Abstract
Most quantum computing architectures can be realized as two-dimensional lattices of qubits that interact with each other. We take transmon qubits and transmission line resonators as promising candidates for qubits and couplers; we use them as basic building elements of a quantum code. We then propose a simple framework to determine the optimal experimental layout to realize quantum codes. We show that this engineering optimization problem can be reduced to the solution of standard binary linear programs. While solving such programs is a NP-hard problem, we propose a way to find scalable optimal architectures that require solving the linear program for a restricted number of qubits and couplers. We apply our methods to two celebrated quantum codes, namely the surface code and the Fibonacci code.
Highlights
Since the theoretical demonstration of fault-tolerant quantum information processing, a holy grail of modern physics has been to realize fault-tolerant quantum computing architectures in the lab
Our analysis is valid for any quantum code and we show that this set of optimization problems are identical to Wosnitzka et al EPJ Quantum Technology (2016) 3:4 well-known binary linear programs
Our starting point is to consider a two-dimensional lattice of transmon qubits that interact with each others over moderate distances by coupling them to transmission line resonators
Summary
Since the theoretical demonstration of fault-tolerant quantum information processing, a holy grail of modern physics has been to realize fault-tolerant quantum computing architectures in the lab. While this still remains a very challenging task, many experimental advances have been achieved. Among the most promising quantum computing platforms, one finds so called topological quantum codes [ ]. The main idea is to encode quantum information (in the form of logical qubits) using a large number of physical qubits. Topological codes are, by definition, immune to local and static perturbations [ ]
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