Abstract Geometric phases and holonomies offer a robust route to quantum control and simulation. We introduce a high-fidelity quantum simulation framework based on the analytically solvable Demkov-Kunike (DK) model, which extends the standard Landau-Zener paradigm by providing richer control over evolution paths. We demonstrate how tailored DK pulse sequences can simulate the braiding statistics of Abelian anyons through Stückelberg interferometry, with a protocol for exact dynamical phase cancellation. Generalizing to a three-level Λ-system, we engineer a non-Abelian Wilczek-Zee connection and construct a universal set of holonomic quantum gates. A detailed analysis of the evolution operator and leakage probability for the three-level DK model is provided, identifying optimal adiabaticity regimes for high fidelity. We propose an experimental implementation using trapped ions, including a rigorous derivation of the effective DK Hamiltonian in a decoherence-free subspace. Numerical simulations confirm the expected interference signatures, gate non-commutativity, and enhanced robustness of geometric gates under decoherence. This work establishes DK pulses as a versatile tool for simulating topological-like phenomena and engineering geometric quantum gates in controllable quantum systems.
Abstract Geometric phases and holonomies offer a robust route to quantum control and simulation. We introduce a high-fidelity quantum simulation framework based on the analytically solvable Demkov-Kunike (DK) model, which extends the standard Landau-Zener paradigm by providing richer control over evolution paths. We demonstrate how tailored DK pulse sequences can simulate the braiding statistics of Abelian anyons through Stückelberg interferometry, with a protocol for exact dynamical phase cancellation. Generalizing to a three-level Λ-system, we engineer a non-Abelian Wilczek-Zee connection and construct a universal set of holonomic quantum gates. A detailed analysis of the evolution operator and leakage probability for the three-level DK model is provided, identifying optimal adiabaticity regimes for high fidelity. We propose an experimental implementation using trapped ions, including a rigorous derivation of the effective DK Hamiltonian in a decoherence-free subspace. Numerical simulations confirm the expected interference signatures, gate non-commutativity, and enhanced robustness of geometric gates under decoherence. This work establishes DK pulses as a versatile tool for simulating topological-like phenomena and engineering geometric quantum gates in controllable quantum systems.
High fidelity universal gates for quantum bits form an essential ingredient of quantum information processing. In particular, geometric gates have attracted attention because they have a higher intrinsic resistance to certain errors. However, their realization remains a challenge because of the need for complicated quantum control on a multi-level structure as well as meeting the adiabatic condition within a short decoherence time. Here, we demonstrate non-adiabatic quantum operations for a two-level system by applying a well-controlled geometric Landau-Zener-Stückelberg interferometry. By characterizing the gate quality, we also investigate the operation in the presence of realistic dephasing. Furthermore, the result provides an essential model suitable for understanding an interplay of geometric phase and Landau-Zener-Stückelberg process which are well explored separately.
High-fidelity quantum gates are essential for large-scale quantum computation. However, any quantum manipulation will inevitably affected by noises, systematic errors and decoherence effects, which lead to infidelity of a target quantum task. Therefore, implementing high-fidelity, robust and fast quantum gates is highly desired. Here, we propose a fast and robust scheme to construct high-fidelity holonomic quantum gates for universal quantum computation based on resonant interaction of three-level quantum systems via shortcuts to adiabaticity. In our proposal, the target Hamiltonian to induce noncyclic non-Abelian geometric phases can be inversely engineered with less evolution time and demanding experimentally, leading to high-fidelity quantum gates in a simple setup. Besides, our scheme is readily realizable in physical system currently pursued for implementation of quantum computation. Therefore, our proposal represents a promising way towards fault-tolerant geometric quantum computation.
Implementing quantum gates as non-Abelian holonomies, a class of topologically protected unitary operators, is a particularly promising paradigm for the design of intrinsically stable quantum computers [1]. In contrast to dynamic phases, the geometric phase accumulated by a quantum system propagating through a Hilbert spaceHdepends exclusively on its path. In general, geometric phases can exhibit arbitrary dimensionality. Wilczek and Zee introduced the idea of multi-dimensional, non-Abelian geometric phases - so called holonomies [2]. Anandan later dropped the requirement of adiabaticity to create holonomies, that are truly time-independent [3]. Non-adiabatic holonomies rely on a subspaceHgeoof the Hilbert-space that is spanned by states{∣Φk⟩}kthat fulfill(Φk∣H^∣Φj⟩=0, whereH^is the system's Hamiltonian. Restricting the propagation toHgeoensures parallel transport and, thus, a purely geometric phase (see Fig. 1a) [4], [5]. Quantum optics constitutes a particularly versatile platform for quantum information processing, and in particular for the construction of non-adiabatic holonomic quantum computers: In addition to integration and miniaturization provided by the platform, the bosonic nature of photons also conveniently allows for multiple excitations of the same mode, readily expandingHgeoand enabling the synthesis of holonomies from higher symmetry groupsU(N)as larger and more capable computational units [6], [7].
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.
Based on the geometrical nature of quantum phases, non-adiabatic holonomic quantum control (NHQC) has become a standard technique for enhancing robustness in constructing quantum gates. However, the conventional approach of NHQC is sensitive to control instability, as it requires the driving pulses to cover a fixed pulse area. Furthermore, even for small-angle rotations, all operations need to be completed with the same duration of time. Here we experimentally demonstrate a time-optimal and unconventional approach of NHQC (called TOUNHQC), which can optimize the operation time of any holonomic gate. Compared with the conventional approach, TOUNHQC provides an extra layer of robustness to decoherence and control errors. The experiment involves a scalable architecture of superconducting circuit, where we achieved a fidelity of 99.51% for a single qubit gate using interleaved randomized benchmarking. Moreover, a two-qubit holonomic control-phase gate has been implemented where the gate error can be reduced by as much as 18% compared with NHQC.
We construct holonomic quantum gates for qubits that are encoded in the near-degenerate vibrational E-doublet of a deformable three-body system. Using Kendall's shape theory, we derive the Wilczek--Zee connection governing adiabatic transport within the E-manifold. We show that its restricted holonomy group is SU(2), implying universal single-qubit control by closed loops in shape space. We provide explicit loops implementing a π/2 phase gate and a Hadamard-type gate. For two-qubit operations, we outline how linked holonomic cycles in arrays generate a controlled Chern--Simons phase, enabling an entangling controlled-X (CNOT) gate. We present a Ramsey/echo interferometric protocol that measures the Wilson loop trace of the Wilczek--Zee connection for a control cycle, providing a gauge-invariant signature of the non-Abelian holonomy. As a physically realizable demonstrator, we propose bond-length modulations of a Cs(6s)--Cs(6s)--Cs(nd3/2)
Rydberg trimer in optical tweezers and specify operating conditions that suppress leakage out of the E-manifold.