Gate-Based Circuit Designs For Quantum Adder Inspired Quantum Random
  Walks on Superconducting Qubits
Quantum Random Walks, which have drawn much attention over the past few
decades for their distinctly non-classical behavior, is a promising subfield
within Quantum Computing. Theoretical framework and applications for these
walks have seen many great mathematical advances, with experimental
demonstrations now catching up. In this study, we examine the viability of
implementing Coin Quantum Random Walks using a Quantum Adder based Shift
Operator, with quantum circuit designs specifically for superconducting qubits.
We focus on the strengths and weaknesses of these walks, particularly circuit
depth, gate count, connectivity requirements, and scalability. We propose and
analyze a novel approach to implementing boundary conditions for these walks,
demonstrating the technique explicitly in one and two dimensions. And finally,
we present several fidelity results from running our circuits on IBM's quantum
volume 32 `Toronto' chip, showcasing the extent to which these NISQ devices can
currently handle quantum walks.
Daniel Koch Michael Samodurov Andrew Projansky Paul M. Alsing