Shaded Tangles for the Design and Verification of Quantum Programs (Extended Abstract)

TL;DR

This paper introduces a topological approach using shaded tangles to interpret, verify, and analyze quantum programs, providing new insights and generalizations in quantum information processing.

Contribution

It presents a novel topological formalism for quantum program design and verification, enabling equivalence checking and new procedure discovery.

Findings

Isotopic tangles correspond to equivalent quantum programs

Formal verification yields new insights into entanglement and error correction

Identifies new or generalized quantum procedures

Abstract

We give a scheme for interpreting shaded tangles as quantum programs, with the property that isotopic tangles yield equivalent programs. We analyze many known quantum programs in this way -- including entanglement manipulation and error correction -- and in each case present a fully-topological formal verification, yielding in several cases substantial new insight into how the program works. We also use our methods to identify several new or generalized procedures.