Hardware-Efficient Rydberg Atomic Quantum Solvers for NP Problems

TL;DR

We introduce a gate-based Grover solver tailored to Rydberg-atom arrays that targets NP problems with a provable quadratic speedup. The solver builds a unified NP-oracle from parallelizable checking units and efficient merging blocks that exploit the tensor-grid connectivity enabled by ×AOD atom transport, achieving linear qubit scaling and polylogarithmic-depth merging. The overall depth scales as $O\left(\mathrm{polylog}(n)\,2^{n/2}\right)$ with linear qubit overhead, providing a concrete pathway toward quantum advantage on NISQ-era devices. The framework supports multiple NP-complete problems (e.g., SAT, MIS, MCP, SCP, ECP), is compatible with common QEC codes, and includes practical demonstrations and a comparative analysis against superconducting platforms, highlighting a hardware-efficient route to gate-based NP problem solving on Rydberg architectures.

Abstract

Developing hardware-efficient implementations of quantum algorithms is crucial in the NISQ era to achieve practical quantum advantage. Here, we construct a generic quantum solver for NP problems based on Grover's search algorithm, specifically tailored for Rydberg-atom quantum computing platforms. We design the quantum oracles in the search algorithm using parallelizable single-qubit and multi-qubit entangling gates in the Rydberg atom system, yielding a unified framework for solving a broad class of NP problems with provable quadratic quantum speedup. We analyze the experimental resource requirements considering the unique qubit connectivity of the dynamically reconfigurable qubits in the optical tweezer array. The required qubit number scales linearly with the problem size, representing a significant improvement over existing Rydberg-based quantum annealing approaches that incur quadratic overhead. These results provide a concrete roadmap for future experimental efforts towards demonstrating quantum advantage in NP problem solving using Rydberg atomic systems. Our construction indicates that atomic qubits offer favorable circuit depth scaling compared to quantum processors with fixed local connectivity.

Figures (13)

• Figure 1: Schematic of the NP-oracle circuit (Eq. \ref{['eq:oracle']}). Data qubits $|z\rangle$ encode the problem variables and the rest serve as ancillae. The circuit comprises checking units ($C_\mu, D_\nu$) and merging blocks ($M^{[1]}, M^{[2]}$), as detailed in the main text. For simplicity, the parameter $b$ ( main text) is set to 1.
• Figure 2: Parallelization of checking units ($t=3$) by properly arranging atoms to satisfy the qubit mapping (Eq. \ref{['eq:Mapping']}). (a), the checking unit $C_\mu$. (b), the qubit mapping. Collect the qubit at a certain position in each checking unit together and they form a tensor grid. Two-qubit gates between tensor grids $\mathcal{G}_\tau =\bigcup_{\mu} P(q_{\mu \tau})$ are parallelizable, indicating the parallelism of the checking units.
• Figure 3: Implementation of the merging block $M^{[1]}$. (a), the circuit for $M^{[1]}$ (QBT), which supports recursive extension. (b), transpilation of the circuit onto the Rydberg-atom array. The blue region contains the output of the checking circuit to be merged. The information is merged from up to down (see main text). Atoms in different regions represent qubits at different levels of QBT. One rearrangement is used in the purple frame to make the total region more compact.
• Figure 4: Schematic of one Grover iteration in the Rydberg quantum solver. The Grover oracle ($U_\omega$) is constructed using checking and merging circuits ($M^{[1]}$ as an example) in step 1--3. The Grover diffusion operator ($U_s$) has a straightforward implementation using $M^{[1]}$ (Supplementary Materials). The curved arrow associated with $M^{[1]}$ indicates the restoration of ancillae, which is necessary to induce phase kickback.
• Figure S1: Using $\times$AOD to move atoms and perform parallel entangling gates. The blue group of atoms can be moved towards the red group in parallel. The Rydberg lasers (orange) can also be shined in parallel. For CCZs, one more tensor grid of atoms needs to be moved into proximity.