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Physical Review Applied

Decoherence-protected holonomic gates with reduced requirements for physical resources

Chunfeng Wu, Chunfang Sun, Jiangang Ma, Ding Huang, Xun‐Li Feng, L. C. Kwek

Published Apr 7, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1103/physrevapplied.23.044016

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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.
Control errors and decoherence are two main obstacles for realization of quantum computation. Nonadiabatic holonomic quantum computation in decoherence-free subspaces can protect quantum gates from both control errors and decoherence, and, therefore, it has received increasing attention. The original protocol of nonadiabatic holonomic quantum computation in decoherence-free subspaces needs two loops in the Grassmann manifold to generate an arbitrary nonadiabatic holonomic one-qubit gate. In this paper, we proposed a protocol of nonadiabatic holonomic quantum computation in decoherence-free subspaces, where an arbitrary one-qubit gate is generated by only a single loop in the Grassmann manifold and an entangling two-qubit gate assisted by two single-qubit gates can be used to construct a two-qubit controlled unitary gate. In addition, the encoding of our protocol for nonadiabatic holonomic gates requires a lower number of physical qubits compared with previous schemes. Our scheme not only maintains the merits of the original protocol but it also avoids the extra work of combining two gates to realize an arbitrary one-qubit gate.
Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of (N - 2)/N. The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities.
Nonadiabatic holonomic quantum computation in decoherence-free subspaces has attracted increasing attention recently, as it allows for high-speed implementation and combines both the robustness of holonomic gates and the coherence stabilization of decoherence-free subspaces. Since the first protocol of nonadiabatic holonomic quantum computation in decoherence-free subspaces, a number of schemes for its physical implementation have been put forward. However, all previous schemes require two noncommuting gates to realize an arbitrary one-qubit gate, which doubles the exposure time of gates to error sources as well as the resource expenditure. In this paper, we propose an alternative protocol for nonadiabatic holonomic quantum computation in decoherence-free subspaces, in which an arbitrary one-qubit gate in decoherence-free subspaces is realized by a single-shot implementation. The present protocol not only maintains the merits of the original protocol but also avoids the extra work of combining two gates to implement an arbitrary one-qubit gate and thereby reduces the exposure time to various error sources.
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.
To implement a set of universal quantum logic gates based on non-Abelian geometric phases, it is conventional wisdom that quantum systems beyond two levels are required, which is extremely difficult to fulfill for superconducting qubits and appears to be a main reason why only single-qubit gates were implemented in a recent experiment [A. A. Abdumalikov, Jr. et al., Nature (London) 496, 482 (2013)]. Here we propose to realize nonadiabatic holonomic quantum computation in decoherence-free subspace on circuit QED, where one can use only the two levels in transmon qubits, a usual interaction, and a minimal resource for the decoherence-free subspace encoding. In particular, our scheme not only overcomes the difficulties encountered in previous studies but also can still achieve considerably large effective coupling strength, such that high-fidelity quantum gates can be achieved. Therefore, the present scheme makes realizing robust holonomic quantum computation with superconducting circuits very promising.