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arXiv:1209.1441

Programming a Topological Quantum Computer

Simon J. Devitt, Kae Nemoto

Published Sep 7, 2012• 0 citations
arXivHTMLPDF

Abstract

Topological quantum computing has recently proven itself to be a powerful computational model when constructing viable architectures for large scale computation. The topological model is constructed from the foundation of a error correction code, required to correct for inevitable hardware faults that will exist for a large scale quantum device. It is also a measurement based model of quantum computation, meaning that the quantum hardware is responsible only for the construction of a large, computationally universal quantum state. This quantum state is then strategically consumed, allowing for the realisation of a fully error corrected quantum algorithm. The number of physical qubits needed by the quantum hardware and the amount of time required to implement an algorithm is dictated by the manner in which this universal quantum state is consumed. In this paper we examine the problem of algorithmic optimisation in the topological lattice and introduce the required elements that will be needed when designing a classical software package to compile and implement a large scale algorithm on a topological quantum computer.

DOI
10.48550/arxiv.1209.1441

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Topological quantum computing has recently proven itself to be a powerful computational model when constructing viable architectures for large scale computation. The topological model is constructed from the foundation of a error correction code, required to correct for inevitable hardware faults that will exist for a large scale quantum device. It is also a measurement based model of quantum computation, meaning that the quantum hardware is responsible only for the construction of a large, computationally universal quantum state. This quantum state is then strategically consumed, allowing for the realisation of a fully error corrected quantum algorithm. The number of physical qubits needed by the quantum hardware and the amount of time required to implement an algorithm is dictated by the manner in which this universal quantum state is consumed. In this paper we examine the problem of algorithmic optimisation in the topological lattice and introduce the required elements that will be needed when designing a classical software package to compile and implement a large scale algorithm on a topological quantum computer.
Topological quantum computing has recently proven itself to be a powerful computational model when constructing viable architectures for large scale computation. The topological model is constructed from the foundation of a error correction code, required to correct for inevitable hardware faults that will exist for a large scale quantum device. It is also a measurement based model of quantum computation, meaning that the quantum hardware is responsible only for the construction of a large, computationally universal quantum state. This quantum state is then strategically consumed, allowing for the realisation of a fully error corrected quantum algorithm. The number of physical qubits needed by the quantum hardware and the amount of time required to implement an algorithm is dictated by the manner in which this universal quantum state is consumed. In this paper we examine the problem of algorithmic optimisation in the topological lattice and introduce the required elements that will be needed when designing a classical software package to compile and implement a large scale algorithm on a topological quantum computer.
Topological quantum computing has recently proven itself to be a very powerful model when considering large-scale, fully error corrected quantum architectures. In addition to its robust nature under hardware errors, it is a software driven method of error corrected computation, with the hardware responsible for only creating a generic quantum resource (the topological lattice). Computation in this scheme is achieved by the geometric manipulation of holes (defects) within the lattice. Interactions between logical qubits (quantum gate operations) are implemented by using particular arrangements of the defects, such as braids and junctions. We demonstrate that junction-based topological quantum gates allow highly regular and structured implementation of large CNOT (controlled-not) gate networks, which ultimately form the basis of the error corrected primitives that must be used for an error corrected algorithm. We present a number of heuristics to optimise the area of the resulting structures and therefore the number of the required hardware resources.
Topological quantum computation is a promising technique to achieve large-scale, error-corrected computation. Quantum hardware is used to create a large, 3-dimensional lattice of entangled qubits while performing computation requires strategic measurement in accordance with a topological circuit specification. The specification is a geometric structure that defines encoded information and fault-tolerant operations. The compilation of a topological circuit is one important aspect of programming a quantum computer, another is the mapping of the topological circuit into the operations performed by the hardware. Each qubit has to be controlled, and measurement results are needed to propagate encoded quantum information from input to output. In this work, we introduce an algorithm for mapping an topological circuit to the operations needed by the physical hardware. We determine the control commands for each qubit in the computer and the relevant measurements that are needed to track information as it moves through the circuit.
Abstract—Topological quantum computing has recently proven itself to be a very powerful model when considering large-scale, fully error corrected quantum architectures. In addition to its robust nature under hardware errors, it is a software driven method of error corrected computation, with the hardware responsible for only creating a generic quantum resource (the topological lattice). Computation in this scheme is achieved by the geometric manipulation of holes (defects) within the lattice. Interactions between logical qubits (quantum gate operations) are implemented by using particular arrangements of the defects, such as braids and junctions. We demonstrate that junction-based topological quantum gates allow highly regular and structured implementation of large CNOT (controlled-not) gate networks, which ultimately form the basis of the error corrected primitives that must be used for an error corrected algorithm. We present a number of heuristics to optimise the area of the resulting structures and therefore the number of the required hardware resources. I.
Topological quantum computation is a promising technique to achieve large-scale, error-corrected computation. Quantum hardware is used to create a large, 3-dimensional lattice of entangled qubits while performing computation requires strategic measurement in accordance with a topological circuit specification. The specification is a geometric structure that defines encoded information and fault-tolerant operations. The compilation of a topological circuit is one important aspect of programming a quantum computer, another is the mapping of the topological circuit into the operations performed by the hardware. Each qubit has to be controlled, and measurement results are needed to propagate encoded quantum information from input to output. In this work, we introduce an algorithm for mapping an topological circuit to the operations needed by the physical hardware. We determine the control commands for each qubit in the computer and the relevant measurements that are needed to track information as it moves through the circuit.
The accelerated development of quantum technology has reached a pivotal point. Early in 2014, several results were published demonstrating that several experimental technologies are now accurate enough to satisfy the requirements of fault-tolerant, error corrected quantum computation. While there are many technological and experimental issues that still need to be solved, the ability of experimental systems to now have error rates low enough to satisfy the fault-tolerant threshold for several error correction models is a tremendous milestone. Consequently, it is now a good time for the computer science and classical engineering community to examine the {\em classical} problems associated with compiling quantum algorithms and implementing them on future quantum hardware. In this paper, we will review the basic operational rules of a topological quantum computing architecture and outline one of the most important classical problems that need to be solved; the decoding of error correction data for a large-scale quantum computer. We will endeavour to present these problems independently from the underlying physics as much of this work can be effectively solved by non-experts in quantum information or quantum mechanics.