Automatically Translating Quantum Programs from a Subset of Common Gates to an Adiabatic Representation

Abstract

Adiabatic computing with two degrees of freedom of 2-local Hamiltonians has been theoretically shown to be equivalent to the gate model of universal quantum computing. But today’s quantum annealers, namely D-Wave’s 2000Q platform, only provide a 2-local Ising Hamiltonian abstraction with a single degree of freedom. This raises the question what subset of gate programs can be expressed as quadratic unconstrained binary problems (QUBOs) on the D-Wave. The problem is of interest because gate-based quantum platforms are currently limited to 20 qubits while D-Wave provides 2,000 qubits. However, when transforming entire gate circuits into QUBOs, additional qubits will be required.

The objective of this work is to determine a subset of quantum gates suitable for transformation into single-degree 2-local Ising Hamiltonians under a common qubit base representation such that they comprise a compound circuit suitable for pure quantum computation, i.e., without having to switch between classical and quantum computing for different bases. To this end, this work contributes, for the first time, a fully automated method to translate quantum gate circuits comprised of a subset of common gates expressed as an IBM Qiskit program to single-degree 2-local Ising Hamiltonians, which are subsequently embedded in the D-Wave 2000Q chimera graph. These gate elements are placed in the chimera graph and augmented by constraints that enforce inter-gate logical relationships, resulting in an annealer embedding that completely characterizes the overall gate circuit. Annealer embeddings for several example quantum gate circuits are then evaluated on D-Wave 2000Q hardware.

This work was funded in part by NSF grants 1525609 and 1813004.