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arXiv:2205.06945 · PRX Quantum

Avoiding Leakage and Errors Caused by Unwanted Transitions in Lambda Systems

Arian Vezvaee, Evangelia Takou, Paul Hilaire, Matthew F. Doty, Sophia E. Economou

Published Jul 28, 2023• 15 citations
arXivHTMLPDF

Abstract

Three-level systems appear in various quantum information processing platforms.In several control schemes, the excited level serves as an auxiliary state for implementing gate operations between the lower qubit states.However, extra excited levels give rise to unwanted transitions that cause leakage and other errors, degrading the gate fidelity.We focus on a coherent-population-trapping scheme for gates and design protocols that reduce the effects of the unwanted off-resonant couplings and improve the gate performance up to several orders of magnitude.For a particular setup of unwanted couplings, we find an exact solution, which leads to error-free gate operations via only a static detuning modification.In the general case, we improve gate operations by adding corrective modulations to the pulses, thereby generalizing the derivative removal by adiabatic gates protocol to systems.Our techniques enable fast and high-fidelity gates and apply to a wide range of optically driven platforms, such as quantum dots, color centers, and trapped ions.

DOI
10.1103/prxquantum.4.030312

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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•May 1, 2013•1 citation
Three-level systems appear in various quantum information processing platforms.In several control schemes, the excited level serves as an auxiliary state for implementing gate operations between the lower qubit states.However, extra excited levels give rise to unwanted transitions that cause leakage and other errors, degrading the gate fidelity.We focus on a coherent-population-trapping scheme for gates and design protocols that reduce the effects of the unwanted off-resonant couplings and improve the gate performance up to several orders of magnitude.For a particular setup of unwanted couplings, we find an exact solution, which leads to error-free gate operations via only a static detuning modification.In the general case, we improve gate operations by adding corrective modulations to the pulses, thereby generalizing the derivative removal by adiabatic gates protocol to systems.Our techniques enable fast and high-fidelity gates and apply to a wide range of optically driven platforms, such as quantum dots, color centers, and trapped ions.
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.
High-fidelity and decoherence-insensitive quantum gates are essential for achieving universal quantum computing. In quantum information processing, decoherence arising from excited states significantly contributes to the scheme's infidelity. Therefore, minimizing the average population of the excited state is crucial when designing quantum protocols. A promising approach involves utilizing capture-and-release dynamics to induce a complex phase on the ground state in a two-level system, effectively suppressing the integrated excited-state population. By applying this dynamics protocol to a $\mathrm{\ensuremath{\Lambda}}$ three-level system, we propose a scheme to construct arbitrary decoherence suppressed single-qubit and nontrivial two-qubit gates; meanwhile, by incorporating the Zeno dynamics process in the construction of two-qubit logic gates, the large detuning and excitation of virtual photons render the scheme insensitive to qubit decoherence and cavity dissipation. Applying our scheme to the nitrogen-vacancy (NV) center as an example, we prove our scheme with higher fidelity than conventional nonadiabatic non-Abelian geometric gates while significantly enhancing the robustness against decoherence and frequency shift errors. These studies provide alternative approaches for constructing robust quantum gate operations. We also emphasize that the scheme is feasible for three-level quantum systems, not limited to NV center systems.
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.
Non-adiabatic two-qubit gate proposals for trapped-ion systems offer superior performance and flexibility over adiabatic schemes at the cost of increased laser control requirements. Existing fast gate schemes are limited by single-qubit transition errors, which constrain the total number of pulses in high-fidelity solutions. We introduce an improved gate search scheme that enables both local and non-local two-qubit gates in chains containing tens of ions. These protocols use a multi-objective machine design approach that incorporates dominant sources of error in the design to ensure the solutions are compatible with existing fast laser controls. We also generalize previous schemes by allowing for unpaired pulses during the gate evolution. By imposing symmetries on the pulse sequences, we eliminate susceptibility to laser phase noise and further simplify the multi-mode control over the state-dependent motion of the ion crystal. We perform a comprehensive analysis of expected gate performance in the presence of random and systematic experimental errors to demonstrate the feasibility of performing microsecond two-qubit gates between arbitrary ion pairs in current linear ion-trap processors of up to 505050 ions with fidelities approaching 99.9%99.9\%99.9%.
In qubits made from a weakly anharmonic oscillator the leading source of error at short gate times is leakage of population out of the two dimensional Hilbert space that forms the qubit. In this article we develop a general scheme based on an adiabatic expansion to find pulse shapes that correct this type of error. We find a family of solutions that allows tailoring to what is practical to implement for a specific application. Our result contains and improves the previously developed derivative removal by adiabatic gate technique [F. Motzoi et al., Phys. Rev. Lett. 103, 110501 (2009)] and allows a generalization to other nonlinear oscillators with more than one leakage transition.
Summary form only given. Experiments in many fields of quantum physics require well-defined quantum states and well-defined interactions. For example, the basic ingredient of the quantum computer is a well-defined qubit - a two-state quantum system. Real quantum systems, however, possess many states and special care is needed to isolate just two of them. In real and artificial atoms this is usually done with polarized laser light, carefully aligned with the quantization axis. However, unwanted transition channels may still be present, which reduce the fidelity of the operations. For example, when an ultracold atomic ensemble held in an optical dipole trap is addressed by right circularly polarized light, many atoms often “see” an admixture of σ+ and σ- light (i.e., elliptical polarization [1]) since not all of them are exactly in the focus of the laser fields. Unwanted transitions may be present also due to imperfect polarization or alignment, off-resonant couplings, perturbing excitations in molecules and solids, etc.We propose a simple and efficient technique for automatic compensation of such errors, even without knowing their magnitudes, which uses composite pulse sequences [2-5] to dynamically suppress unwanted transitions, while simultaneously controlling the qubit in a robust way. We illustrate the technique in threeand four-state quantum systems forming linkages reminiscent of the letters V, Ξ and Y, but it can readily be adapted to more complex systems. By suitably choosing the phases of the constituent pulses, the unwanted transitions can be suppressed with very high fidelity, while compensation of deviations in laser polarizations, intensities and detunings can be done simultaneously. The accuracy, the flexibility and the simplicity of the proposed technique make it a potentially important tool in applications requiring high control fidelity, such as quantum information processing and quantum optics.transitions