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arXiv:1905.09524 · Journal of the Optical Society of America B

Berry-phase-based quantum gates assisted by transitionless quantum driving

Shi-fan Qi, Jun Jing

Published Jan 9, 2020• 9 citations
arXivHTMLPDF

Abstract

We propose a novel method for constructing geometric quantum gates using three- or two-level systems, in which a controllable variable, the detuning between the driving frequency and the atomic energy spacing, is introduced to realize geometric transformations. In particular, we have two instantaneous eigenstates with opposite eigenvalues constituting a closed loop in the parameter space. The accumulated dynamical phase is then exactly cancelled when the loop is completed, which is beyond the traditional parallel-transport restriction. We apply the transitionless quantum driving method to enhance the speed and fidelity of geometric gates. Gate fidelity in the presence of decoherence is also estimated.

DOI
10.1364/josab.381706

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We propose a novel method for constructing geometric quantum gates using three- or two-level systems, in which a controllable variable, the detuning between the driving frequency and the atomic energy spacing, is introduced to realize geometric transformations. In particular, we have two instantaneous eigenstates with opposite eigenvalues constituting a closed loop in the parameter space. The accumulated dynamical phase is then exactly cancelled when the loop is completed, which is beyond the traditional parallel-transport restriction. We apply the transitionless quantum driving method to enhance the speed and fidelity of geometric gates. Gate fidelity in the presence of decoherence is also estimated.
Abstract Geometric quantum computation relies on the geometric phase that arises in adiabatic cyclic evolutions of non-degenerate quantum systems, enabling the design of robust quantum gates. However, the adiabatic condition requires long evolution times, making the system vulnerable to decoherence. In this work, we propose a scheme to realize fast and high-fidelity geometric quantum gates by applying the superadiabatic transitionless driving protocol within the dressed-state framework. We analyze the implementation of single-qubit gates in a two-level system driven by a microwave field, focusing in particular on the nitrogen-vacancy center in diamond. We show how the dynamical phase can be canceled to obtain purely geometric operations. The robustness of the gates is assessed under systematic errors and environmental decoherence, demonstrating high fidelity even in regimes with strong fluctuations. Finally, we extend the protocol to construct nontrivial two-qubit gates, highlighting its feasibility for scalable quantum information processing.
In the quantum-computation scenario, the geometric phase gates are becoming increasingly attractive for their intrinsic fault tolerance to disturbance. With an adiabatic cyclic evolution, Berry phase appears to realize a geometric transformation. Performing the quantum gates as many as possible within the timescale of coherence, however, remains an inconvenient bottleneck due to the systematic errors. Here we propose an accelerated adiabatic quantum gate based on the Berry phase, the transitionless driving, and the dynamical decoupling. It reconciles a high fidelity with a high speed in the presence of control noise or imperfection. We optimize the dynamical-decoupling sequence in the time domain under a popular Gaussian noise spectrum following the inversely quadratic power law.
ABSTRACT Geometric quantum gates, leveraging the geometric properties of evolution paths, offer inherent robustness against certain types of operational errors. In this work, we extend the concept of adiabatic geometric quantum gates to non‐Hermitian two‐level systems. Starting from the biorthogonal formalism, we derive the general expression for the complex Berry phase in non‐Hermitian quantum systems. By constructing a non‐Hermitian Hamiltonian driven by complex pulses and employing a single‐loop multiple‐pulse strategy, we demonstrate that the adiabatic cyclic evolution accumulates a purely geometric Abelian phase, enabling the realization of a universal set of single‐qubit geometric gates. We further analyze the impact of systematic errors on geometric gates, demonstrating their robustness against small pulse parameter variations. Finally, we propose a feasible scheme to implement a controlled‐phase () gate in a non‐Hermitian system of two Rydberg‐interacting atoms. Our results establish non‐Hermitian adiabatic geometric quantum gates as a viable and error‐resilient approach for quantum information processing. This work provides comprehensive theoretical support for non‐Hermitian geometric quantum computation and lays the foundation for the design and experimental realization of high‐fidelity, noise‐resilient quantum gates in open quantum systems.
A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer.
We propose a high-fidelity quantum control framework based on the quasi-topological number (νqua), which extends the traditional Chern number to characterize geometric responses in non-closed paths. By introducing an Adiabatic Gauge Potential that dynamically suppresses non-adiabatic transitions and reconstructs path curvature, we demonstrate that νqua—a relative homotopy invariant of compact manifolds in parameter space—quantifies the robustness of geometric phases during open-path quantum evolution. This integer invariant ensures gauge-invariant suppression of decoherence errors arising from dynamical phase coupling. Numerical simulations in the Kitaev superconducting chain and 2D transverse field Ising model confirm that our protocol achieves high quantum gate fidelity. We bridge geometric quantum control with topological protection, offering a universal approach to obtain high-fidelity and robust quantum gates.
Geometric gates that use the global property of the geometric phase is believed to be a powerful tool to realize fault-tolerant quantum computation. However, for singlet-triplet qubits in semiconductor quantum dot, the low Rabi frequency of the microwave control leads to overly long gating time, and thus the constructing geometric gate suffers more from the decoherence effect. Here we investigate the key issue of whether the fast geometric gate can be realized for singlet-triplet qubits without introducing an extra microwave-driven pulse, while maintaining the high-fidelity gate operation at the same time. We surprisingly find that both the single- and two-qubit geometric gates can be implemented via only modulating the time-dependent exchange interaction of the Hamiltonian, which can typically be on the order of $\ensuremath{\sim}\mathrm{GHz}$, and thus the corresponding gate time is of several nanoseconds. Furthermore, the obtained geometric gates are superior to their counterparts, i.e., the conventional dynamical gates for singlet-triplet qubits, with a relatively high fidelity surpassing 99%. Therefore our scheme is particularly applied to singlet-triplet qubits to obtain fast and high-fidelity geometric gates. Our scheme can also be extended to other systems without a microwave drive.