Faster Simulation of Quantum Entanglement with BPGates.jl

BPGates.jl is a tool for extremely fast simulation of quantum circuits, as long as the circuit is limited to only performing entanglement purification over Bell pairs.

Quantum dynamics is famously infeasible to simulate efficiently by classical hardware. However, there are important classes of processes that can be simulated efficiently: Gaussian optics and Clifford circuits being the prototypical examples. In particular, the ease of simulating Clifford circuits was crucial for the development of quantum error correcting codes.

The purification of entangled Bell pairs can already be efficiently (polynomially) simulated by Clifford circuits. However, if we restrict ourselves to only purification circuits, not general Clifford circuits, the simulation can be even faster, both asymptotically and practically.

BPGates.jl implements this new simulation algorithm, providing for simulating bilateral quantum gates in 𝒪(1) assymptotic time (and ns wall time), instead of the typical 𝒪(n) complexity. We introduce the new algorithm, implementation, and discuss applications, including the immense effect it has had on simulating and optimizing entanglement purification circuits.