Search

Dispersive readout of superconducting qubits is often limited by readout-drive-induced transitions between qubit levels. While there is a growing understanding of such effects in transmon qubits, the case of highly nonlinear fluxonium qubits is more complex. We theoretically analyze measurement-induced state transitions (MIST) during the dispersive readout of a fluxonium qubit. We focus on a new mechanism: a simultaneous transition/excitation involving the qubit and an internal mode of the Josephson junction array in the fluxonium circuit. Using an adiabatic Floquet approach, we show that these new kinds of MIST processes can be relevant when using realistic circuit parameters and relatively low readout drive powers. They also contribute to excess qubit dephasing even after a measurement is complete. In addition to outlining basic mechanisms, we also investigate the dependence of such transitions on the circuit parameters. We find that with a judicious choice of frequency allocations or coupling strengths, these parasitic processes can most likely be avoided., Comment: 23 pages, 23 figures

Quantum error correction is essential for bridging the gap between the error rates of physical devices and the extremely low logical error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting processors have focused primarily on the surface code, which offers a high error threshold but poses limitations for logical operations. In contrast, the color code enables much more efficient logic, although it requires more complex stabilizer measurements and decoding techniques. Measuring these stabilizers in planar architectures such as superconducting qubits is challenging, and so far, realizations of color codes have not addressed performance scaling with code size on any platform. Here, we present a comprehensive demonstration of the color code on a superconducting processor, achieving logical error suppression and performing logical operations. Scaling the code distance from three to five suppresses logical errors by a factor of $\Lambda_{3/5}$ = 1.56(4). Simulations indicate this performance is below the threshold of the color code, and furthermore that the color code may be more efficient than the surface code with modest device improvements. Using logical randomized benchmarking, we find that transversal Clifford gates add an error of only 0.0027(3), which is substantially less than the error of an idling error correction cycle. We inject magic states, a key resource for universal computation, achieving fidelities exceeding 99% with post-selection (retaining about 75% of the data). Finally, we successfully teleport logical states between distance-three color codes using lattice surgery, with teleported state fidelities between 86.5(1)% and 90.7(1)%. This work establishes the color code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors in the near future.

In order to solve problems of practical importance, quantum computers will likely need to incorporate quantum error correction, where a logical qubit is redundantly encoded in many noisy physical qubits. The large physical-qubit overhead typically associated with error correction motivates the search for more hardware-efficient approaches. Here, using a microfabricated superconducting quantum circuit, we realize a logical qubit memory formed from the concatenation of encoded bosonic cat qubits with an outer repetition code of distance $d=5$. The bosonic cat qubits are passively protected against bit flips using a stabilizing circuit. Cat-qubit phase-flip errors are corrected by the repetition code which uses ancilla transmons for syndrome measurement. We realize a noise-biased CX gate which ensures bit-flip error suppression is maintained during error correction. We study the performance and scaling of the logical qubit memory, finding that the phase-flip correcting repetition code operates below threshold, with logical phase-flip error decreasing with code distance from $d=3$ to $d=5$. Concurrently, the logical bit-flip error is suppressed with increasing cat-qubit mean photon number. The minimum measured logical error per cycle is on average $1.75(2)\%$ for the distance-3 code sections, and $1.65(3)\%$ for the longer distance-5 code, demonstrating the effectiveness of bit-flip error suppression throughout the error correction cycle. These results, where the intrinsic error suppression of the bosonic encodings allows us to use a hardware-efficient outer error correcting code, indicate that concatenated bosonic codes are a compelling paradigm for reaching fault-tolerant quantum computation., Comment: Comments on the manuscript welcome!

Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this exponential suppression only occurs if the physical error rate is below a critical threshold. In this work, we present two surface code memories operating below this threshold: a distance-7 code and a distance-5 code integrated with a real-time decoder. The logical error rate of our larger quantum memory is suppressed by a factor of $\Lambda$ = 2.14 $\pm$ 0.02 when increasing the code distance by two, culminating in a 101-qubit distance-7 code with 0.143% $\pm$ 0.003% error per cycle of error correction. This logical memory is also beyond break-even, exceeding its best physical qubit's lifetime by a factor of 2.4 $\pm$ 0.3. We maintain below-threshold performance when decoding in real time, achieving an average decoder latency of 63 $\mu$s at distance-5 up to a million cycles, with a cycle time of 1.1 $\mu$s. To probe the limits of our error-correction performance, we run repetition codes up to distance-29 and find that logical performance is limited by rare correlated error events occurring approximately once every hour, or 3 $\times$ 10$^9$ cycles. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms., Comment: 10 pages, 4 figures, Supplementary Information

The conditional displacement (CD) gate between an oscillator and a discrete-variable ancilla plays a key role in quantum information processing tasks, such as enabling universal control of the oscillator and longitudinal readout of the qubit. However, the gate is unprotected against the propagation of ancilla decay errors and hence not fault-tolerant. Here, we propose a CD gate scheme with fluxonium as the ancilla, which has been experimentally demonstrated to have a large noise bias and millisecond-level lifetimes. The proposed gate is applied cross-resonantly by modulating the external flux of the fluxonium at the frequency of the target oscillator, which requires minimal hardware overhead and does not increase sensitivity to decoherence mechanisms like dephasing. We further provide a perturbative description of the gate mechanism and identify the error budget. Additionally, we develop an approximate procedure for choosing device and gate parameters that optimizes gate performance. Following the procedure for multiple sets of fluxonium parameters from the literature, we numerically demonstrate CD gates with unitary fidelity exceeding 99.9% and gate times of hundreds of nanoseconds.

We take a bottom-up, first-principles approach to design a two-qubit gate between fluxonium qubits for minimal error, speed, and control simplicity. Our proposed architecture consists of two fluxoniums coupled via a linear resonator. Using a linear coupler introduces the possibility of material optimization for suppressing its loss, enables efficient driving of state-selective transitions through its large charge zero point fluctuation, reduces sensitivity to junction aging, and partially mitigates coherent coupling to two-level systems. Crucially, a resonator-as-coupler approach also suggests a clear path to increased connectivity between fluxonium qubits, by reducing capacitive loading when the coupler has a high impedance. After performing analytic and numeric analyses of the circuit Hamiltonian and gate dynamics, we tune circuit parameters to destructively interfere sources of coherent error, revealing an efficient, fourth-order scaling of coherent error with gate duration. For component properties from the literature, we predict an open-system average CZ gate infidelity of $1.86 \times 10^{-4}$ in 70ns., Comment: Changes from peer review

Localized electronic and nuclear spin qubits in the solid state constitute a promising platform for storage and manipulation of quantum information, even at room temperature. However, the development of scalable systems requires the ability to entangle distant spins, which remains a challenge today. We propose and analyze an efficient, heralded scheme that employs a parity measurement in a decoherence free subspace to enable fast and robust entanglement generation between distant spin qubits mediated by a hot mechanical oscillator. We find that high-fidelity entanglement at cryogenic and even ambient temperatures is feasible with realistic parameters, and show that the entangled pair can be subsequently leveraged for deterministic controlled-NOT operations between nuclear spins. Our results open the door for novel quantum processing architectures for a wide variety of solid-state spin qubits.

We demonstrate a new mechanical transduction platform for individual spin qubits. In our approach, single micro-magnets are trapped using a type-II superconductor in proximity of spin qubits, enabling direct magnetic coupling between the two systems. Controlling the distance between the magnet and the superconductor during cooldown, we demonstrate three dimensional trapping with quality factors around one million and kHz trapping frequencies. We further exploit the large magnetic moment to mass ratio of this mechanical oscillator to couple its motion to the spin degree of freedom of an individual nitrogen vacancy center in diamond. Our approach provides a new path towards interfacing individual spin qubits with mechanical motion for testing quantum mechanics with mesoscopic objects, realization of quantum networks, and ultra-sensitive metrology., Comment: 5 pages, 4 figures

We present experimental observations and a study of quantum dynamics of strongly interacting electronic spins, at room temperature in the solid state. In a diamond substrate, a single nitrogen vacancy (NV) center coherently interacts with two adjacent S = 1/2 dark electron spins. We quantify NV-electron and electron-electron couplings via detailed spectroscopy, with good agreement to a model of strongly interacting spins. The electron-electron coupling enables an observation of coherent flip-flop dynamics between electronic spins in the solid state, which occur conditionally on the state of the NV. Finally, as a demonstration of coherent control, we selectively couple and transfer polarization between the NV and the pair of electron spins. These results demonstrate a key step towards full quantum control of electronic spin registers in room temperature solids.