Measurement-based quantum computation with qubit and continuous-variable systems

Quantum computers offer impressive computational speed-ups over their present-day (classical) counterparts. In the measurement-based model, quantum computation is driven by single-site measurements on a large entangled quantum state known as a cluster state. This thesis explores extensions of the measurement-based model for quantum computation in qubit and continuous-variable systems. Within the qubit setting, we consider the task of characterizing how well a small-scale measurement-based quantum device can perform logic gates. We adapt a pre-existing scheme known as randomized benchmarking into the setting of measurement-based quantum computation on a one-dimensional cluster state. A key feature of randomized benchmarking is that it uses random sequences of gates. We show how the intrinsic randomness of measurement-based quantum computation can be harnessed when implementing them. Within the continuous-variable setting, we consider optical cluster states that can be generated with current technology. We propose a compact method for generating universal cluster states based on optical-parametric-oscillator technology. We consider how finitesqueezing effects manifest in computation and show that pre-existing measurement-based protocols are suboptimal. We propose new measurement-based protocols that have better noise properties, compactness, and circuit flexibility. As an application, we introduce a measurement-based method for implementing interferometry. In this model, the finitesqueezing noise can be dealt with as a photon-loss process. Building further on this work, we investigate the resource requirements of a measurement-based BosonSampling device, proving simultaneous efficiency in time, space, and squeezing (energy) resources. These results offer new insights into how to build, use, and characterize a measurementbased quantum computer. Statement of contribution The research contributions presented in chapters 2-6 of this thesis have been published within five refereed (or currently under review) research journal articles, as described below. Note that these chapters are not presented in the order in which they were published. On all five papers, I am the primary (lead) author. Chapter 2: Randomized benchmarking in measurement-based quantum computation This chapter contains the published paper Ref. [1]. This project was suggested by Stephen Bartlett. I undertook the technical analysis under the supervision of Stephen Bartlett and with input from Peter Turner. I wrote the paper with edits from Stephen Bartlett and Peter Turner. Chapter 3: Noise analysis of single-qumode Gaussian operations using continuous-variable cluster states This chapter contains the published paper Ref. [2]. This project continued from work completed during my Honours year under the supervision of Nicolas Menicucci. During Honours, I specified how to implement gates using the single-rail continuous-variable quantum wire (CVW), macronode, and dictionary protocols, and had preliminary noise results. This constituted approximately 50% of the results in Secs. 3.3 and 3.4. The remainder of the results in these sections as well as those in Sec. 3.5 were completed during my PhD. I undertook the technical analysis under supervision of Nicolas Menicucci. The entirety of the paper was written by me during my PhD with edits from Nicolas Menicucci and Seiji Armstrong and input from Ryuji Ukai. The results in Sec. 3.4. 1 were independently derived by Ryuji Ukai and Seiji Armstrong. Chapter 4: One-way quantum computing with arbitrarily large time-frequency continuous-variable cluster states from a single optical parametric oscillator This chapter contains the accepted paper Ref. [3]. This project was based on an initial experimental design suggested by Pei Wang, Niranjan Sridhar, Moran Chen, and Olivier Pfister. Further development of the experimental design was undertaken by all authors, lead by Pei Wang under the supervision of Olivier Pfister. This part of the project is included as Secs. 4.3 and 4.4 of the paper, which were written by Pei Wang and Olivier Pfister with edits by all authors. I undertook design of the measurement protocol ii and theoretical analysis under the supervision of Nicolas Menicucci. These theoretical aspects make up the majority of the paper. I wrote the other sections of the paper with edits by Pei Wang, Olivier Pfister, Nicolas Menicucci, and input from all authors. Chapter 5: Flexible quantum circuits using scalable continuous-variable cluster states This chapter contains the published paper Ref. [4]. I suggested this project. I undertook the technical analysis with input from Nicolas Menicucci. I wrote the paper with edits from Nicolas Menicucci. Chapter 6: Measurement-based linear optics This chapter contains the preprint article Ref. [5], which has been submitted for publication. This work is based on initial calculations I performed with Natasha Gabay with input from Nicolas Menicucci. I undertook the technical analysis supervised by Nicolas Menicucci with input from Natasha Gabay and Peter Rohde. I wrote the paper with edits from all authors.