Quantum compilation using the ZX calculus
summary
ZX calculus is a graphical compiler backend that uses concrete rewrites—spider fusion, local complementation and pivot—to transform circuits into graph-like diagrams and phase gadgets, extract circuits via g-flow, and reduce non‑Clifford count (T gates). It gives an efficient amplitude evaluation (Gottesman–Knill class for Clifford phases) because each rewrite removes one spider (linear steps, each affecting at most quadratic neighbors), produces a Clifford normal form, and actually lowers T‑counts on many benchmarks; the verifier composes optimized circuit with the adjoint and simplifies, which even caught a bug in another optimizer.
AI-written summary · about
chapters (31)
- 0:00Start
- 1:00Further Reading
- 1:38Circuit identities
- 2:02Quantum circuits bad!
- 3:34Circuit identity in ZX
- 7:27Formal composition
- 8:13Building ZX diagrams
- 8:25Symmetries
- 9:13ZX-diagrams Summary
- 10:19Spider fusion
- 11:01State and pi-copy
- 11:52Hadamards and colour-changing
- 13:39Three CNOTs make SWAP
- 14:36Rules for ZX-diagrams: The ZX-calculus
- 15:09Example 1: GHZ.preparation circuit
- 15:54Example 2 Teleportation
- 17:25Use-case of ZX 41: Clifford computation
- 17:44Cliffords in ZX
- 18:41Graph-like diagrams
- 20:25Graph-theoretic rewriting
- 21:29Local complementation on graph states
- 22:15Removing vertices
- 22:54Clifford simplification
- 24:20Clifford normal form
- 26:03Simplifying general circuits
- 26:52Non-Clifford optimisation
- 28:03T count optimisation
- 28:43Circuit equality verification
- 29:51circuit optimisation
- 30:03Circuit simulation with ZX-calculus
- 30:31Conclusion
related talks
14mHybrid quantum-classical circuit simplification with the ZX-calculus
23mFrom Fermions to Qubits: A ZX-Calculus Perspective
17mEncoding High-level Quantum Programs as SZX-diagrams
20mFock, the rules (... or how to ZX-calculus for continuous variable quantum computation)
17mOptimization and Synthesis of Quantum Circuits with Global Gates
20mOptimal compilation of parametrised quantum circuits
32mFault tolerance with the ZX-calculus and fusion complexes: tools for QEC development in the...
26mQrisp: A Framework for Compilable High-Level Programming of Gate-Based Quantu...