Developing a Binary Control Plane for a Quantum Computer

Robert Calderbank 

Charles S. Sydnor Professor of Computer Science, Duke University

 

Abstract

Quantum error-correcting codes serve to protect qubits involved in quantum computation. This requires that logical operators acting on protected qubits be translated to physical operators (circuits) acting on physical quantum states. We will present a mathematical framework for synthesizing physical circuits that implement logical Clifford operators for stabilizer codes. Circuit synthesis is enabled by representing the desired physical Clifford operator in N-dimensional complex space as a 2m x 2m binary symplectic matrix, where N = 2^m. This is an exponential reduction in size, and the symplectic matrices serve as a binary control plane for the quantum computer. We show that for an [[m, m-k]] stabilizer code, every logical Clifford operator has 2^k(k+1)/2 symplectic solutions. We describe how to find them all, and how to obtain the desired circuits. For a given operator, this assembly of all possible physical realizations enables optimization over them with respect to a suitable metric. This enables integration of hardware (Hamiltonians) with software (error-correcting codes)

Implementations are available at https://github.com/nrenga/symplectic-arxiv18a.

This is joint work with Narayanan Rengaswamy, Swanand Kadhe and Henry Pfister