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arXiv:2102.08336 · PRX Quantum

Hardware-Efficient Leakage-Reduction Scheme for Quantum Error Correction with Superconducting Transmon Qubits

Francesco Battistel, Boris Varbanov, Barbara M. Terhal

Published Jul 26, 2021• 46 citations
arXivHTMLPDF

Abstract

Leakage outside of the qubit computational subspace poses a threatening challenge to quantum error correction (QEC).We propose a scheme using two leakage-reduction units (LRUs) that mitigate these issues for a transmon-based surface code, without requiring an overhead in terms of hardware or QECcycle time as in previous proposals.For data qubits, we consider a microwave drive to transfer leakage to the readout resonator, where it quickly decays, ensuring that this negligibly disturbs the computational states for realistic system parameters.For ancilla qubits, we apply a |1 ↔ |2 π pulse conditioned on the measurement outcome.Using density-matrix simulations of the distance-3 surface code, we show that the average leakage lifetime is reduced to almost one QEC cycle, even when the LRUs are implemented with limited fidelity.Furthermore, we show that this leads to a significant reduction of the logical error rate.This LRU scheme opens the prospect for near-term scalable QEC demonstrations.

DOI
10.1103/prxquantum.2.030314

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Leakage outside of the qubit computational subspace poses a threatening challenge to quantum error correction (QEC).We propose a scheme using two leakage-reduction units (LRUs) that mitigate these issues for a transmon-based surface code, without requiring an overhead in terms of hardware or QECcycle time as in previous proposals.For data qubits, we consider a microwave drive to transfer leakage to the readout resonator, where it quickly decays, ensuring that this negligibly disturbs the computational states for realistic system parameters.For ancilla qubits, we apply a |1 ↔ |2 π pulse conditioned on the measurement outcome.Using density-matrix simulations of the distance-3 surface code, we show that the average leakage lifetime is reduced to almost one QEC cycle, even when the LRUs are implemented with limited fidelity.Furthermore, we show that this leads to a significant reduction of the logical error rate.This LRU scheme opens the prospect for near-term scalable QEC demonstrations.
Minimizing leakage from computational states is a challenge when using many-level systems like superconducting quantum circuits as qubits. We realize and extend the quantum-hardware-efficient, all-microwave leakage reduction unit (LRU) for transmons in a circuit QED architecture proposed by Battistel et al. This LRU effectively reduces leakage in the second- and third-excited transmon states with up to 99% efficacy in 220 ns, with minimum impact on the qubit subspace. As a first application in the context of quantum error correction, we show how multiple simultaneous LRUs can reduce the error detection rate and suppress leakage buildup within 1% in data and ancilla qubits over 50 cycles of a weight-2 stabilizer measurement.
Leakage to non-computational states is a source of correlated errors in both time and space that limits the effectiveness of quantum error correction (QEC) with superconducting circuits. We present and experimentally demonstrate a high-fidelity, leakage reduction unit (LRU) operating concurrently with transmon measurement without incurring time overhead. Adapted from double-drive reset of population (DDROP), the protocol utilizes simultaneous drives on the transmon and its readout resonator, leveraging the dispersive shift to create a directional process that returns the transmon to the computational subspace. The LRU achieves a 98.4% leakage removal fraction without compromising the computational-state assignment fidelity (99.2%). We combine LRU-enhanced measurement and neural-network decoding to successfully suppress logical error rates in both memory and stability QEC experiments without any post-selection.
Abstract Leakage outside of the qubit computational subspace, present in many leading experimental platforms, constitutes a threatening error for quantum error correction (QEC) for qubits. We develop a leakage-detection scheme via Hidden Markov models (HMMs) for transmon-based implementations of the surface code. By performing realistic density-matrix simulations of the distance-3 surface code (Surface-17), we observe that leakage is sharply projected and leads to an increase in the surface-code defect probability of neighboring stabilizers. Together with the analog readout of the ancilla qubits, this increase enables the accurate detection of the time and location of leakage. We restore the logical error rate below the memory break-even point by post-selecting out leakage, discarding less than half of the data for the given noise parameters. Leakage detection via HMMs opens the prospect for near-term QEC demonstrations, targeted leakage reduction and leakage-aware decoding and is applicable to other experimental platforms.
Quantum error correction (QEC) enables practical quantum computing by encoding logical qubits in many physical qubits, which can exponentially suppress the logical error rate with increasing code size provided that the physical error rate is below a critical threshold. However, the leakage of quantum information from the computational subspace presents a critical challenge to the development of scalable QEC, which creates long-lived, correlated errors that spread across space and time. Here, we demonstrate a quantum memory operating below the threshold by implementing an all-microwave leakage suppression architecture on a distance-7 surface code. We achieve a logical error suppression factor of Λ=1.40(6), definitively reversing the above-threshold scaling (Λ<1) caused by unmitigated leakage. This scheme integrates a hardware-efficient leakage reduction unit for data qubits with a fast, unconditional reset for ancilla qubits, suppressing the average leakage population after 40 cycles by a factor of 72 to 6.4(5)×10^{-4}. Our results demonstrate the viability of all-microwave control architectures for suppressing critical errors at scale, paving the way for more advanced quantum error correction implementations.
Superconducting qubits are a promising platform for building fault-tolerant quantum computers, with recent achievement showing the suppression of logical error with increasing code size. However, leakage into noncomputational states, a common issue in practical quantum systems including superconducting circuits, introduces correlated errors that undermine quantum error correction (QEC) scalability. Here, we propose and demonstrate a leakage reduction scheme utilizing tunable couplers, a widely adopted ingredient in large-scale superconducting quantum processors. Leveraging the strong frequency tunability of the couplers and stray interaction between the couplers and readout resonators, we eliminate state leakage on the couplers, thus suppressing space-correlated errors caused by population propagation among the couplers. Assisted by the couplers, we further reduce leakage to higher qubit levels with high efficiency (98.1%) and low error rate on the computational subspace (0.58%), suppressing time-correlated errors during QEC cycles. The performance of our scheme demonstrates its potential as an indispensable building block for scalable QEC with superconducting qubits.
Quantum computers will require quantum error correction to reach the low error rates necessary for solving problems that surpass the capabilities of conventional computers. One of the dominant errors limiting the performance of quantum error correction codes across multiple technology platforms is leakage out of the computational subspace arising from the multilevel structure of qubit implementations. Here, we present a resource-efficient universal leakage reduction unit for superconducting qubits using parametric flux modulation. This operation removes leakage down to our measurement inaccuracy of 7×10^{-4} in approximately 50 ns with a low error of 2.5(1)×10^{-3} on the computational subspace, thereby reaching durations and fidelities comparable to those of single-qubit gates. We demonstrate that using the leakage reduction unit in repeated weight-two stabilizer measurements reduces the total number of detected errors in a scalable fashion to close to what can be achieved using leakage-rejection methods that do not scale. Our approach does not require additional control electronics or on-chip components and is applicable to both auxiliary and data qubits. These benefits make our method particularly attractive for mitigating leakage in large-scale quantum error correction circuits, a crucial requirement for the practical implementation of fault-tolerant quantum computation.