Abstract
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 A- and Y-state distillation circuits. We then provide a benchmark of our method against a small set of Clifford+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.
Highlights
Quantum computers hold the promise of finding solutions to problems that cannot be efficiently treated using the general classical model of computation [1,2,3]
Mapping a quantum algorithm to any practical large-scale quantum computer will require a sequence of compilations and optimizations
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
Summary
Quantum computers hold the promise of finding solutions to problems that cannot be efficiently treated using the general classical model of computation [1,2,3]. Motivated by the search for low-overhead error-corrected circuits to bring forward the regime of quantum practicality, we here focus on the compression of defectbased topological quantum circuits Given such a circuit, we want to reduce the resources associated with the circuit volume, i.e., the time and number of defects (and, physical qubits). We show how the primitive elements of the ZX-calculus can be mapped directly to elements of a topological circuit each requiring specified resources Using this route we can optimize the circuit with the ZX-calculus and convert back to the 3D representation to apply final arrangements and trivial transformations for a further packing of the braids. III), we demonstrate the use of the ZX-calculus as an intermediate language for circuit
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