Alternating ZX Circuit Extraction for Hardware-Adaptive Compilation

TL;DR

The paper tackles the problem that hardware-aware quantum compilation cannot be optimal when circuit extraction and hardware routing are optimized in isolation. It introduces an alternating scheme that iteratively extracts graph-like ZX diagrams and evaluates multiple extraction paths against the target hardware routing, using feedback to steer subsequent extraction choices. The approach extends standard ZX extraction by incorporating hardware constraints and routing costs, and it demonstrates fidelity improvements on small-to-mid-scale circuits using a SWAP-based neutral-atom routing reference implementation, with open-source code for fast integration. The work presents a modular building block that can be combined with diverse extraction and routing tools across different hardware platforms, laying groundwork for further improvements in hardware-adaptive compilation.

Abstract

We present a novel quantum circuit extraction scheme that tightly integrates graph-like ZX diagrams with hardware-adaptive routing. The method utilizes the degrees of freedom during the conversion from a ZX diagram to a quantum circuit (extraction). It alternates between generating multiple extraction options and evaluating them based on hardware constraints, allowing the routing algorithm to inform and guide the extraction process. This feedback loop extends existing graph-like ZX extraction and supports modular integration of different extraction algorithms, routing strategies, and target hardware, making it a versatile building block during compilation. To perform numerical evaluations, a reference instance of the scheme is implemented with SWAP-based routing for neutral atom hardware and evaluated using various benchmark collections on small-to mid-scale circuits. The reference code is available as open-source, allowing fast integration of other extraction and/or routing tools to stimulate further research and foster improvements of the proposed scheme.

Figures (9)

• Figure 1: Definition of Z(X)-spiders and the identity (Hadamard) wire.
• Figure 2: Two of the ZX-calculus rules, namely the fusion rule $(f)$ merging connected spiders and the Hadamard rule $(h)$ inverting colors.
• Figure 3: Example of a two-qubit Grover search circuit, which is translated first to a ZX diagram and then converted to a graph-like ZX-diagram using the rules from \ref{['fig:zx-rules']}.
• Figure 4: Basic circuit extraction from a graph-like ZX diagram.
• Figure 5: Full ZX circuit extraction of a graph-like diagram using a CX gate to rearrange the graph connections.

Theorems & Definitions (4)

• Example 1
• Example 2
• Example 3
• Example 4