Resource Estimation via Efficient Compilation of Key Quantum Primitives

Abstract

Resource estimation is a significant challenge in evaluating fault tolerant quantum computers. Existing approaches often rely on either fixed architectural assumptions or coarse analytical models that fail to capture the interaction between hardware constraints and circuit compilation. This challenge is particularly acute for neutral atom quantum computers, where architectural features such as atom movement, measurement zones, and multi-species arrays introduce a broad design space for implementing fault tolerant computation. Addressing the need for a tighter feedback loop between hardware design and practical application development, we present a compilation-driven framework for quantum resource estimation that translates arbitrary quantum circuits into logical primitive operations with known physical resource costs. This framework allows for easily configurable hardware assumptions that enable rapid comparison of different architectural design choices. We apply our approach to two early fault tolerant quantum simulation and optimization workloads, assuming the use of the surface code, revealing several architectural trends. While the production of magic states continues to be the dominant source of overhead for these benchmarks, access to movement can save time on cultivation and important transversal gates. As problem size grows, routing and qubit movement become dominant bottlenecks, highlighting the need for movement-aware compiler optimizations and frugal routing strategies. Finally, our results suggest that neutral atom architectures combining dual-species arrays with controlled qubit movement offer a promising path toward near-term advantage on fault tolerant devices.

Figures (13)

• Figure 1: Overview of the resource estimation pipeline. The compiler takes as input an arbitrary quantum circuit and an Architecture class. The Architecture stores information including a universal fault tolerant set of logical operations called primitives, a logical layout of qubits, and a set of keyword arguments to further specify assumptions. The Compiler uses a two-stage approach to produce a circuit composed of primitives amenable to resource estimation. The first stage compiles to Clifford gates and single qubit rotations approximated by discrete gates. The second stage iteratively applies replacement rules until only primitives remain. Since the Architecture also contains pre-compiled physical decompositions of primitives, the resources can be estimated according to the sum of primitives along the output circuit's critical path.
• Figure 2: Typical space of tradeoffs between formula-based hardware-agnostic resource estimates and application specific estimates optimized for real hardware. Thorough analyses dedicated to a single application or circuit, taking months or years to produce, are not easily reconfigurable under new assumptions. On the other hand, writing down logical circuits or performing scaling studies without knowledge of the underlying hardware can be rapidly re-analyzed under different assumptions, but they often lack the necessary precision need to understand the challenges of running on real hardware. Our work aims to bridge this gap in precision by making the assumptions both reasonable and reconfigurable and the inputs arbitrary quantum circuits, balancing the need for the highest quality estimates against the need for rapid answers facilitating architectural comparisons.
• Figure 3: The relationship between sets of primitives for movement and lattice surgery. The resource costs will vary between Architectures and hardware implementations.
• Figure 4: (a) T gate teleportation circuit with access to transversal S gate. (b) T gate teleportation circuit without access to a transversal S gate. The semi-classical CNOT represents performing a quantum CNOT if the classical wire is in the $|1\rangle$ state.
• Figure 5: Example stabilizer measurement circuits for $X$ (Top) and $Z$ (Bottom) in the rotated surface code. The Syndrome Extraction primitive is the measurement of all stabilizers across a full code patch.