Finding fault-tolerant Clifford circuits using satisfiability modulo theories solvers and decoding merged color-surface codes

Universal fault-tolerant quantum computers will require the use of efficient protocols to implement encoded operations necessary in the execution of algorithms. In this work, we show how satisfiability modulo theories (SMT) solvers can be used to automate the construction of Clifford circuits with certain fault-tolerance properties and apply our techniques to a fault-tolerant magic state preparation protocol. Part of the protocol requires converting magic states encoded in the color code to magic states encoded in the surface code. Since the teleportation step involves decoding a color code merged with a surface code, we develop a new decoding algorithm applicable to such codes.