pygridsynth: A fast numerical tool for ancilla-free Clifford+T synthesis

TL;DR

pygridsynth is an open-source Python library enabling fast, high-precision ancilla-free Clifford+$T$ synthesis for quantum circuits, with scalable algorithms for multiple qubits and mixed-synthesis capabilities.

Contribution

It introduces a novel partial-decomposition technique for multi-qubit synthesis and a mixed-synthesis workflow, improving efficiency and error reduction in quantum circuit approximation.

Findings

Achieves $O( ext{log}(1/\epsilon))$ runtime for synthesis

Reduces T-count constants for $n\ge 3$ qubits

Empirically lowers synthesis error from $\epsilon$ to $\epsilon^2/(2n)$

Abstract

We present pygridsynth, an open-source Python library for ancilla-free approximate Clifford+$T$ synthesis that runs in $O(\log(1/\epsilon))$ for precision $\epsilon$. For $n=1, 2$ qubits, the library builds upon established efficient and high-precision synthesis routines, such as nearly optimal $Z$-rotation synthesis and magnitude approximation. For $n\ge 3$ qubits, we introduce a partial-decomposition technique that generalizes the magnitude approximation, reducing constant factors in the $T$-count as $(\frac{21}{8}\cdot 4^n - \frac{9}{2}\cdot 2^n + 9)\log_2(1/\epsilon) + o(\log(1/\epsilon))$. The package also exposes a mixed-synthesis workflow that approximates target unitary channels by probabilistic mixtures of Clifford+$T$ circuits, for which we empirically find that the synthesis error is reduced from $\epsilon$ to $\epsilon^2/(2n)$. Taken together, these features make pygridsynth a Python-native platform for high-precision Clifford$+T$ synthesis and for benchmarking unitary and mixed synthesis strategies on multi-qubit instances.