Software for Quantum Computation

Abstract

Some computational tasks, such as solving the discrete logarithm problem, can be computed with exponential better scaling on quantum computers than using classical hardware. Due to these algorithms, a digital quantum computer is strongly sought after. A scalable quantum computer needs fault-tolerant protocols to correct for errors and deviations due to the environment. These protocols add additional layers of complexity because of their non-trivial logical operations which need to be decomposed into operations on many physical qubits. This thesis covers an essential part for the endeavor of building a quantum computer: classical control software for a large, fault-tolerant quantum computer. It will explain how to implement a quantum algorithm by manipulations of logical qubits, i.e. degrees of freedom that the algorithm uses for its computation. These logical qubits are encoded in many qubits, such that a single logical operation requires operations on many different qubits. A quantum compiler can perform a translation from the high-level quantum algorithm into individual hardware instructions. The surface code is one of the most promising error-correction protocols because of its 2D nearest-neighbor interactions and high threshold. The topological nature of this code allows logical operations to be understood by simple geometric manipulations. Therefore, the surface code and its variants are used as the underlying error-correcting codes throughout this thesis. Lattice surgery is a means to perform logical operations while using boundary operations between different planar surface codes. Other methods, such as braiding, have already been investigated, but their optimization seems to be more difficult than lattice surgery. This thesis presents an alternative way to perform computation using the fundamental operations of lattice surgery directly, instead of simulating a predefined set of universal gates. To this end, a representation is developed that is similar to measurement-based quantum computation in an encoded environment. The optimization of this method is still NP-hard. While the previous error-correction protocols are hardware agnostic, the surface code can be reformulated to better match a specific hardware architecture. In particular fault-tolerant computation on linear-optics quantum computers are explored. On such architectures, measurements are used to teleport information through an entangled lattice, called the Raus\-sendorf lattice. This lattice has intrinsic error-correction capabilities, and the previous lattice surgery protocols can be applied to this measurement-based setting. Finally, it is investigated how fault-tolerance can be maintained with realistic failure rates for the non-deterministic creation of the lattice.