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 $10^{-8}$ are achievable for controlled-X gates on cat qubits using the 0-n qubit as an ancilla with $n \geq 9$ (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 $d=9$.
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 10−8 are achievable for controlled-X gates on cat qubits using the 0-n qubit as an ancilla with n≥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=9.
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.
Dissipatively stabilized cat qubits provide a promising route toward fault-tolerant quantum computation, exhibiting exponential suppression of bit-flip errors with increasing phase-space separation of the logical states, while incurring only a linear increase in phase-flip errors. Existing implementations rely on engineered two-photon dissipation via nonlinear coupling to a lossy environment, an approach largely confined to superconducting platforms and limited by spurious decay channels and finite dissipation rates. Here, we propose a fundamentally different stabilization paradigm based on repeated interactions with an auxiliary two-level system mediated by a quadratic Hamiltonian, enabling dissipative stabilization without reservoir engineering. Our approach overcomes key limitations of existing schemes and is compatible with a wider class of experimental platforms. Furthermore, it preserves the noise bias and extends to squeezed cat qubits, rendering single-photon loss errors partially correctable.
We present a 1D repetition code based on the so-called cat qubits as a viable approach toward hardwareefficient universal and fault-tolerant quantum computation.The cat qubits that are stabilized by a twophoton driven-dissipative process exhibit a tunable noise bias where the effective bit-flip errors are exponentially suppressed with the average number of photons.We propose a realization of a set of gates on the cat qubits that preserve such a noise bias.Combining these base qubit operations, we build, at the level of the repetition cat qubit, a universal set of fully protected logical gates.This set includes single-qubit preparations and measurements, NOT, controlled-NOT, and controlled-controlled-NOT (Toffoli) gates.Remarkably, this construction avoids the costly magic state preparation, distillation, and injection.Finally, all required operations on the cat qubits could be performed with slight modifications of existing experimental setups.
Qubits with strongly biased noise, in which phase-flip errors are orders of magnitude more frequent than bit-flips, arise both naturally, as in electron and nuclear spins, and by engineering, as in stabilized cat qubits. This noise structure holds the promise of reducing the daunting hardware overhead of fault-tolerant quantum computing, but exploiting it requires physical operations that do not convert frequent phase-flips into rare bit-flips. In this review, we analyze the most prominent fault-tolerant protocols for biased-noise qubits, organized according to the available set of such bias-preserving operations. When this set is restricted to the CZ gate together with preparation and measurement in the X basis, we show that the complexity of the required syndrome extraction gadgets essentially cancels the benefit of the noise bias: at experimentally relevant error rates, one may as well ignore the bias and rely on standard error correction designed for depolarizing noise. The situation changes drastically when a bias-preserving CX gate is available: the hierarchy of errors can then be reflected in the structure of the code, with frequent phase-flips corrected by a dedicated high-threshold code and rare bit-flips by concatenation with a high-rate code. The same hierarchy also enables hardware-efficient preparation of magic states. Finally, as a bias-preserving CX is forbidden in naturally biased platforms and challenging in engineered ones, we present a measurement-based architecture in which a high-fidelity quantum non-demolition readout of multi-qubit Pauli Z operators takes its place, extending these overhead reductions to a much broader range of physical platforms.
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.
Cat qubits can exhibit strong noise bias due to their exponentially enhanced bit-flip times and only polynomially reduced phase-flip times with increasing photon number, which makes them attractive candidates for hardware-efficient quantum error correction. However, it is difficult to maintain this strong noise bias in logical operations such as CNOT gates between cats. Here, we propose a coherent CNOT gate scheme between two dissipative cats that preserves the exponential noise bias. The proposed gate relies only on unitary operations, which avoids the non-idealities associated with many existing gate schemes that rely on engineered dissipations. Assuming good component lifetimes and precise nonlinearity engineering, the proposed gate can enable logical memory in the megaquop regime (logical error rates < 10^-6) with a distance-7 repetition code consisting of 13 cat qubits.