Complexity separations for optimal matchgate-Clifford synthesis
quant-ph, cs.CC
Submitted: 2026-10-05
Updated: 2026-10-05
Comments: 20 + 21 pages, 4 + 1 figures
Code: https://github.com/yuxuanzhang1995/matchgate-clifford-synthesis
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Sources
- Optimising quantum circuits is generally hard
- Provably optimal exact gate synthesis from a discrete gate set
- Representation of Quantum Circuits with Clifford and $\pi/8$ Gates
- Remarks on Matsumoto and Amano's normal form for single-qubit Clifford+T operators
- pygridsynth: A fast numerical tool for ancilla-free Clifford+T synthesis
- Optimal ancilla-free Clifford+T synthesis for general single-qubit unitaries
- CNOT-Distance is NP-complete under all-to-all connectivity
- Vanilla Exact Synthesis of CNOT Circuits is NP-hard
- (A Variant of) Clifford Circuit Synthesis is NP-Complete
- Matchgate synthesis via Clifford matchgates and $T$ gates
- Particle-preserving fermionic shadows with mode-independent sample complexity
- Clifford Volume and Free Fermion Volume: Complementary Scalable Benchmarks for Quantum Computers
- Quantum computing with Qiskit
- Fermionic Linear Optics and Matchgates
- Efficient Eigenstate Preparation in an Integrable Model with Hilbert Space Fragmentation
- Showcasing a Barren Plateau Theory Beyond the Dynamical Lie Algebra
- Solving Free Fermion Problems on a Quantum Computer
- Optimal Haar random fermionic linear optics circuits
- Theory of the Matchgate Commutant
- The commutant of fermionic Gaussian unitaries
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