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Advanced Quantum Technologies

Protecting Quantum Gates from Arbitrary Single‐ and Two‐Qubit Errors

Gangcheng Wang, Chunfeng Wu, Chunfang Sun, Xun‐Li Feng

Published May 14, 2025• 1 citation
Publisher

Abstract

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.

DOI
10.1002/qute.202500041

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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.
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.
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.
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 study how dynamical decoupling (DD) pulse sequences can improve the reliability of quantum computers. We prove upper bounds on the accuracy of DD-protected quantum gates and derive sufficient conditions for DD-protected gates to outperform unprotected gates. Under suitable conditions, fault-tolerant quantum circuits constructed from DD-protected gates can tolerate stronger noise and have a lower overhead cost than fault-tolerant circuits constructed from unprotected gates. Our accuracy estimates depend on the dynamics of the bath that couples to the quantum computer and can be expressed either in terms of the operator norm of the bath's Hamiltonian or in terms of the power spectrum of bath correlations; we explain in particular how the performance of recursively generated concatenated pulse sequences can be analyzed from either viewpoint. Our results apply to Hamiltonian noise models with limited spatial correlations.
Abstract A protocol for implementing a universal set of quantum gates, which are safeguarded from noise through geometric, dephasing‐free, and dynamical‐decoupling approaches is proposed. With properly designed Hamiltonians, the desired interactions are realized directly within the Schrödinger picture rather than relying on the interaction picture. This design confers two advantages. One is that the system's evolution remains continuously protected by the noise‐mitigation strategies at every stage, eliminating the need to revert to the Schrödinger picture. The other one is that the dynamical decoupling technique effectively averages out small residual free terms in the system's Hamiltonian, thus reducing the stringent requirements for precise control of system parameters to avoid errors. Furthermore, numerical results are presented to support our protocol by finding gate fidelities in the absence (presence) of noises or errors, without or with dynamical decoupling technique.
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.