REVIEW 4 cited by
The ZX-calculus is complete for stabilizer quantum mechanics
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original abstract
The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics, meaning any pure state, unitary operation and post-selected pure projective measurement can be expressed in the ZX-calculus. The calculus is also sound, i.e. any equality that can be derived graphically can also be derived using matrix mechanics. Here, we show that the ZX-calculus is complete for pure qubit stabilizer quantum mechanics, meaning any equality that can be derived using matrices can also be derived pictorially. The proof relies on bringing diagrams into a normal form based on graph states and local Clifford operations.
Forward citations
Cited by 4 Pith papers
-
Working with measurement-based computations on qudits
Simpler qudit flow definition yields O(n^3) flow-finding algorithm and flow-preserving operations for measurement-based quantum computing on prime-dimensional qudits.
-
A diagrammatic field theory of quantum error correction
Exact correctability of fusion-space codes is equivalent to fibrewise Knill–Laflamme conditions on syndrome-admissible footprint algebras, with a conditional Peierls threshold for growing families and explicit Ising e...
-
Quantum Information Flow under String-Diagram Rewriting
The authors define Coecke flow lines as branch-independent paths through quantum protocol diagrams that survive every semantics-preserving rewrite down to a bare wire.
-
Certified Misty-State Rewriting (A Question-and-Answer Guide)
Misty-state terms are assigned an unnormalized-amplitude semantics with scoped normalization, canonical normal forms, and branch-based measurement, so the notation's rewrites become exactly checkable.
Discussion (0). Continue with ORCID to comment.