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arXiv:2511.21608

Lazy Quantum Walks with Native Multiqubit Gates

Steph Foulds, Viv Kendon

quant-phSubmitted Nov 26, 2025• Announced Nov 27, 2025• 0 citations
v1 · Nov 26, 2025v2 · Jan 12, 2026v3 · Mar 16, 2026v4 · Apr 15, 2026
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Abstract

Quantum walks, the quantum analogue to the classical random walk, have been shown to model fluid dynamics. Neutral atom hardware is a promising choice of platform for implementing quantum walks due to its ability to implement native multiqubit ($\geq\!3$-qubit) gates and to dynamically re-arrange qubits. Using error modelling for multiqubit Rydberg gates via two-photon adiabatic rapid passage, we present the gate sequences and predicted final state fidelities for some toy quantum walks, including `lazy' quantum walks. These `lazy' quantum walks include a rest state and therefore provide an integral step towards quantum walks for fluid simulation.

Comments
11 pages, 10 figures

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Quantum walks, the quantum analogue to the classical random walk, have been shown to model fluid dynamics. Neutral atom hardware is a promising choice of platform for implementing quantum walks due to its ability to implement native multiqubit (≥ ⁣3\geq\!3≥3-qubit) gates and to dynamically re-arrange qubits. Using error modelling for multiqubit Rydberg gates via two-photon adiabatic rapid passage, we present the gate sequences and predicted final state fidelities for some toy quantum walks, including lazy' quantum walks. These lazy' quantum walks include a rest state and therefore provide an integral step towards quantum walks for fluid simulation.
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A clever choice and design of gate sets can reduce the depth of a quantum circuit, and can improve the quality of the solution one obtains from a quantum algorithm. This is especially important for near-term quantum computers that suffer from various sources of error that propagate with the circuit depth. Parametrized gates in particular have found use in both near-term algorithms and circuit compilation. The one- and two-qubit versions of these gates have been demonstrated on various computing architectures. The neutral atom platform has the capability to implement native NNN-qubit gates (for N≥2N \geq 2N≥2). However, one needs to first find the control functions that implement these gates on the hardware. We study the numerical optimization of neural networks towards obtaining families of controls −-− laser pulses to excite an atom to Rydberg states −-− that implement phase gates with one and two controls, the C1P\mathrm{C_1P}C1​P and C2P\mathrm{C_2P}C2​P gates respectively, on neutral atom hardware. The pulses we obtain have a duration significantly shorter than the loss time scale, set by decay from the Rydberg state. Further, they do not require single-site addressability and are smooth. Hence, we expect our gates to have immediate benefits for quantum algorithms implemented on current neutral atom hardware.
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Neutral atom quantum processors provide a viable route to scalable quantum computing, with recent demonstrations of high-fidelity and parallel gate operations and initial implementation of quantum algorithms using both physical and logical qubit encodings. In this work we present a characterization of the algorithmic performance of near term Rydberg atom quantum computers through device simulation to enable comparison against competing architectures. We consider three different quantum algorithm related tests, exploiting the ability to dynamically update qubit connectivity and multi-qubit gates. We calculate a quantum volume of VQ=29\mathbf{\mathit{V_{Q}}=2^{9}}VQ​=29 for 9 qubit devices with realistic parameters, which is the maximum achievable value for this device size and establishes a lower bound for larger systems. We also simulate highly efficient implementations of both the Bernstein-Vazirani algorithm with >0.95 success probability for 9 data qubits and 1 ancilla qubit without loss correction, and Grover's search algorithm with a loss-corrected success probability of 0.97 for an implementation of the algorithm using 6 data qubits and 3 ancilla qubits using native multi-qubit CCZ\mathbf{CCZ}CCZ gates. Our results indicate Rydberg atom processors are a highly competitive near-term platform which, bolstered by the potential for further scalability, can pave the way toward useful quantum computation.
Quantum random walks, which drew much attention over the past few decades for their distinctly nonclassical behavior, are a promising subfield within quantum computing. Theoretical framework and applications for these walks have seen many great mathematical advances, with experimental demonstrations now catching up. In this study, we examine the viability of implementing coin quantum random walks using a Quantum Adder-based Shift Operator, with quantum circuit designs specifically for superconducting qubits. We focus on the strengths and weaknesses of these walks, particularly circuit depth, gate count, connectivity requirements and scalability. We propose and analyze a novel approach to implementing boundary conditions for these walks, demonstrating the technique explicitly in one and two dimensions. Finally, we present several fidelity results from running our circuits on IBM’s quantum volume 32 ‘Toronto’ chip, showcasing the extent to which these noisy intermediate-scale quantum devices can currently handle quantum walks.
Advanced neutral atom quantum systems are being developed by the industry due to its unique hardware features that enable efficient quantum circuit execution. In fact, neutral atom quantum systems are the only platforms that simultaneously support both long-range qubit interactions and native multi-qubit gates. However, the unique characteristics of neutral atom devices limit the applicability of existing qubit mapping methods developed for other quantum devices, and the state-of-the-art mapping approach [13] for neutral atom devices suffers from long runtime and low shuttle scheduling parallelism. We introduce a novel mapping and shuttling framework for neutral atom devices. We first partition the input circuit into a sequence of subcircuits, each associated with a mapping that enables the execution of all gates in the subcircuit. To find these mappings efficiently, we adopt a flexible strategy that dynamically switches between two mapping search methods. Then, for each pair of consecutive mappings, we schedule the shuttling operations required to transition between them and prioritize timing-critical operations to improve parallelism. We performed experiments on three benchmark sets, including circuits with up to 1617 qubits and more than 100,000\mathbf{1 0 0, 0 0 0}100,000 gates. Our proposed framework resulted in high-quality routing solutions and consistently achieves higher fidelity with shorter runtime compared to existing approaches.