Scheme Pearl: Quantum Continuations

Abstract

We advance the thesis that the simulation of quantum circuits is fundamentally about the efficient management of a large (potentially exponential) number of delimited continuations. The family of Scheme languages, with its efficient implementations of first-class continuations and with its imperative constructs, provides an elegant host for modeling and simulating quantum circuits.

Figures (5)

• Figure 1: Circuit for a small instance of Simon's problem with $n=2$ and $a=3$. Given a 2-1 function $f : \mathbb{B}^n \rightarrow \mathbb{B}^n$ with the property that there exists an $a$ such that $f(x) = f(x~\textsc{xor}~a)$ for all $x$, the problem is to determine $a$.
• Figure 2: Visualizing the evaluation of the pure gates in \ref{['fig:simon']}
• Figure 3: Continuation-based evaluator for quantum gates
• Figure 4: Continuation-based evaluator for complete circuits
• Figure 5: Two small quantum circuits