Resource Efficient Gadgets for Compiling Adiabatic Quantum Optimization Problems

TL;DR

This paper introduces resource-efficient reduction gadgets that transform k-local Hamiltonians into (k-1)-local Hamiltonians, reducing ancilla qubits and control precision for implementing adiabatic quantum optimization problems.

Contribution

The authors develop new reduction gadgets that minimize ancilla qubits and control precision, enabling more practical implementation of adiabatic quantum algorithms.

Findings

Significant reduction in ancilla qubits for 2-local Hamiltonians

Novel gadget minimizes control precision for 3-local problems

Numerical results show decreased resource requirements compared to existing methods

Abstract

We develop a resource efficient method by which the ground-state of an arbitrary k-local, optimization Hamiltonian can be encoded as the ground-state of a (k-1)-local optimization Hamiltonian. This result is important because adiabatic quantum algorithms are often most easily formulated using many-body interactions but experimentally available interactions are generally 2-body. In this context, the efficiency of a reduction gadget is measured by the number of ancilla qubits required as well as the amount of control precision needed to implement the resulting Hamiltonian. First, we optimize methods of applying these gadgets to obtain 2-local Hamiltonians using the least possible number of ancilla qubits. Next, we show a novel reduction gadget which minimizes control precision and a heuristic which uses this gadget to compile 3-local problems with a significant reduction in control precision. Finally, we present numerics which indicate a substantial decrease in the resources required to implement randomly generated, 3-body optimization Hamiltonians when compared to other methods in the literature.