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arXiv:2405.04090

Protecting quantum gates from arbitrary single- and two-qubit errors

Chunfeng Wu, Gangcheng Wang, Xun‐Li Feng

Published May 7, 2024• 0 citations
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Abstract

We explore the protection of quantum gates from arbitrary single- and two-qubit noises with properly designed dynamical decoupling pulses. The proposed dynamical decoupling method is a concatenation of a sequence of pulses formed by $σ_x$, $σ_xσ_x$ with another sequence constructed by $σ_z$, $σ_zσ_z$. The concatenation of the two sequences results in desired pulses to fight agianst any single- and two-qubit errors. The success of our method relies on the ability to adjust system parameters or interaction terms, which can be achieved in different physical systems, including trapped ions and superconducting qubits. We finally explore the performance of our method numerically with the above-mentioned errors that are changing at any moment and show the preferred protection offered by the method. Therefore, our method is a timely step forward in preserving quantum gates at the level of physical qubits.

DOI
10.48550/arxiv.2405.04090

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We explore the protection of quantum gates from arbitrary single- and two-qubit noises with properly designed dynamical decoupling pulses. The proposed dynamical decoupling method is a concatenation of a sequence of pulses formed by σxσ_xσx​, σxσxσ_xσ_xσx​σx​ with another sequence constructed by σzσ_zσz​, σzσzσ_zσ_zσz​σz​. The concatenation of the two sequences results in desired pulses to fight agianst any single- and two-qubit errors. The success of our method relies on the ability to adjust system parameters or interaction terms, which can be achieved in different physical systems, including trapped ions and superconducting qubits. We finally explore the performance of our method numerically with the above-mentioned errors that are changing at any moment and show the preferred protection offered by the method. Therefore, our method is a timely step forward in preserving quantum gates at the level of physical qubits.
Abstract The protection of quantum gates from arbitrary single‐ and two‐qubit noises with properly designed dynamical decoupling (DD) pulses is explored. The proposed dynamical decoupling method is a concatenation of a sequence of pulses formed by , with another sequence constructed by , . The concatenation of the two sequences results in desired pulses to fight against any single‐ and two‐qubit errors. The success of the method relies on the ability to adjust system parameters or interaction terms, which can be achieved in different physical systems, including trapped ions and superconducting qubits. Finallythe performance of the method is explored numerically with the above‐mentioned errors that are changing at any moment and show the preferred protection offered by the method. Therefore, the method is a timely step forward in preserving quantum gates at the level of physical qubits.
Dephasing--phase randomization of a quantum superposition state--is a major obstacle for the realization of high fidelity quantum logic operations. Here, we implement a two-qubit controlled-NOT gate using dynamical decoupling (DD), despite the gate time being more than 1 order of magnitude longer than the intrinsic coherence time of the system. For realizing this universal conditional quantum gate, we have devised a concatenated DD sequence that ensures robustness against imperfections of DD pulses that otherwise may destroy quantum information or interfere with gate dynamics. We compare its performance with three other types of DD sequences. These experiments are carried out using a well-controlled prototype quantum system--trapped atomic ions coupled by an effective spin-spin interaction. The scheme for protecting conditional quantum gates demonstrated here is applicable to other physical systems, such as nitrogen vacancy centers, solid state nuclear magnetic resonance, and circuit quantum electrodynamics.
We introduce a method for designing smooth single-qubit control pulses that implement a desired gate while suppressing the effect of unknown static error sources to first order. Unlike dynamically corrected gate constructions that require prior knowledge of the noise model, the present approach is agnostic to the detailed form of the target-bath interaction. The method parametrizes the control propagator through an auxiliary matrix expansion over orthogonal basis functions and enforces decoupling through algebraic orthogonality and equal-norm constraints on the expansion coefficients. These conditions guarantee that the leading Magnus contribution of an arbitrary static interaction reduces to a term proportional to the identity on the target system, thereby cancelling first-order error effects independently of the microscopic origin of the noise. We further show that the same construction suppresses, to first order, mediated couplings between simultaneously controlled qubits when their interaction occurs through intermediate environmental degrees of freedom, yielding effective second-order decoupling of the induced inter-qubit interaction. By using a discrete cosine transform parametrization, the pulse-synthesis problem is cast into a numerically stable constrained optimization with a minimal number of free parameters. Numerical examples for RzR_zRz​ rotations and random single-qubit unitaries demonstrate smooth control fields that realize the target gates while remaining robust against arbitrary static single-qubit noise and mediated multi-qubit couplings. These results provide a hardware-friendly route toward noise-agnostic dynamically corrected single-qubit gates.
We study the implementation of holonomic quantum gates preserved from arbitrary single-qubit and two-qubit decoherence or errors using a dynamical decoupling approach. To integrate the holonomic feature with the dynamical decoupling technique, we require only one auxiliary qubit for single-qubit gates and no auxiliary qubit for two-qubit gates. Our scheme uses far fewer physical qubits to achieve this integration compared to existing proposals in the literature. Moreover, the scheme is based on system interactions that can be experimentally realized with superconducting qubits. These advantages suggest that our scheme is a promising step toward developing noise-resistant quantum devices.
We present a scheme to implement a universal set of quantum gates based on achievable interactions, and the gates can be protected against decoherences through dynamical-decoupling approach without encoding. By properly designing system evolutions, the desired system interactions commute with the elements forming dynamical decoupling pulses. Thus, the effect of decoherences can be eliminated by repeatedly applying the pulses, without noticeably affecting the system evolutions governed by the desired system interactions given small enough time interval between pulses. Moreover, due to the commutation between the elements forming the pulses and the desired system interactions, our scheme is resistant to different types of decoherences, and so not limited to specific decoherences. Our scheme also works well in the case that the desired system interactions cannot be achieved ideally due to imperfect control of system parameters, through the action of dynamical-decoupling pulses.
Dynamical decoupling (DD) refers to a well-established family of methods for error mitigation, comprising pulse sequences aimed at averaging away slowly evolving noise in quantum systems. Here we revisit the question of its efficacy in the presence of noisy pulses in scenarios important for quantum devices today: pulses with gate control errors, and the computational setting where DD is used to reduce noise in every computational gate. We focus on the well-known schemes of periodic (or universal) DD and its extension, concatenated DD, for scaling up its power. The qualitative conclusions from our analysis of these two schemes nevertheless apply to other DD approaches. In the presence of noisy pulses, DD does not always mitigate errors. It does so only when the added noise from the imperfect DD pulses does not outweigh the increased ability in averaging away the original background noise. We present break-even conditions that delineate when DD is useful, and further find that there is a limit in the performance of concatenated DD, specifically in how far one can concatenate the DD pulse sequences before the added noise no longer offers any further benefit in error mitigation.