Effective Compression of Quantum Braided Circuits Aided by ZX-Calculus

Agustín Borgna, Simon Perdrix, Benoît Valiron

Thomas Kelly, Aleks Kissinger

Tobias Fischbach, P. Talbot, Pascal Bouvry

Alexandru Paler

We present a systematic method for translating fault-tolerant quantum circuits between their braiding and lattice surgery (LS) representations within the surface code. Our approach employs the ZX calculus to establish an equivalence between these two paradigms, enabling verified, bidirectional conversion of arbitrary surface-code-level circuits. We show that both braiding and LS operations can be uniformly expressed as compositions of multibody measurements and demonstrate that the Raussendorf compression rule encompasses all known braid and bridge optimizations. We also introduce a novel CNOT circuit with LS. Our framework provides a foundation for the automated verification, compilation, and benchmarking of large-scale surface code computations, advancing toward a unified formal language for topological quantum computation.

Lukas Burgholzer, Robert Wille

Michael Hanks, Marta P. Estarellas, William J. Munro +1 more

Mapping a quantum algorithm to any practical large-scale quantum computer will require a sequence of compilations and optimizations.At the level of fault-tolerant encoding, one likely requirement of this process is the translation into a topological circuit, for which braided circuits represent one candidate model.Given the large overhead associated with encoded circuits, it is paramount to reduce their size in terms of computation time and qubit number through circuit compression.While these optimizations have typically been performed in the language of three-dimensional diagrams, such a representation does not allow an efficient, general, and scalable approach to reduction or verification.We propose the use of the ZX-calculus as an intermediate language for braided circuit compression, demonstrating advantage by comparing results using this approach with those previously obtained for the compression of jAi and jYi state distillation circuits.We then provide a benchmark of our method against a small set of Clifford þ T circuits, yielding compression percentages of ∼77%.Our results suggest that the overheads of braided, defect-based circuits are comparable to those of their lattice-surgery counterparts, restoring the potential of this model for surface-code quantum computation.