Abstract Realization of a large‐scale quantum computation relies on fast and high‐fidelity quantum control. Geometric quantum control is thought to be a promising candidate for quantum computation which consolidates the robustness against both random noise (through the global geometrical feature) and systematic errors (through adiabatic characteristic). The adiabatic process of geometric control can be accelerated through an auxiliary Hamiltonian in different scenarios by means of shortcuts to adiabaticity (STA). Especially, the auxiliary Hamiltonian can be absorbed into the original interacting configuration in most of the cases, which allows STA to coalesce with the Abelian or the non‐Abelian geometric control. As a consequence, geometric quantum control can have an enhanced robustness against decoherence after speeding up by STA. Here, the recent theoretical and experimental advances in geometric quantum computation based on STA are reviewed.
Abstract Realization of a large‐scale quantum computation relies on fast and high‐fidelity quantum control. Geometric quantum control is thought to be a promising candidate for quantum computation which consolidates the robustness against both random noise (through the global geometrical feature) and systematic errors (through adiabatic characteristic). The adiabatic process of geometric control can be accelerated through an auxiliary Hamiltonian in different scenarios by means of shortcuts to adiabaticity (STA). Especially, the auxiliary Hamiltonian can be absorbed into the original interacting configuration in most of the cases, which allows STA to coalesce with the Abelian or the non‐Abelian geometric control. As a consequence, geometric quantum control can have an enhanced robustness against decoherence after speeding up by STA. Here, the recent theoretical and experimental advances in geometric quantum computation based on STA are reviewed.
Quantum control that is robust against control errors and dephasing process is a key ingredient of quantum computation. In article no. 1900013, Yanxiong Du and co-workers review the recent progresses on the geometric quantum computation with shortcut to adiabaticity. Geometric phase, as acquired in the evolution of Hilbert space, can be used to realize geometric quantum computation that is robust against random noise and systematic errors. Through optimizing the control waveform with shortcut to adiabatic manner, the operation will consolidate the virtues of being fast and robust. Theoretical and experimental results have proven the effectiveness of combining the geometric phase and shortcut to adiabaticity.
Fast and robust quantum gates are the cornerstones of fault-tolerance quantum computation. In this paper, as opposed to the previous proposals which use cyclic geometric phases, we propose to realize quantum computation based on noncyclic geometric evolution. The superiority of the noncyclic scheme is that the operation time is proportional to the rotation angle of the quantum state. Therefore, the noncyclic scheme becomes fairly fast in the case of quantum gates with small rotation angle, which will be more insensitive to the decoherence and the leakage to the states outside the computational basis. Similar to the cyclic version of geometric quantum computation, dynamical phases here during the evolution are canceled by spin-echo process and the adiabatic control can be sped up through shortcut to adiabaticity. The proposed scheme is robust against random noise due to the geometric characteristic of projective Hilbert space. Since the proposed scheme is fast and robust, it is a particularly suitable way to manipulate the physical systems with weak nonlinearity, such as superconducting systems.
Geometric phases are used to construct quantum gates since it naturally resists local noises, acting as the modularized units of geometric quantum computing. Meanwhile, fast nonadiabatic geometric gates are required for reducing the information loss induced by decoherence. Here, we propose a digital simulation of nonadiabatic geometric quantum gates in terms of shortcuts to adiabaticity (STA). More specifically, we combine the invariant-based inverse engineering with optimal control theory for designing the fast and robust Abelian geometric gates against systematic error, in the context of two-level qubit systems. We exemplify X and T gates, in which the fidelities and robustness are evaluated by simulations in ideal quantum circuits. Our results can also be extended to constructing two-qubit gates, for example, a controlled-PHASE gate, which shares the equivalent effective Hamiltonian with rotation around the Z-axis of a single qubit. These STA-inspired nonadiabatic geometric gates can realize quantum error correction physically, leading to fault-tolerant quantum computing in the Noisy Intermediate-Scale Quantum (NISQ) era.
Shortcuts to adiabaticity (STA) are fast methods to realize the same final state evolution of quantum adiabatic process. We develop a general theory to construct a new kind of STA by solely sampling the points of the adiabatic path of the original adiabatic Hamiltonian. In contrast to previous methods, our approach does not require any additional control resources, has inherent robustness, and does not use any complicated unitary transformation. Based on path sampling, the resulting STA protocols are simple and can avoid points of adiabatic path that are challenging to implement. As applications of our theory, we demonstrate reduction of the effects of both dissipation and dephasing noise by a novel robust three-level control, as well as reliable and fast ground state evolution in an adiabatic quantum computing model. Our theory offers a new route to design robust and fast control methods for general quantum systems.
A nonadiabatic geometric quantum gate is realized by integrating nonadiabatic geometric phases with global geometric features into the unitary quantum control, thereby removing the limitation of a long evolution time in the adiabatic case. However, systematic errors are inevitable in practical quantum control; these lead to the deviation of the evolution from target conditions to inducing geometric phases, smearing the robustness of the induced geometric quantum gates. Here, we present a general theoretical framework with enhanced robustness for geometric quantum gates by preserving fundamental geometric conditions. We first analytically evaluate the influence of systematic errors on geometric gates and then propose an optimized approach to mitigate this influence. Numerical simulations indicate that, as the geometric conditions are still maintained in the presence of systematic errors in our scheme, the constructed geometric quantum gates exhibit strong robustness, far superior to that of conventional schemes. Furthermore, we propose implementing the scheme in superconducting quantum circuits, where geometric quantum gates can achieve high fidelity with current experimental parameters. Therefore, the enhanced gate performance highlights the promise of our scheme for large-scale quantum computations.
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.