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arXiv:1612.00568 · Physical review. B./Physical review. B

Pulse sequences for suppressing leakage in single-qubit gate operations

Joydip Ghosh, S. N. Coppersmith, Mark G. Friesen

Published Jun 29, 2017• 22 citations
arXivHTMLPDF

Abstract

Many realizations of solid-state qubits involve couplings to leakage states lying outside the computational subspace, posing a threat to high-fidelity quantum gate operations. Mitigating leakage errors is especially challenging when the coupling strength is unknown, e.g., when it is caused by noise. Here we show that simple pulse sequences can be used to strongly suppress leakage errors for a qubit embedded in a three-level system. As an example, we apply our scheme to the recently proposed charge quadrupole (CQ) qubit for quantum dots. These results provide a solution to a key challenge for fault-tolerant quantum computing with solid-state elements.

DOI
10.1103/physrevb.95.241307

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Many realizations of solid-state qubits involve couplings to leakage states lying outside the computational subspace, posing a threat to high-fidelity quantum gate operations. Mitigating leakage errors is especially challenging when the coupling strength is unknown, e.g., when it is caused by noise. Here we show that simple pulse sequences can be used to strongly suppress leakage errors for a qubit embedded in a three-level system. As an example, we apply our scheme to the recently proposed charge quadrupole (CQ) qubit for quantum dots. These results provide a solution to a key challenge for fault-tolerant quantum computing with solid-state elements.
Quantum computing promises significant speed-up for certain types of computational problems. However, robust implementations of semiconducting qubits must overcome the effects of charge noise that currently limit coherence during gate operations. Here we describe a scheme for protecting solid-state qubits from uniform electric field fluctuations by generalizing the concept of a decoherence-free subspace for spins, and we propose a specific physical implementation: a quadrupole charge qubit formed in a triple quantum dot. The unique design of the quadrupole qubit enables a particularly simple pulse sequence for suppressing the effects of noise during gate operations. Simulations yield gate fidelities 10-1,000 times better than traditional charge qubits, depending on the magnitude of the environmental noise. Our results suggest that any qubit scheme employing Coulomb interactions (for example, encoded spin qubits or two-qubit gates) could benefit from such a quadrupolar design.
Leakage errors damage a qubit by coupling it to other levels. Over the years, several theoretical approaches to dealing with such errors have been developed based on perturbation arguments. Here we propose a different strategy: we use a sequence of finite rotation gates to exactly eliminate leakage errors. The strategy is illustrated by the recently proposed charge quadrupole qubit in a triple quantum dot, where there are two logical states to support the qubit and one leakage state. We have found an su(2) subalgebra in the three-level system, and by using the subalgebra we show that ideal Pauli x and z rotations, which are universal for single-qubit gates, can be generated by two or three propagators of experimentally-available Hamiltonians. The proposed strategy does not require additional pulses, is independent of error magnitude, and potentially reduces experimental overheads. In addition, the magnitude of detuning fluctuation can be estimated based on the exact solution.
High-fidelity quantum operations require the system dynamics to be strictly confined to the computational subspace. In practice, however, control fields inevitably couple to leakage levels, giving rise to quantum state leakage that significantly reduces the fidelity of the operation. To address this challenge, we propose a general strategy for actively suppressing leakage errors by applying small, static offsets to tunable system parameters. This approach systematically mitigates leakage's detrimental impact on quantum control, without modifying the original control framework or incurring additional time overhead. By avoiding the need for extra suppression pulses or complex optimization procedures altogether, it offers a streamlined solution for leakage compensation while remaining fully compatible with subsequent optimal control techniques. Numerical validation conducted on superconducting quantum circuits demonstrates effective leakage suppression, enabling high-fidelity single-qubit gates, precise control of two-qubit interactions, and perfect state transfer in multi-level systems. Moreover, when integrated with optimal control techniques, our approach also allows for the cooperative suppression of both leakage errors and residual crosstalk. Therefore, this work provides a feasible technical pathway toward the low error thresholds required for fault-tolerant quantum computation.
Fault-tolerant quantum computing requires high-fidelity quantum gates that are resilient to control errors and device imperfections. Here, we develop energy-optimal control pulses for single-qubit gates that are simultaneously robust against frequency detuning and waveform inhomogeneities while also suppressing leakage outside the computational subspace. Combining the optimized pulse envelopes with an adaptive control scheme, we experimentally demonstrate optimal robust gates on a superconducting quantum processor. For a gate duration of 90ns, we achieve fidelities above 99.9% for the X gate and 99.6% for Hadamard-type gates. For the X gate, we maintain fidelities above 99.5% for simultaneous drive-amplitude variations up to 20% and qubit detuning up to 4 MHz. This robustness outperforms that of conventional Gaussian pulses by an order of magnitude, without much difference in peak gate fidelity. These results establish a route towards robust single-qubit control in large-scale quantum processors, advancing the development of fault-tolerant quantum computing.
Leakage errors damage a qubit by coupling it to other levels. Over the years, several theoretical approaches to dealing with such errors have been developed based on perturbation arguments. Here we propose a different strategy: we use a sequence of finite rotation gates to exactly eliminate leakage errors. The strategy is illustrated by the recently proposed charge quadrupole qubit in a triple quantum dot, where there are two logical states to encode the qubit and one leakage state. We found an su(2) subalgebra in the three-level system, and by using the subalgebra we show that ideal Pauli x and z rotations, which are universal for single-qubit gates, can be generated by two or three propagators. In addition, the magnitude of detuning fluctuation can be estimated based on the exact solution.
We present a scheme for correcting for crosstalk- and noise-induced errors in exchange-coupled singlet-triplet semiconductor double quantum dot qubits. While exchange coupling allows the coupling strength to be controlled independently of the intraqubit exchange couplings, there is also the problem of leakage, which must be addressed. We show that, if a large magnetic field difference is present between the two qubits, leakage is suppressed. We then develop pulse sequences that correct for crosstalk- and noise-induced errors and present parameters describing them for the 24 Clifford gates. We determine the infidelity for both the uncorrected and corrected gates as a function of the error-inducing terms and show that our corrected pulse sequences reduce the error by several orders of magnitude.