Linear optics quantum computation (LOQC) eliminates the need for a strongly nonlinear photon‐photon interaction to create entangling gate operation, instead replacing it with the fundamental nonlinearity of quantum measurement. The LOQC gates rely on nondeterministic performance conditioned on detection or nondetection of events in ancillary modes, and are normally characterized in the multiple photon basis in which they are designed to operate. By assuming that the underlying physical structure of an LOQC gate is linear, and therefore describable entirely by it’s action on single‐photon input states, it is possible to exponentially reduce the number of parameters necessary to characterize that gate.
Linear optics quantum computation (LOQC) eliminates the need for a strongly nonlinear photon‐photon interaction to create entangling gate operation, instead replacing it with the fundamental nonlinearity of quantum measurement. The LOQC gates rely on nondeterministic performance conditioned on detection or nondetection of events in ancillary modes, and are normally characterized in the multiple photon basis in which they are designed to operate. By assuming that the underlying physical structure of an LOQC gate is linear, and therefore describable entirely by it’s action on single‐photon input states, it is possible to exponentially reduce the number of parameters necessary to characterize that gate.
One of the earliest proposals for implementing quantum computation was based on encoding each qubit in two optical modes, each containing exactly one photon. However, it is extremely difficult to unitarily couple two optical modes containing few photons. In 2001, Knill, Laflamme, and Milburn (KLM) found a way to circumvent this restriction and implement efficient quantum computation using only passive linear optics, photodetectors, and single photon sources. This efficient linear optical quantum computing (LOQC) is distinct from other linear optical schemes that are not efficiently scalable. The technological requirements for even the simplest gates in the KLM proposal initially seemed out of reach. However, Ralph, White, Munro and Milburn soon showed that, in principle, demonstrations of key gates and techniques could be achieved with current technology. The objective of the research undertaken in this project was to produce, in three years, a prototype two-qubit gate for photons using the KLM linear optics quantum computation approach, and to develop a blue-print for a multiple qubit device that might be implemented over a longer time scale. A non-deterministic two-qubit gate was demonstrated that operates with high fidelity. A number of key tasks were demonstrated using this gate, and several theoretical investigations of short, medium, and longer term issues for the LOQC approach were successfully completed.
We explain the use of quantum process calculus to describe and analyse linear optical quantum computing (LOQC). The main idea is to define two processes, one modelling a linear optical system and the other expressing a specification, and prove that they are behaviourally equivalent. We extend the theory of behavioural equivalence in the process calculus Communicating Quantum Processes (CQP) to include multiple particles (namely photons) as information carriers, described by Fock states or number states. We summarise the theory in this paper, including the crucial result that equivalence is a congruence, meaning that it is preserved by embedding in any context. In previous work, we have used quantum process calculus to model LOQC but without verifying models against specifications. In this paper, for the first time, we are able to carry out verification. We illustrate this approach by describing and verifying two models of an LOQC CNOT gate.
Photonics is a promising architecture for the realisation of quantum information processing, since the two-photon interaction, or non-linearity, necessary to build logical gates can efficiently be realised by the use of interference with ancillary photons and detection 1 Knill, E, Laflamme, R and Milburn, GJ. 2001. Nature, 409: 46–52. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]. Although single-photon sources and detectors are pivotal in realisations of such systems, clear guidelines for the required performance of realistic systems are yet to be defined. We present our detailed numerical simulation of several quantum optics circuits including sources and detectors all represented in multi-dimensional Fock-spaces, which allows us to obtain experimentally realistic performance bounds for these devices. In addition, the single-photon source based on switched parametric down-conversion is studied, which in principle could reach the required performance. Three approaches for implementing the switching hierarchy of the photons are simulated, and their anticipated performance is obtained. Our results define the bar for the optical devices needed to achieve the first level of linear-optics quantum computing outside the coincidence basis.
Typically linear optical quantum computing (LOQC) models assume that all input photons are completely indistinguishable. In practice there will inevitably be nonidealities associated with the photons and the experimental setup which will introduce a degree of distinguishability between photons. We consider a nondeterministic optical controlled-NOT gate, a fundamental LOQC gate, and examine the effect of temporal and spectral distinguishability on its operation. We also consider the effect of utilizing nonideal photon counters, which have finite bandwidth and time response.
One intriguing but difficult route to scalable quantum information processing (QIP) is linear optical quantum computing (LOQC). The systematic growth of LOQC is examined in this research. It focuses on significant experimental developments, fault-tolerant methods, and the enduring difficulties influencing the field area. In addition, it highlights the incorporation of Gottesman-Kitaev-Preskill (GKP) encoding which is an essential step towards fault-tolerant quantum computation. We analyze the importance of the Knill-Laflamme-Milburn (KLM) protocol in addressing the probabilistic limits of two-qubit gates. Strong quantum structures are made possible by this synergy, which increases resistance to phase errors and photon loss. Notwithstanding these developments, problems with state preparation, measurement accuracy, and error correction still exist, requiring multidisciplinary efforts to improve methods and investigate fresh ideas.Beyond its scope, the knowledge gathered from LOQC may have an impact on secure quantum communication networks and hybrid quantum systems. Enhancing error correction codes, creating new quantum optical technologies, and encouraging cooperation within quantum computing paradigms should be the main goals of future research. The present work intends to stimulate more developments and push QIP towards scalable and useful quantum computation by reviewing the state of LOQC today and defining strategic directions.
This thesis deals with the implementation of quantum channels using linear optics. We begin with overviews of some important concepts in both quantum information and quantum optics. First, we discuss the quantum bit and describe the evolution of the states via quantum channels. We then discuss both quantum state and process tomography, methods for how to determine which states and operations we are experimentally implementing in the lab. Second, we discuss topics in quantum optics such the generation of single photons, polarization entanglement, and the construction of an entangling gate. \n \nThe first experiment is the implementation of a quantum damping channel, which intentionally can add a specific type and amount of decohering noise to a photonic qubit. Specifically, we realized a class of quantum channels which contains both the amplitude-damping channel and the bit-flip channel, and did so with a single, static, optical setup. Many quantum channels, and some gates, can only be implemented probabilistically when using linear optics and postselection. Our main result is that the optical setup achieves the optimal success probability for each channel. Using a novel ancilla-assisted tomography, we characterize each case of the channel, and find process fideilities of 0.98pm0.01 for the amplitude-damping channel and 0.976pm0.009 for the bit-flip. \n \nThe second experiment is an implementation of a protocol for quantum computing on encrypted data. The protocol provides the means for a client with very limited quantum power to use a server's quantum computer while maintaining privacy over the data. We perform a quantum process tomography for each gate in a universal set, showing that only when the proper decryption key is used on the output states, which is hidden from the server, then the action of the quantum gate is recovered. Otherwise, the gate acts as the completely depolarizing channel.