Cat-state qubits formed by photonic cat states have a biased noise channel, i.e., one type of error dominates over all the others. We demonstrate that such biased-noise qubits are also promising for error-tolerant simulations of the quantum Rabi model (and its varieties) by coupling a cat-state qubit to an optical cavity. Using the cat-state qubit can effectively enhance the counterrotating coupling, allowing us to explore several fascinating quantum phenomena relying on the counterrotating interaction. Moreover, another benefit from biased-noise cat qubits is that the two main error channels (frequency and amplitude mismatches) are both exponentially suppressed. Therefore, the simulation protocols are robust against parameter errors of the parametric drive that determines the projection subspace. We analyze three examples: (i) collapse and revivals of quantum states; (ii) hidden symmetry and tunneling dynamics; and (iii) pair-cat-code computation.
Cat-state qubits formed by photonic cat states have a biased noise channel, i.e., one type of error dominates over all the others. We demonstrate that such biased-noise qubits are also promising for error-tolerant simulations of the quantum Rabi model (and its varieties) by coupling a cat-state qubit to an optical cavity. Using the cat-state qubit can effectively enhance the counterrotating coupling, allowing us to explore several fascinating quantum phenomena relying on the counterrotating interaction. Moreover, another benefit from biased-noise cat qubits is that the two main error channels (frequency and amplitude mismatches) are both exponentially suppressed. Therefore, the simulation protocols are robust against parameter errors of the parametric drive that determines the projection subspace. We analyze three examples: (i) collapse and revivals of quantum states; (ii) hidden symmetry and tunneling dynamics; and (iii) pair-cat-code computation.
We estimate and analyze the error rates and the resource overheads of the repetition cat qubit approach to universal and fault-tolerant quantum computation. The cat qubits stabilized by two-photon dissipation exhibit an extremely biased noise where the bit-flip error rate is exponentially suppressed with the mean number of photons. In a recent work we suggested that the remaining phase-flip error channel could be suppressed using a one-dimensional repetition code. Indeed, using only bias-preserving gates on the cat qubits, it is possible to build a universal set of fault-tolerant logical gates at the level of the repetition cat qubit. In this paper we perform Monte Carlo simulations of all the circuits implementing the protected logical gates, using a circuit-level error model. Furthermore, we analyze two different approaches to implement a fault-tolerant Toffoli gate on repetition cat qubits. These numerical simulations indicate that very low logical error rates could be achieved with a reasonable resource overhead, and with parameters that are within the reach of near-term circuit QED experiments.
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.
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.
We propose a theoretical protocol to implement multiqubit geometric gates (i.e., the M\o{}lmer-S\o{}rensen gate) using photonic cat-state qubits. These cat-state qubits stored in high-Q resonators are promising for hardware-efficient universal quantum computing. Specifically, in the limit of strong two-photon drivings, phase-flip errors of the cat-state qubits are effectively suppressed, leaving only a bit-flip error to be corrected. Because this dominant error commutes with the evolution operator, our protocol preserves the error bias, and, thus, can lower the code-capacity threshold for error correction. A geometric evolution guarantees the robustness of the protocol against stochastic noise along the evolution path. Moreover, by changing detunings of the cavity-cavity couplings at a proper time, the protocol can be robust against parameter imperfections (e.g., the total evolution time) without introducing extra noises into the system. As a result, the gate can produce multimode entangled cat states in a short time with high fidelities.
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.
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.