The ubiquitous noise in quantum system hinders the advancement of quantum information processing and has driven the emergence of different hardware-efficient quantum error correctionprotocols. Among them, qubits with structured noise, especially with biased noise, are one of the most promising platform to achieve fault-tolerance due to the high error thresholds of quantum error correction codes tailored for them. Nevertheless, their quantum operations are challenging and the demonstration of their performance beyond the fault-tolerant threshold remain incomplete. Here, we leverage Schrödinger cat states in a scalable planar superconducting nonlinear oscillator to thoroughly characterize the high-fidelity single-qubit quantum operations with systematic quantum tomography and benchmarking tools, demonstrating the state-of-the-art performance of operations crossing the fault-tolerant threshold of the XZZX surface code. These results thus embody a transformative milestone in the exploration of quantum systems with structured error channels. Notably, our framework is extensible to other types of structured-noise systems, paving the way for systematic characterization and validation of novel quantum platforms with structured noise.
The Kerr-cat qubit is a bosonic qubit in which multi-photon Schrodinger cat states are stabilized by applying a two-photon drive to an oscillator with a Kerr nonlinearity. The suppressedbit-flip rate with increasing cat size makes this qubit a promising candidate to implement quantum error correction codes tailored for noise-biased qubits. However, achieving strong light-matter interactions necessary for stabilizing and controlling this qubit has traditionally required strong microwave drives that heat the qubit and degrade its performance. In contrast, increasing the coupling to the drive port removes the need for strong drives at the expense of large Purcell decay. By integrating an effective band-block filter on-chip, we overcome this trade-off and realize a Kerr-cat qubit in a scalable 2D superconducting circuit with high coherence. This filter provides 30 dB of isolation at the qubit frequency with negligible attenuation at the frequencies required for stabilization and readout. We experimentally demonstrate quantum non-demolition readout fidelity of 99.6% for a cat with 8 photons. Also, to have high-fidelity universal control over this qubit, we combine fast Rabi oscillations with a new demonstration of the X(90) gate through phase modulation of the stabilization drive. Finally, the lifetime in this architecture is examined as a function of the cat size of up to 10 photons in the oscillator achieving a bit-flip time higher than 1 ms and only a linear decrease in the phase-flip time, in good agreement with the theoretical analysis of the circuit. Our qubit shows promise as a building block for fault-tolerant quantum processors with a small footprint.
The fundamental trade-off between robustness and tunability is a central challenge in the pursuit of quantum simulation and fault-tolerant quantum computation. In particular, many emergingquantum architectures are designed to achieve high coherence at the expense of having fixed spectra and consequently limited types of controllable interactions. Here, by adiabatically transforming fixed-frequency superconducting circuits into modifiable Floquet qubits, we demonstrate an XXZ Heisenberg interaction with fully adjustable anisotropy. This interaction model is on one hand the basis for many-body quantum simulation of spin systems, and on the other hand the primitive for an expressive quantum gate set. To illustrate the robustness and versatility of our Floquet protocol, we tailor the Heisenberg Hamiltonian and implement two-qubit iSWAP, CZ, and SWAP gates with estimated fidelities of 99.32(3)%, 99.72(2)%, and 98.93(5)%, respectively. In addition, we implement a Heisenberg interaction between higher energy levels and employ it to construct a three-qubit CCZ gate with a fidelity of 96.18(5)%. Importantly, the protocol is applicable to various fixed-frequency high-coherence platforms, thereby unlocking a suite of essential interactions for high-performance quantum information processing. From a broader perspective, our work provides compelling avenues for future exploration of quantum electrodynamics and optimal control using the Floquet framework.