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arXiv:2411.04101

High-fidelity gates in a transmon using bath engineering for passive leakage reset

Ted Thorbeck, McDonald, Alexander, Olivia Lanes, Blair, John, George Keefe, Adam Stabile, Baptiste Royer, Luke C. G. Govia, Alexandre Blais

Published Nov 6, 2024• 0 citations
arXivHTMLPDF

Abstract

Leakage, the occupation of any state not used in the computation, is one of the of the most devastating errors in quantum error correction. Transmons, the most common superconducting qubits, are weakly anharmonic multilevel systems, and are thus prone to this type of error. Here we demonstrate a device which reduces the lifetimes of the leakage states in the transmon by three orders of magnitude, while protecting the qubit lifetime and the single-qubit gate fidelties. To do this we attach a qubit through an on-chip seventh-order Chebyshev filter to a cold resistor. The filter is engineered such that the leakage transitions are in its passband, while the qubit transition is in its stopband. Dissipation through the filter reduces the lifetime of the transmon's $f$ state, the lowest energy leakage state, by three orders of magnitude to 33 ns, while simultaneously keeping the qubit lifetime to greater than 100 $μ$s. Even though the $f$ state is transiently populated during a single qubit gate, no negative effect of the filter is detected with errors per gate approaching 1e-4. Modelling the filter as coupled linear harmonic oscillators, our theoretical analysis of the device corroborate our experimental findings. This leakage reduction unit turns leakage errors into errors within the qubit subspace that are correctable with traditional quantum error correction. We demonstrate the operation of the filter as leakage reduction unit in a mock-up of a single-qubit quantum error correcting cycle, showing that the filter increases the seepage rate back to the qubit subspace.

DOI
10.48550/arxiv.2411.04101

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Leakage, the occupation of any state not used in the computation, is one of the of the most devastating errors in quantum error correction. Transmons, the most common superconducting qubits, are weakly anharmonic multilevel systems, and are thus prone to this type of error. Here we demonstrate a device which reduces the lifetimes of the leakage states in the transmon by three orders of magnitude, while protecting the qubit lifetime and the single-qubit gate fidelties. To do this we attach a qubit through an on-chip seventh-order Chebyshev filter to a cold resistor. The filter is engineered such that the leakage transitions are in its passband, while the qubit transition is in its stopband. Dissipation through the filter reduces the lifetime of the transmon's fff state, the lowest energy leakage state, by three orders of magnitude to 33 ns, while simultaneously keeping the qubit lifetime to greater than 100 μμμs. Even though the fff state is transiently populated during a single qubit gate, no negative effect of the filter is detected with errors per gate approaching 1e-4. Modelling the filter as coupled linear harmonic oscillators, our theoretical analysis of the device corroborate our experimental findings. This leakage reduction unit turns leakage errors into errors within the qubit subspace that are correctable with traditional quantum error correction. We demonstrate the operation of the filter as leakage reduction unit in a mock-up of a single-qubit quantum error correcting cycle, showing that the filter increases the seepage rate back to the qubit subspace.
Rapid and accurate initialization of qubits, known as reset, is a crucial building block for various tasks in quantum information processing, such as quantum error correction and estimation of the statistics of noisy quantum devices with many qubits. We demonstrate unconditional reset of a frequency-tunable transmon qubit that simultaneously resets multiple excited states using a metamaterial waveguide engineered to provide a cold bath over a wide spectral range, while providing strong protection against Purcell decay of the qubit. We report a reset error below 0.13% (0.16%) when prepared in the first (second) excited state of the transmon within 88 ns. In addition, through the sharp roll-off in the density of states of the metamaterial waveguide, we implement a leakage-reduction unit that selectively resets the transmon’s second excited state to 0.285(3)% residual population within 44 ns while acting trivially in the computational subspace as an identity operation that preserves encoded information with an infidelity of 0.72(1)%.
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.
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.
One of the main enablers in quantum computing is having qubit control that is precise and fast. However, qubits typically have multilevel structures making them prone to unwanted transitions from fast gates. This leakage out of the computational subspace is especially detrimental to algorithms as it has been observed to cause long-lived errors, such as in quantum error correction. This forces a choice between either achieving fast gates or having low leakage. Previous works focus on suppressing leakage by mitigating the first to second excited state transition, overlooking multi-photon transitions, and achieving faster gates with further reductions in leakage has remained elusive. Here, we demonstrate single qubit gates with a total leakage error consistently below 2.0×10−52.0\times10^{-5}2.0×10−5, and obtain fidelities above 99.98%99.98\%99.98% for pulse durations down to 6.8 ns for both XXX and X/2X/2X/2 gates. This is achieved by removing direct transitions beyond nearest-neighbor levels using a double recursive implementation of the Derivative Removal by Adiabatic Gate (DRAG) method, which we name the R2D method. Moreover, we find that at such short gate durations and strong driving strengths the main error source is from these higher order transitions. This is all shown in the widely-used superconducting transmon qubit, which has a weakly anharmonic level structure and suffers from higher order transitions significantly. We also introduce an approach for amplifying leakage error that can precisely quantify leakage rates below 10−610^{-6}10−6. The presented approach can be readily applied to other qubit types as well.
Quantum error correction imposes stringent requirements on the underlying hardware: all core operations of a quantum processor – single-qubit gates, two-qubit entangling gates, qubit readout, and qubit reset – must operate well below the error thresholds of leading codes. While such thresholds have already been crossed in several platforms, the associated overhead in physical qubits and circuit depth remains extremely sensitive to the physical error rate. This thesis investigates how far a superconducting platform based on transmon qubits can be pushed toward its physical limits, and how architectural and control choices can be optimized to reduce the overhead required for fault-tolerant quantum computation. First, we develop and characterize tunable-coupler architectures that enable fast, high-fidelity controlled-Z (CZ) gates. A long-distance coupler increases the qubit-qubit separation, freeing chip area for additional on-chip components, while still achieving CZ fidelities above 99.8%. Building on this, we optimize the qubit-coupler coupling to simultaneously support high-performance single- and two-qubit gates. We achieve simultaneous single- and two-qubit gate fidelities exceeding 99.9% on the same chip using a CZ calibration experiment based on our phase-averaged leakage error amplification (PALEA) protocol. PALEA coherently amplifies small over- and under-rotations of the diabatic CZ gate, making calibration errors easier to detect and correct. Second, we address single-qubit gates. Using spectrally engineered FAST-DRAG and higherderivative DRAG pulses, we demonstrate sub-8 ns gates with errors of order 10!" and strongly suppressed leakage. Third, we address readout by combining shelving to a higher qubit level with Purcell-filtered resonators and quantum-limited amplification, achieving readout errors below 10!#. Beyond the transmon workhorse, we explore the unimon qubit, which combines large anharmonicity with reduced charge sensitivity, and investigate a quantum circuit refrigerator as an integrated resource for fast, unconditional qubit reset via engineered dissipation. Finally, we demonstrate a cryogenic microwave link between two dilution refrigerators, enabling remote state transfer and entanglement over a five-meter distance and illustrating a path toward modular and distributed superconducting quantum processors. Together, these results show that with careful co-design of device layout, coupling topology, pulse shaping, and calibration protocols, all core operations – except qubit reset – of a superconducting quantum processor can be operated in the 10!#–10!" error regime within a coherent hardware and control stack, substantially lowering the resource overhead required for future fault-tolerant architectures.