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arXiv:2307.08737 · Physical Review X

Demonstrating a Long-Coherence Dual-Rail Erasure Qubit Using Tunable Transmons

Harry Levine, Arbel Haim, Jimmy S. C. Hung, Nasser Alidoust, Mahmoud Kalaee, Laura DeLorenzo, E. Alex Wollack, Patricio Arrangoiz-Arriola, Amirhossein Khalajhedayati, Rohan Sanil, Hesam Moradinejad, Yotam Vaknin, Aleksander Kubica, David J. Hover, Shahriar Aghaeimeibodi, Joshua Ari Alcid, Chungheon Baek, J. Barnett, K. Bawdekar, Przemysław Bienias, Hugh A. Carson, C. Chen, L. Chen, Harutiun Chinkezian, E. M. Chisholm, A. Clifford, R. Cosmic, Nicole Crisosto, A. M. Dalzell, E. Davis, John M. D'Ewart, S. Diez, Noel D’Souza, Philipp T. Dumitrescu, E. S. Elkhouly, M. T. Fang, Yawen Fang, Steven T. Flammia, Matthew J. Fling, G. Garcia, M. K. Gharzai, Alexey Vyacheslavovich Gorshkov, Mason Gray, Sebastian Grimberg, Arne L. Grimsmo, Connor T. Hann, Y. He, Steven Heidel, S. Howell, M. Hunt, Joseph K. Iverson, Ignace Jarrige, Liang Jiang, William M. Jones, Rassul B. Karabalin, Peter J. Karalekas, Andrew J. Keller, D. Lasi, Menyoung Lee, Victoria Ly, Gregory S. MacCabe, Neha Mahuli, Guillaume Marcaud, Matthew H. Matheny, Sam McArdle, Gavin McCabe, G. Merton, C. Miles, Ashley Milsted, Anurag Mishra, Lorenzo Moncelsi, Mahdi Naghiloo, Kyungjoo Noh, Eric Oblepias, Gerson Ortuno, John Clai Owens, Jason Pagdilao, A. Panduro, Jean-Philip Paquette, Rishi N. Patel, G. A. Peairs, David Perello, Eric Peterson, S. Ponte, Harald Putterman, Gil Refael, Philip Reinhold, R. Resnick, Omar A. Reyna, R. Rodriguez, J. Rose, Alex H. Rubin, Marcus C. Runyan, Colm A. Ryan, Abdulrahman Sahmoud, Thomas Scaffidi, B. Shah, Salome Siavoshi, Prasahnt Sivarajah, Trenton Skogland

Published Mar 20, 2024• 66 citations
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Abstract

Quantum error correction with erasure qubits promises significant advantages over standard error correction due to favorable thresholds for erasure errors. To realize this advantage in practice requires a qubit for which nearly all errors are such erasure errors, and the ability to check for erasure errors without dephasing the qubit. We demonstrate that a “dual-rail qubit” consisting of a pair of resonantly coupled transmons can form a highly coherent erasure qubit, where transmon T 1 errors are converted into erasure errors and residual dephasing is strongly suppressed, leading to millisecond-scale coherence within the qubit subspace. We show that single-qubit gates are limited primarily by erasure errors, with erasure probability p erasure = 2.19 ( 2 ) × 10 − 3 per gate while the residual errors are ∼ 40 times lower. We further demonstrate midcircuit detection of erasure errors while introducing < 0.1 % dephasing error per check. Finally, we show that the suppression of transmon noise allows this dual-rail qubit to preserve high coherence over a broad tunable operating range, offering an improved capacity to avoid frequency collisions. This work establishes transmon-based dual-rail qubits as an attractive building block for hardware-efficient quantum error correction. Published by the American Physical Society 2024

DOI
10.1103/physrevx.14.011051

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Qubits with predominantly erasure errors present distinctive advantages for quantum error correction (QEC) and fault-tolerant quantum computing. Logical qubits based on dual-rail encoding that exploit erasure detection have been recently proposed in superconducting circuit architectures, with either coupled transmons or cavities. Here, we implement a dual-rail qubit encoded in a compact, double-post superconducting cavity. Using an auxiliary transmon, we perform erasure detection on the dual-rail subspace. We characterize the behavior of the code space by a novel method to perform joint-Wigner tomography. This is based on modifying the cross-Kerr interaction between the cavity modes and the transmon. We measure an erasure rate of 3.981±0.003 (ms)^{-1} and a residual, postselected dephasing error rate up to 0.17 (ms)^{-1} within the code space. This strong hierarchy of error rates, together with the compact and hardware-efficient nature of this novel architecture, holds promise in realizing QEC schemes with enhanced thresholds and improved scaling.

arXiv:2311.04423•Physical Review Letters•May 2, 2024•37 citations
Quantum error correction with erasure qubits promises significant advantages over standard error correction due to favorable thresholds for erasure errors. To realize this advantage in practice requires a qubit for which nearly all errors are such erasure errors, and the ability to check for erasure errors without dephasing the qubit. We demonstrate that a “dual-rail qubit” consisting of a pair of resonantly coupled transmons can form a highly coherent erasure qubit, where transmon T 1 errors are converted into erasure errors and residual dephasing is strongly suppressed, leading to millisecond-scale coherence within the qubit subspace. We show that single-qubit gates are limited primarily by erasure errors, with erasure probability p erasure = 2.19 ( 2 ) × 10 − 3 per gate while the residual errors are ∼ 40 times lower. We further demonstrate midcircuit detection of erasure errors while introducing < 0.1 % dephasing error per check. Finally, we show that the suppression of transmon noise allows this dual-rail qubit to preserve high coherence over a broad tunable operating range, offering an improved capacity to avoid frequency collisions. This work establishes transmon-based dual-rail qubits as an attractive building block for hardware-efficient quantum error correction. Published by the American Physical Society 2024
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Quantum error correction using erasure qubits offers higher fault-tolerant thresholds and improved scaling by converting dominant physical errors into detectable erasures. In superconducting circuits, erasure qubits can be constructed using the dual-rail approach, which, however, requires additional qubit-count overhead and tailored coupling elements. Here, we demonstrate a hardware-efficient scheme that operates transmon qutrits as erasure qubits, which is compatible with standard superconducting circuit-QED hardware. The logical states ∣0L⟩\ket{0_\text{L}}∣0L​⟩ and ∣1L⟩\ket{1_\text{L}}∣1L​⟩ are represented by the ground and second excited states, while the dominant relaxation errors can be detected via an ancilla qubit using a microwave-activated two-qutrit SWAP gate. We demonstrate a logical qubit T1T_1T1​ lifetime exceeding 500 μs500\,μ\mathrm{s}500μs, post-selected with repeated mid-circuit erasure detection, which is ten times longer than the T1T_1T1​ time of the transmon physical qubit. Coherence times beyond 300 μs300\,μ\mathrm{s}300μs are achieved using dynamical decoupling. Single-qubit gate operations reach average Clifford gate infidelity on the order of 10−410^{-4}10−4. We further demonstrate dual-purposing an ancilla qubit for both erasure detection and parity checking, showing heralded generation of Bell states between erasure qubits. These results suggest that mainstream architectures of transmon qubit arrays may already be capable of implementing erasure-based QEC strategies for hardware-efficient fault-tolerant quantum computing.
Erasure qubits -- qubits designed to have an error profile that is dominated by detectable leakage errors -- are a promising way to cut down the resources needed for quantum error correction. There have been several recent experiments demonstrating erasure qubits in superconducting quantum processors, most notably the dual-rail qubit defined by the one-photon subspace of two coupled cavities. An outstanding challenge is that the ancillary transmons needed to facilitate erasure checks and two-qubit gates introduce a substantial amount of noise, limiting the benefits of working with erasure-biased qubits. Here, we show how to suppress the adverse effects of transmon-induced noise while performing erasure checks or two-qubit gates. We present control schemes for these operations that suppress erasure check errors by three orders of magnitude and reduce the logical two-qubit gate infidelities by up to three orders of magnitude.
Quantum error correction (QEC) will likely be required to realize the full potential of quantum computing, but comes with daunting hardware overheads and demands low gate errors on the physical qubits1–4. These requirements can be eased by engineering qubits with a strong error hierarchy, in which the most common noise channels are also the easiest to correct. Erasure qubits can achieve this when detectable leakage errors out of the computational subspace dominate over the residual Pauli errors5–11, resulting in higher thresholds and improved scaling with code distance5,12,13. In practice, these advantages come to fruition only if the error hierarchy is preserved as much as possible throughout all gates and operations. Here we design and realize a two-qubit entangling gate for dual-rail cavity qubits, a type of erasure qubit encoded in a pair of superconducting microwave cavities7. Our experimental demonstration confirms that the error hierarchy is largely preserved during the gate. The gate is fast (about 500 ns duration) and shows low erasure rates of approximately 0.5% per gate, remaining Pauli errors below 0.1%, and a strong bias towards dephasing errors, in which bit-flips are practically non-existent at the 10−6 level. These results enable a faster path to error-corrected systems that rapidly suppress errors as they scale; a claim we support with our detailed surface code simulations. A fast, low-error entangling gate for dual-rail cavity erasure qubits preserves a strong error hierarchy, advancing scalable quantum error correction with substantially improved fault-tolerant performance.
Erasure qubits are beneficial for quantum error correction due to their relaxed threshold requirements. While dual-rail erasure qubits have been demonstrated with a strong error hierarchy in circuit quantum electrodynamics, biased-erasure qubits -- where erasures originate predominantly from one logical basis state -- offer further advantages. Here, we realize a hardware-efficient biased-erasure qubit encoded in the vacuum and two-photon Fock states of a single microwave cavity. The qubit exhibits an erasure bias ratio of over 265. By using a transmon ancilla for logical measurements and mid-circuit erasure detections, we achieve logical state assignment errors below 1% and convert over 99.3% leakage errors into detected erasures. After postselection against erasures, we achieve effective logical relaxation and dephasing rates of (6.2 ms)−1(6.2~\mathrm{ms})^{-1}(6.2 ms)−1 and (3.1 ms)−1(3.1~\mathrm{ms})^{-1}(3.1 ms)−1, respectively, which exceed the erasure error rate by factors of 31 and 15, establishing a strong error hierarchy within the logical subspace. These postselected error rates indicate a coherence gain of about 6.0 beyond the break-even point set by the best physical qubit encoded in the two lowest Fock states in the cavity. Moreover, randomized benchmarking with interleaved erasure detections reveals a residual logical gate error of 0.29%. This work establishes a compact and hardware-efficient platform for biased-erasure qubits, promising concatenations into outer-level stabilizer codes toward fault-tolerant quantum computation.
Qubits with predominantly erasure errors present distinctive advantages for quantum error correction (QEC) and fault-tolerant quantum computing. Logical qubits based on dual-rail encoding that exploit erasure detection have been recently proposed in superconducting circuit architectures, with either coupled transmons or cavities. Here, we implement a dual-rail qubit encoded in a compact, double-post superconducting cavity. Using an auxiliary transmon, we perform erasure detection on the dual-rail subspace. We characterize the behavior of the code space by a novel method to perform joint-Wigner tomography. This is based on modifying the cross-Kerr interaction between the cavity modes and the transmon. We measure an erasure rate of 3.981±0.003 (ms)^{-1} and a residual, postselected dephasing error rate up to 0.17 (ms)^{-1} within the code space. This strong hierarchy of error rates, together with the compact and hardware-efficient nature of this novel architecture, holds promise in realizing QEC schemes with enhanced thresholds and improved scaling.