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 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.
Quantum measurements are basic operations that play a critical role in the study and application of quantum information. We study how the use of quantum, coherent, and classical thermalstates of light in a circuit quantum electrodynamics setup impacts the performance of quantum measurements, by comparing their respective measurement backaction and measurement signal to noise ratio per photon. In the strong dispersive limit, we find that thermal light is capable of performing quantum measurements with comparable efficiency to coherent light, both being outperformed by single-photon light. We then analyze the thermodynamic cost of each measurement scheme. We show that single-photon light shows an advantage in terms of energy cost per information gain, reaching the fundamental thermodynamic cost.
Qubits are physical, a quantum gate thus not only acts on the information carried by the qubit but also on its energy. What is then the corresponding flow of energy between the qubitand the controller that implements the gate? Here we exploit a superconducting platform to answer this question in the case of a quantum gate realized by a resonant drive field. During the gate, the superconducting qubit becomes entangled with the microwave drive pulse so that there is a quantum superposition between energy flows. We measure the energy change in the drive field conditioned on the outcome of a projective qubit measurement. We demonstrate that the drive’s energy change associated with the measurement backaction can exceed by far the energy that can be extracted by the qubit. This can be understood by considering the qubit as a weak measurement apparatus of the driving field.
The storage and processing of quantum information are susceptible to external noise, resulting in computational errors that are inherently continuous A powerful method to suppress theseeffects is to use quantum error correction. Typically, quantum error correction is executed in discrete rounds where errors are digitized and detected by projective multi-qubit parity measurements. These stabilizer measurements are traditionally realized with entangling gates and projective measurement on ancillary qubits to complete a round of error correction. However, their gate structure makes them vulnerable to errors occurring at specific times in the code and errors on the ancilla qubits. Here we use direct parity measurements to implement a continuous quantum bit-flip correction code in a resource-efficient manner, eliminating entangling gates, ancilla qubits, and their associated errors. The continuous measurements are monitored by an FPGA controller that actively corrects errors as they are detected. Using this method, we achieve an average bit-flip detection efficiency of up to 91%. Furthermore, we use the protocol to increase the relaxation time of the protected logical qubit by a factor of 2.7 over the relaxation times of the bare comprising qubits. Our results showcase resource-efficient stabilizer measurements in a multi-qubit architecture and demonstrate how continuous error correction codes can address challenges in realizing a fault-tolerant system.
Heat flow management at the nanoscale is of great importance for emergent quantum technologies. For instance, a thermal sink that can be activated on-demand is a highly desirable toolthat may accommodate the need to evacuate excess heat at chosen times, e.g. to maintain cryogenic temperatures or reset a quantum system to ground, and the possibility of controlled unitary evolution otherwise. Here we propose a design of such heat switch based on a single coherently driven qubit. We show that the heat flow provided by a hot source to the qubit can be switched on and off by varying external parameters, the frequency and the intensity of the driving. The complete suppression of the heat flow is a quantum effect occurring for specific driving parameters that we express and we analyze the role of the coherences in the free qubit energy eigenbasis. We finally study the feasibility of this quantum heat switch in a circuit QED setup involving a charge qubit coupled to thermal resistances. We demonstrate robustness to experimental imperfections such as additional decoherence, paving the road towards experimental verification of this effect.
We propose a solid state refrigeration technique based on repeated adiabatic magnetization/demagnetization cycles of a superconductor which acts as the working substance. The gradualcooling down of a substrate (normal metal) in contact with the working substance is demonstrated for different initial temperatures of the substrate. Excess heat is given to a hot large-gap superconductor. The on-chip refrigerator works in a cyclic manner because of an effective thermal switching mechanism: Heat transport between N/N versus N/S junctions is asymmetric because of the appearance of the energy gap. This switch permits selective cooling of the metal. We find that this refrigeration technique can cool down a 0.3cm3 block of Cu by almost two orders of magnitude starting from 200mK, and down to about 1mK starting from the base temperature of a dilution fridge (10mK). The corresponding cooling power for a 1cm×1cm interface are 25 nW and 0.06 nW respectively, which scales with the area of the interface.
We consider the temporal correlations of the quantum state of a qubit subject to simultaneous continuous measurement of two non-commuting qubit observables. Such qubit state correlatorsare defined for an ensemble of qubit trajectories, which has the same fixed initial state and can also be optionally constrained by a fixed final state. We develop a stochastic path integral description for the continuous quantum measurement and use it to calculate the considered correlators. Exact analytic results are possible in the case of ideal measurements of equal strength and are also shown to agree with solutions obtained using the Fokker-Planck equation. For a more general case with decoherence effects and inefficiency, we use a diagrammatic approach to find the correlators perturbatively in the quantum efficiency. We also calculate the state correlators for the quantum trajectories which are extracted from readout signals measured in a transmon qubit experiment, by means of the quantum Bayesian state update. We find an excellent agreement between the correlators based on the experimental data and those obtained from our analytical and numerical results.
The state of a continuously monitored qubit evolves stochastically, exhibiting competition between coherent Hamiltonian dynamics and diffusive partial collapse dynamics that followthe measurement record. We couple these distinct types of dynamics together by linearly feeding the collected record for dispersive energy measurements directly back into a coherent Rabi drive amplitude. Such feedback turns the competition cooperative, and effectively stabilizes the qubit state near a target state. We derive the conditions for obtaining such dispersive state stabilization and verify the stabilization conditions numerically. We include common experimental nonidealities, such as energy decay, environmental dephasing, detector efficiency, and feedback delay, and show that the feedback delay has the most significant negative effect on the feedback protocol. Setting the measurement collapse timescale to be long compared to the feedback delay yields the best stabilization.
We experimentally and theoretically investigate the quantum trajectories of jointly monitored transmon qubits embedded in spatially separated microwave cavities. Using nearly quantum-noiselimited superconducting amplifiers and an optimized setup to reduce signal loss between cavities, we can efficiently track measurement-induced entanglement generation as a continuous process for single realizations of the experiment. The quantum trajectories of transmon qubits naturally split into low and high entanglement classes corresponding to half-parity collapse. The distribution of concurrence is found at any given time and we explore the dynamics of entanglement creation in the state space. The distribution exhibits a sharp cut-off in the high concurrence limit, defining a maximal concurrence boundary. The most likely paths of the qubits‘ trajectories are also investigated, resulting in three probable paths, gradually projecting the system to two even subspaces and an odd subspace. We also investigate the most likely time for the individual trajectories to reach their most entangled state, and find that there are two solutions for the local maximum, corresponding to the low and high entanglement routes. The theoretical predictions show excellent agreement with the experimental entangled qubit trajectory data.