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Between NISQ (noisy intermediate scale quantum) approaches without any proof of robust quantum advantage and fully fault-tolerant quantum computation, we propose a scheme to achieve a provable superpolynomial quantum advantage (under some widely accepted complexity conjectures) that is robust to noise with minimal error correction requirements. We choose a class of sampling problems with commuting gates known as sparse IQP (Instantaneous Quantum Polynomial-time) circuits and we ensure its fault-tolerant implementation by introducing the tetrahelix code. This new code is obtained by merging several tetrahedral codes (3D color codes) and has the following properties: each sparse IQP gate admits a transversal implementation, and the depth of the logical circuit can be traded for its width. Combining those, we obtain a depth-1 implementation of any sparse IQP circuit up to the preparation of encoded states. This comes at the cost of a space overhead which is only polylogarithmic in the width of the original circuit. We furthermore show that the state preparation can also be performed in constant depth with a single step of feed-forward from classical computation. Our construction thus exhibits a robust superpolynomial quantum advantage for a sampling problem implemented on a constant depth circuit with a single round of measurement and feed-forward.

Bosonic cat qubits stabilized with a driven two-photon dissipation are systems with exponentially biased noise, opening the door to low-overhead, fault-tolerant, and universal quantum computing. However, current gate proposals for such qubits induce substantial noise of the unprotected type, the poor scaling of which with the relevant experimental parameters limits their practical use. In this work, we provide a new perspective on dissipative cat qubits by reconsidering the reservoir mode used to engineer the tailored two-photon dissipation and showing how it can be leveraged to mitigate gate-induced errors. Doing so, we introduce four new designs of high-fidelity and bias-preserving cat-qubit gates and compare them to the prevalent gate methods. These four designs should give a broad overview of gate engineering for dissipative systems with different and complementary ideas. In particular, we propose both already achievable low-error gate designs and longer-term implementations.

Quantum error correction with biased-noise qubits can drastically reduce the hardware overhead for universal and fault-tolerant quantum computation. Cat qubits are a promising realization of biased-noise qubits as they feature an exponential error bias inherited from their nonlocal encoding in the phase space of a quantum harmonic oscillator. To confine the state of an oscillator to the cat-qubit manifold, two main approaches have been considered so far: a Kerr-based Hamiltonian confinement with high gate performances, and a dissipative confinement with robust protection against a broad range of noise mechanisms. We introduce a new combined dissipative and Hamiltonian confinement scheme based on two-photon dissipation together with a two-photon exchange (TPE) Hamiltonian. The TPE Hamiltonian is similar to Kerr nonlinearity, but unlike the Kerr it induces only a bounded distinction between even- and odd-photon eigenstates, a highly beneficial feature for protecting the cat qubits with dissipative mechanisms. Using this combined confinement scheme, we demonstrate fast and bias-preserving gates with drastically improved performance compared to dissipative or Hamiltonian schemes. In addition, this combined scheme can be implemented experimentally with only minor modifications of existing dissipative cat-qubit experiments.

When a two-level system—a qubit—is used as a probe of a larger system, it naturally leads to answering a single yes-no question about the system state. Here we propose a method where a single qubit is able to extract, not a single, but many bits of information about the photon number of a microwave resonator using continuous measurement. We realize a proof-of-principle experiment by recording the fluorescence emitted by a superconducting qubit reflecting a frequency comb, thus implementing multiplexed photon counting where the information about each Fock state—from 0 to 8—is simultaneously encoded in independent measurement channels. Direct Wigner tomography of the quantum state of the resonator evidences the backaction of the measurement as well as the optimal information extraction parameters. Our experiment unleashes the full potential of quantum meters by replacing sequential quantum measurements with simultaneous and continuous measurements separated in the frequency domain.

We propose a modified integral controller to treat actuation biases in nonholonomic systems. In such systems, although one cannot directly counter biases along all directions, one can still aim at restoring the symmetry of coordinated motion that the biases would break. Focusing on the example of steering controlled planar vehicles, we indeed show how to perfectly stabilize a circular trajectory coordinated with the leader, despite any unknown actuation bias. The proposed solution is a simple modified integral control term, and we prove via a detailed analysis of averaging theory that this control gadget globally stabilizes the perfect coordinated motion. The corresponding general observation is that stabilizing such symmetry-preserving situation can be viewed as rejecting a bias affecting the output measurement, instead of the input command. The symmetry-restoring control then becomes an output bias rejection, dual to the more standard input bias rejection with standard integral control.