Lazy Quantum Walks with Native Multiqubit Gates

TL;DR

This work assesses the feasibility of implementing lazy quantum walks on near-term neutral-atom hardware by exploiting native multiqubit gates facilitated by Rydberg blockade. The authors develop gate sequences for 1q-coin and lazy 2q-coin walks on rings with 4–16 nodes, embed position and coin registers in a scalable qubit encoding, and model errors using ARP-based multiqubit gates with realistic fidelities. Key contributions include quantifying how gate rank and hardware fidelity limit the achievable walk fidelity, and demonstrating that incorporating a four-qubit gate (C3Z) can substantially improve performance for small rings while highlighting the challenges of scaling to larger walks. The study provides practical hardware guidance (favoring max-rank 4 as a sweet spot and recommending C3Z-gate readiness) for realizing QW-based fluid simulations and outlines avenues for optimization and future work, such as Gray-code encoding or qutrit coins, in extending quantum walks to larger systems.

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.

Figures (21)

• Figure 1: Binary position and coin encodings for a $2^n$-node ring, with the $2^n$ position nodes on the left encoded by the $n$ physical qubits $x_j$ in black on the right. Arrows denote available shift directions around the ring for a 2-qubit coin/'lazy' QW: the solid blue clockwise and anticlockwise directions are encoded by the solid blue physical qubit $c_1$, and the dashed purple rest state is encoded by the dashed purple physical qubit $c_2$. Omission of $c_2$ and therefore the rest state yields a 1-qubit coin/'non-lazy' QW.
• Figure 2: Gate circuit for one-qubit coin (1q-coin) quantum walk on a $2^n$-node ring Douglas_2009.
• Figure 3: Gate circuit for a two-qubit coin (2q-coin) quantum walk on a $2^n$-node ring.
• Figure 4: Pulse sequence for a CZ gate.
• Figure 5: Gate decomposition examples Barenco_1995 for C4X. Qubits $q_j$ are qubits undergoing the gate operation and qubits $a_j$ are ancilla.