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.
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.
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.
Geometric phases accompanying adiabatic quantum evolutions can be used to construct robust quantum control for quantum information processing due to their noise-resilient feature. A significant development along this line is to construct geometric gates using nonadiabatic quantum evolutions to reduce errors due to decoherence. However, it has been shown that nonadiabatic geometric gates are not necessarily more robust than dynamical ones, in contrast to an intuitive expectation. Here we experimentally investigate this issue for the case of nonadiabatic holonomic quantum computation~(NHQC) and show that conventional NHQC schemes cannot guarantee the expected robustness due to a cross coupling to the states outside the computational space. We implement a new set of constraints for gate construction in order to suppress such cross coupling to achieve an enhanced robustness. Using a superconducting quantum circuit, we demonstrate high-fidelity holonomic gates whose infidelity against quasi-static transverse errors can be suppressed up to the fourth order, instead of the second order in conventional NHQC and dynamical gates. In addition, we explicitly measure the accumulated dynamical phase due to the above mentioned cross coupling and verify that it is indeed much reduced in our NHQC scheme. We further demonstrate a protocol for constructing two-qubit NHQC gates also with an enhanced robustness.
While geometric quantum gates are often theorized to possess intrinsic resilience to control errors by exploiting the global properties of evolution paths, this promise has not consistently translated into practical robustness. We present a streamlined framework for nonadiabatic geometric quantum gates (NGQGs) that incorporates additional auxiliary constraints to suppress dynamical contamination and achieve super-robust performance. Within this framework, we also design NGQGs using noncyclic paths, offering enhanced design flexibility. Implemented on superconducting transmon qubits, our scheme realizes high-fidelity single-qubit gates that are robust against Rabi amplitude error ε, with infidelity scaling as O(ε4), in contrast to the O(ε2) behavior of conventional dynamical gates. We further analyze two-qubit NGQGs under parametric driving. Our results identify subtle limitations that compromise performance in two-qubit scenarios, underscoring the importance of phase compensation and waveform calibration. The demonstrated simplicity and generality of our super-robust NGQG scheme make it applicable across diverse quantum platforms.
Geometric phases accompanying adiabatic quantum evolutions can be used to construct robust quantum control for quantum information processing due to their noise-resilient feature. A significant development along this line is to construct geometric gates using nonadiabatic quantum evolutions to reduce errors due to decoherence. However, it has been shown that nonadiabatic geometric gates are not necessarily more robust than dynamical ones, in contrast to an intuitive expectation. Here we experimentally investigate this issue for the case of nonadiabatic holonomic quantum computation (NHQC) and show that conventional NHQC schemes cannot guarantee the expected robustness due to a cross-coupling to the states outside the computational space. We implement a different set of constraints for gate construction in order to suppress such cross-coupling to achieve an enhanced robustness. Using a superconducting quantum circuit, we demonstrate high-fidelity holonomic gates whose infidelity against quasistatic transverse errors can be suppressed up to the fourth order, instead of the second order in conventional NHQC and dynamical gates. In addition, we explicitly measure the accumulated dynamical phase due to the abovementioned cross-coupling and verify that it is indeed much reduced in our NHQC scheme. We further demonstrate a protocol for constructing two-qubit NHQC gates also with an enhanced robustness.
Abstract Nonadiabatic geometric quantum computation is dedicated to the realization of high‐fidelity and robust quantum gates, which are necessary for fault‐tolerant quantum computation. However, it is limited by cyclic and mutative evolution path, which usually requires longer gate‐time and abrupt pulse control, weakening the gate performance. Here, a scheme to realize geometric quantum gates with noncyclic and nonadiabatic evolution via invariant‐based shortcuts is proposed, where universal quantum gates can be induced in one step without path mutation and the gate time is also effectively shortened. Our numerical simulations show that, comparing with the conventional dynamical gates, the constructed geometric gates have stronger resistance not only to systematic errors, induced by both qubit‐frequency drift and the deviation of the amplitude of the driving fields, but also to environment‐induced decoherence effect. In addition, this scheme can also be implemented on a superconducting circuit platform, with the fidelities of single‐qubit and two‐qubit gates higher than 99.97% and 99.84%, respectively. Therefore, this scheme provides a promising way to realize high‐fidelity fault‐tolerant quantum gates for scalable quantum computation.
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.