Adiabatic geometric phase gates offer enhanced robustness against fluctuations compared to con- ventional Rydberg blockade-based phase gates that rely on dynamical phase accumulation. We theoretically demonstrate two- and multi-qubit phase gates in a neutral atom architecture, relying on a double stimulated Raman adiabatic passage (double-STIRAP) pulse sequence that imprints a controllable geometric phase on the qubit systems. The system is designed in such a way that every atom is individually addressable, and moreover, no extra laser is required to be applied on the target atom while scaling up the system from two- to multi-qubit quantum gates. The gate fidelity has been numerically analyzed by changing the gate operation time, and we find that 98% to 99% fidelity can be achieved for gate time ≃ 0.6 μs. We perform a systematic error analysis, which re- veals that our proposed gates can exhibit strong resilience against fluctuations in Rabi frequencies, finite blockade strength, and atomic position variations. These results establish our approach as a physically feasible and scalable pathway toward fault-tolerant quantum computation with neutral atoms. We simulate Grover's search algorithm for two-, three-, and four-qubit systems with high success probability and thereby demonstrate the utility and scalability of our proposed gates for quantum computation.
A physical implementation of the adiabatic Grover search is theoretically investigated in a system of N identical three-level atoms trapped in a single-mode cavity. Some of the atoms are marked through the presence of an energy gap between their two ground states. The search is controlled by two partially delayed lasers which allow a deterministic adiabatic transfer from an initially entangled state to the marked states. Pulse schemes are proposed to satisfy the Grover speedup either exactly or approximately, and the success rate of the search is calculated.
Abstract Grover’s search algorithms, including various partial Grover searches (PGS), experience scaling problems when multiple solutions are sought, as the number of iterations increases with the number of solutions or marked states, making implementation more computationally expensive. Inspired by recent PGS algorithms for multi-solution searchers, this article proposes a scalable Grover quantum search algorithm, referred to as Bi-directional Multi-solution scalable Grover Search (BMGS), to efficiently search for an arbitrary number of solutions from an unstructured database. We introduced a novel multi-segment bidirectional search tactic with PGS across multiple equal segments of each state, starting from an initial state and multiple marked states in parallel, obviating the need for merge operations. We have shown in this work that for each solution our novel approach requires at most N(1−b⌊dkr⌋1) N 1 - 1 b ⌊ r dk ⌋ iterations (here, N=2r N = 2 r elements, k=log2b k = log 2 b , d is the number of equal segments on r qubits, and b is the branching factor). Our proposed BMGS algorithm is benchmarked against state-of-the-art Depth-First Grover Search (DFGS) and PGS implementations for an arbitrary number of solutions, ranging from 2 to 20 qubits, as a proof of concept. We also show that our BMGS requires fewer iterations for shallow quantum circuits and achieves an optimal O O ( sN s N ) average complexity for s solutions, when dk<r d k < r . The Qiskit Python implementation of the proposed BMGS algorithm is available on GitHub ( https://github.com/hafeezzwiz21/Multi-Solution-DFGS-BMGS ).