq 9n≥9 (i.e. ten or more levels), for realistic experimental parameters. Building on this, we simulate syndrome extraction in a repetition code, achieving logical error rates in the megaquop regime with only a distance of d=9d=9d=9.
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.
Stabilized cat qubits that possess biased noise channel with bit-flip errors exponentially smaller than phase-flip errors. Together with a set of bias-preserving (BP) gates, cat qubits are a promising candidate for realizing hardware efficient quantum error correction and fault-tolerant quantum computing. Compared to dissipatively stabilized cat qubits, the Kerr cat qubits can in principle support faster gate operations with higher gate fidelity, benefiting from the large energy gap that protects the code space. However, the leakage of the Kerr cats can increase the minor type of errors and compromise the noise bias. Both the fast implementation of gates and the interaction with environment can lead to such detrimental leakage if no sophisticated controls are applied. In this work, we introduce new fine-control techniques to overcome the above obstacles for Kerr cat qubits. To suppress the gate leakage, we use the derivative-based transition suppression technique to design derivative-based controls for the Kerr BP gates. We show that the fine-controlled gates can simultaneously have high gate fidelity and high noise bias and when applied to concatenated quantum error correction, can not only improve the logical error rate but also reduce resource overhead. To suppress the environment-induced leakage, we introduce colored single-photon dissipation, which can continuously cool the Kerr cats and suppress the minor errors while not enhancing the major errors.
Quantum error correction using erasure qubits offers higher fault-tolerant thresholds and improved scaling by converting dominant physical errors into detectable erasures. In superconducting circuits, erasure qubits can be constructed using the dual-rail approach, which, however, requires additional qubit-count overhead and tailored coupling elements. Here, we demonstrate a hardware-efficient scheme that operates transmon qutrits as erasure qubits, which is compatible with standard superconducting circuit-QED hardware. The logical states ∣0L⟩\ket{0_\text{L}}∣0L​⟩ and ∣1L⟩\ket{1_\text{L}}∣1L​⟩ are represented by the ground and second excited states, while the dominant relaxation errors can be detected via an ancilla qubit using a microwave-activated two-qutrit SWAP gate. We demonstrate a logical qubit T1T_1T1​ lifetime exceeding 500 μs500\,μ\mathrm{s}500μs, post-selected with repeated mid-circuit erasure detection, which is ten times longer than the T1T_1T1​ time of the transmon physical qubit. Coherence times beyond 300 μs300\,μ\mathrm{s}300μs are achieved using dynamical decoupling. Single-qubit gate operations reach average Clifford gate infidelity on the order of 10−410^{-4}10−4. We further demonstrate dual-purposing an ancilla qubit for both erasure detection and parity checking, showing heralded generation of Bell states between erasure qubits. These results suggest that mainstream architectures of transmon qubit arrays may already be capable of implementing erasure-based QEC strategies for hardware-efficient fault-tolerant quantum computing.