Repeated Quantum Error Detection in a Surface Code (1912.09410v1)

Abstract: The realization of quantum error correction is an essential ingredient for reaching the full potential of fault-tolerant universal quantum computation. Using a range of different schemes, logical qubits can be redundantly encoded in a set of physical qubits. One such scalable approach is based on the surface code. Here we experimentally implement its smallest viable instance, capable of repeatedly detecting any single error using seven superconducting qubits, four data qubits and three ancilla qubits. Using high-fidelity ancilla-based stabilizer measurements we initialize the cardinal states of the encoded logical qubit with an average logical fidelity of 96.1%. We then repeatedly check for errors using the stabilizer readout and observe that the logical quantum state is preserved with a lifetime and coherence time longer than those of any of the constituent qubits when no errors are detected. Our demonstration of error detection with its resulting enhancement of the conditioned logical qubit coherence times in a 7-qubit surface code is an important step indicating a promising route towards the realization of quantum error correction in the surface code.

• The paper demonstrates repeated detection of single-qubit errors in a minimal surface code with an average fidelity of 96.1%.
• It employs a pipeline stabilizer measurement scheme using three ancilla qubits, enabling logical qubits to maintain coherence significantly longer than physical qubits.
• The experiment reports logical lifetimes up to 72.5 μs and error rates around 2.6%–3.1%, highlighting a scalable approach to fault-tolerant quantum computing.

Insights into "Repeated Quantum Error Detection in a Surface Code"

In "Repeated Quantum Error Detection in a Surface Code," Andersen et al. present an experimental implementation of a minimal surface code, utilizing seven superconducting qubits to enable quantum error correction for fault-tolerant quantum computation. The authors focus on demonstrating a framework that can repeatedly detect single-qubit errors, which is critical for scaling up to more complex quantum systems. Their work leverages three ancilla qubits to perform high-fidelity stabilizer measurements, crucial for initializing logical qubits and maintaining their coherence over time—key goals in quantum error correction.

The paper delineates the use of a seven-qubit array, consisting of four data qubits and three ancilla qubits, to construct the smallest viable surface code capable of detecting single errors. Central to this effort is the implementation of a pipeline stabilizer measurement scheme, which optimizes qubit interactions and error detection without introducing significant decoherence. The logical qubits are initialized in their cardinal states with an impressive average fidelity of 96.1%, a demonstration of high-fidelity qubit operations. This is an essential step in maintaining quantum information integrity, particularly when no errors are detected—thus preserving the logical qubit's state significantly longer than that of the individual physical qubits.

The successful repeated error detection experiment showcases the potential to preserve logical coherence for extended durations: coherence times that exceed those of the constituent qubits are observed. This finding indicates a feasible route toward the realization of quantum error correction within a surface code, which is noted for its promising high error threshold capability for robust fault-tolerant quantum computing.

Readers should note the essential numerical results underpinning this paper. The measured logical lifetime is determined to be 62.7 $\mu$s and the coherence time extends up to 72.5 $\mu$s, both surpassing the best physical qubit's respective lifetimes. Furthermore, logical error probabilities per cycle are quantified at approximately 2.6% for $Z_L$ errors and 3.1% for $X_L$ errors. These results suggest the potential for optimizations through improved gate fidelities and error correction protocols, which might render even more effective quantum systems.

Theoretical implications of Andersen et al.'s work include advancements in stabilizer codes for error correction by harnessing the conditional stabilization of logical qubits. Practically, the techniques described—entangling stabilizer measurements using superconducting circuits and multiplexed readout—are applicable to other quantum error correction codes that require repeated ancillary measurements with negligible disturbance to data qubits. Also, the realization of a pipeline approach to perform sequential stabilizer measurements stands as a scalable strategy for extending to larger quantum systems.

Future developments, catalyzed by this work, could include scaling the surface code by increasing the number of qubits, improving ancilla readout fidelities, and fully integrating autonomous error correction cycles. Moreover, the adaptability of the readout and low-crosstalk architecture offers advantages in expanding beyond superconducting systems to other quantum computing platforms. This research exemplifies a concerted step towards achieving reliable quantum computation at scales necessary for practical applications.