Entanglement stabilization using ancilla-based parity detection and real-time feedback in superconducting circuits

Abstract

Fault tolerant quantum computing relies on the ability to detect and correct errors, which in quantum error correction codes is typically achieved by projectively measuring multi-qubit parity operators and by conditioning operations on the observed error syndromes. Here, we experimentally demonstrate the use of an ancillary qubit to repeatedly measure the ZZ and XX parity operators of two data qubits and to thereby project their joint state into the respective parity subspaces. By applying feedback operations conditioned on the outcomes of individual parity measurements, we demonstrate the real-time stabilization of a Bell state with a fidelity of F ≈ 74% in up to 12 cycles of the feedback loop. We also perform the protocol using Pauli frame updating and, in contrast to the case of real-time stabilization, observe a steady decrease in fidelity from cycle to cycle. The ability to stabilize parity over multiple feedback rounds with no reduction in fidelity provides strong evidence for the feasibility of executing stabilizer codes on timescales much longer than the intrinsic coherence times of the constituent qubits.The inevitable interaction of quantum mechanical systems with their environment renders quantum information vulnerable to decoherence [1][2][3]. Quantum error correction aims to overcome this challenge by redundantly encoding logical quantum states into a larger-dimensional Hilbert space and performing repeated measurements to detect and correct for errors [4][5][6][7]. For sufficiently small error probabilities of individual operations, logical errors are expected to become increasingly unlikely when scaling up the number of physical qubits per logical qubit [8,9]. As the concept of quantum error correction provides a clear path toward fault tolerant quantum computing [10], it has been explored in a variety of physical systems ranging from nuclear magnetic resonance [11], to trapped ions [12-15] and superconducting circuits, both for conventional [16][17][18][19] and for continuous variable based encoding schemes [20].Quantum error correction typically relies on the measurement of a set of commuting multi-qubit parity operators, which ideally project the state of the data qubits onto a subspace of their Hilbert space -known as the code space -without extracting information about the logical qubit state [7]. A change in the outcome of repeated parity measurements signals the occurrence of an error, which brings the state of the qubits out of the code space. Such errors can either be corrected for in real-time by applying conditional feedback, or by keeping track of the measurement outcomes in a classical register to reconstruct the quantum state evolution in post-processing. The latter approach -also known as Pauli frame updating [21] -has the advantage of avoiding errors introduced by imperfect feedback and additional decoherence due to feedback latency. Real-time feedback, on the other hand, could be beneficial in the presence of * These authors contributed equally to this work. asymmetric relaxation e...

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