Abstract
Quantum computing promises exponential speedup over classical computing for specific algorithms, such as integer factoring and quantum simulation. While a classical computer follows the rules of classical physics, a quantum computer follows the rules of quantum physics. These rules include superposition and entanglement. Classical computers store the information into bits, 0 and 1, and quantum computers typically use qubits, superpositions of |0> and |1>, to store the information. However, in this work, the information is stored in quantized electromagnetic fields called qumodes. Just like the qubits are regarded as discrete variables due to their basis being composed of |0> and |1>, the qumodes are named continuous variables because their basis is formed of the eigenstates of amplitude quadratures (or phase quadratures) which are continuous. To use qumodes for quantum computing, measurement-based quantum computing is preferred, which requires a particular type of large entangled quantum states, cluster states, as calculation resources. Simply speaking, cluster states are sparsely (i.e., locally) but fully entangled networks of qubits or qumodes, represented by a two-dimensional graph.
The computing is performed by local measurements on each qumode with feedforward. To perform universal quantum computing, preparing a 2-dimensional (2-d) cluster state is one of the criteria to achieve the quantum speed up. Suppose one can prepare a 3-d cluster state. In that case, it is possible to perform topological quantum error correction encoding to decrease the error rate to a small amount. Therefore, this thesis aims to provide a method to generate 2-d and 3-d cluster states and then experimentally verify the states.
This thesis will discuss a theoretical method that generates 1-d, 2-d, and 3-d cluster states in the frequency domain by employing only one optical parametric oscillator (OPO) and one electro-optic modulator (EOM). This thesis will also discuss how the author approaches the experimental realization and verification of 1-d cluster states in the lab. In order to increase the performance and stability of the systems, several improvements have been performed: first and foremost, the observed squeezing was improved from 3.2 dB to 5.0 dB; also, a quantum heterodyne measurement method was devised to verify the cluster states by reconstructing their covariance matrix; last but not least, vast improvements of the stability and performance of the quantum optical setup were achieved by increasing signal-to-noise ratios by one order of magnitude on quantum detection and by two orders of magnitude on servo loops, and by implementing two new servo loops to phase lock all quantum fields.
