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. 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 downconversion 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
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. 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 downconversion 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
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.
The experiments described in this thesis form an investigation into the path towards establishing the requirements of quantum computing in a linear optical system. Our qubits are polarisation encoded photons for which the basic operations of quantum computing, single qubit rotations, are a well understood problem. The difficulty lies in the interaction of photons. To achieve these we use measurement induced non-linearities. The first experiment in this thesis describes the thorough characterisation of a controlled-sign gate based on such non-linearities. The photons are provided as pairs generated through parametric down-conversion, and as such share correlations unlikely to carry over into large scale implementations of the future. En route to such larger circuits, a characterisation of the actions of the controlled-sign gate is conducted, when the input qubits have been generated independently from each other, revealing a large drop in process fidelity. To explore the cause of this degradation of the gate performance a thorough and highly accurate model of the gate is derived including the realistic description of faulty circuitry, photon loss and multi-photon emission by the source. By simulating the effects of the various noise sources individually, the heretofore largely ignored multi-photon emission is identified as the prime cause of the degraded gate performance, causing a drop in fidelity nearly three times as large as any other error source. I further draw the first comparison between the performance of an experimental gate to the error probabilities per gate derived as thresholds for fault-tolerant quantum computing. In the absence of a single vigourous threshold value, I compare the gate performance to the models that yielded the highest threshold to date as an upper bound and to the threshold of the Gremlin-model, which allows for the most general errors. Unsurprisingly this comparison reveals that the implemented gate is clearly insufficient, however just remedying the multi-photon emission error will allow this architecture to move to within striking distance of the boundary for fault-tolerant quantum computing. The utilised methodology can be applied to any gate in any architecture and can, combined with a suitable model of the noise sources, become an important guide for developments required to achieve fault tolerant quantum computing. The final experiment on the path towards linear optical quantum computing is the demonstration of a pair of basic versions of Shor's algorithm which display the essential entanglement for the algorithm. The results again highlight the need for extensive measurements to reveal the fundamental quality of the implemented algorithm, which is not accessible with limited indicative measurements. In the second part of the thesis, I describe two experiments on other forms of entanglement by extending the actions of a Fock-State filter, a filter that is capable of attenuating single photon states stronger than multi-photon states, to produce entangled states. Furthermore this device can be used in conjunction with standard wave-plates to extend the range of operations possible on the bi-photonic qutrit space, showing that this setup suffices to produce any desired qutrit state, thereby giving access to new measurement capabilities and in the process creating and proving the first entanglement between a qubit and a qutrit.
Optical quantum computation was limited to a few photon applications such as quantum cryptography and partial teleportation until 2001. Then the possibility of performing arbitrary logic conditional on certain detection outcomes was introduced by Knill, Laflamme and Milburn ( Nature 2001 409 46). Simple circuits consisting of single photon sources, entangled pair sources, linear optical elements and high efficiency photon counting detectors can be used to develop probabilistic two-photon logic gates. Initially such gates show a low probability of success but can approach the success rate of deterministic (non-linear) logic at the cost of added complexity. These developments have led to the emergence of a novel field of research aimed at improving the efficiency of linear logic and developing the efficient sources and detectors for its implementation. This topical issue of Journal of Optics B: Quantum and Semiclassical Optics is devoted to recent advances in this field. Key to all linear optics gates is the interference effect between separate photons that have no previous history. In this issue we include the first experiment to show such an effect (Rarity et al ), on which many later experiments are based. These interference effects can then be used to entangle separate pairs of particles into higher order entangled states (Zou et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 119–121) and also to establish entanglement between matter qubits (Kok et al ). Quantum dot single photon sources suitable for linear optics quantum logic are discussed in the paper by Unitt et al while a waveguide source of pair photons is presented by Ducci et al . The difficulties in scaling linear optics quantum computing arise from the low success probabilities of the gates. Introducing a small amount of non-linearity could allow unit efficiency gates to be designed (Munro et al ) while large non-linearities generated by the collective effects in EIT could be used to implement a wide variety of quantum logic functions (Petrosyan). The development of algorithms suitable for optical implementation is addressed by Ellinas et al . Key contributors to this issue are collaborating in the project IST:38864 RAMBOQ which has a primary goal of developing linear optics computation tools and techniques.
Single photons are the smallest excitation states of the elctromagnetic field. They can be experimentally created but there is no apparatus that performs this task with 100% efficiency. Many techniques and theorems of optical quantum information theory use single photons. In order to utilize them for information processing, it is reasonable to know if they had been successfully produced. In other words: One needs heralded single photons. How to achieve this, is the main result of this diploma thesis. The task has been to improve the efficiency of already existing single photon sources. An apparatus had to be found which postprocesses the output of such sources in order to either herald the photons or at least to improve the efficiency. This apparatus is explicitly allowed to use other optical sources, for example coherent states (laser). The situation has been formally represented by the assumption that single photon sources produce a mixture of vacuum and the single photon state. It is known that experimental set-ups also create higher photon contributions. These contributions are considered to be small in corresponding publications. For some cases they even seem to vanish at all. One can distinguish two regimes concerning the techniques which have been used in this work: linear and nonlinear optics. Linear optical tools, for example the beam splitter, do not absorb photons in the ideal case, but it is not easy to implement useful transformations by their means. Absorption and weak coupling are drawbacks which arise mainly in nonlinear optical media. This work shows that the interactions two-photon absorption and cross phase modulation can be used in schemes, which enable the heralding of single photons. Already there are some linear optical quantum gates which manipulate optical states by means of single photons. Photons do not interact with each other directly, in contrast to electrons for example. Therefore quantum gates which act on more than one mode are interesting. The effective interaction of these gates is not quitecomparable to unitary dynamics. Moreover, these gates do not function in each case. Measurements required in auxiliary modes yield different results for each single case and in order to obtain the desired effect the cases have to be selected according to the measurement results. It has been investigated, how such gates perform if they have statistical mixtures as a resource instead of perfect single-photon states. Yet, no improvement of the single-photon contribution has been accomplished by means of these apparatuses. Hereby it has not been disproved that it is possible to achieve this goal using other apparatuses and techniques of linear optics. Yet, it has been shown that an enhancement is possible but then a non-vanishing two-photon contribution is appended. One of the most basic quantum gates is the conditional sign flip. The optical 8 interaction cross phase modulation acts in quite the same way considering only single photons. This effect enables the heralding of single photons in the ideal case. Within this work it has been shown that a Mach-Zehnder interferometer, a cross phase modulating medium and a photo-detector can be employed for this purpose. One could use any source of light as input to the interferometer but a strong coherent state (laser) may be preferred for the purpose of enhancing the interaction. The absorption of two-photon states is another non-linear effect. Astonishingly this effect serves to generate a heralded single-photon state given two imperfect single-photon sources. First the photon adding tool is employed which consists of a beam splitter and a photo-detector. By means of that and the statistical mixtures of two single-photon sources one creates a mixture which contains vacuum, the single-photon state and additionally the two-photon Fock state. This mixture propagates through a Mach-Zehnder interferometer. The interferometer is adjusted such that it is transparent for incoming light. In addition to the interferometer alone a two-photon absorbing medium is placed in one of its arms. For this reason there is a chance that the two-photon contribution entering the interferometer is absorbed within this medium. We cannot exclude this unfortunate case. A detector is placed in one of the two output modes. The interferometer is adjusted such that the single photon state does not leave in the mode in which the detector is placed, but always in the other mode. The detector can only click if the two-photon state propagates through the interferometer and if it is not destroyed in the absorbing medium. If the detector then receives one photon it is obvious that another one must leave in the other mode. The whole phenomenon is very similar to the concept of null measurement. Although not a main result, it has been shown here that the so-called Hong-Ou-Mandel effect can be generalized. It has been proven that the beam splitter transforms Fock states with equal Fock number into superpositions of Fock numbers which are even in each mode. Another effect on special odd Fock states is conjectured.
Implementation of a linear optics quantum multibit half-adder that could show potential scalability is discussed. Parametric down-conversion sources are assumed that are pumped by a mode carrying orbital angular momentum l. A single photon from a pair is prepared by detection of its twin. This preparation of a single photon defines two bits to be summed and the starting carry control bit. This hyperentangled single photon enters a sequence of optical gates that acts on this photon and ancilla photons. At the adder output, each single photon detected gives the sum operation plus carry. The photons belong to a hyperentangled system with a 23 Hilbert space describing each photon. Conditions to have a scalable system for quantum computation define the requirements for construction of this photon source.
Probabilistic quantum logic operations can be performed using linear optical elements and post-selection based on the results of measurements on ancilla photons. We review the results of a number of recent experiments in this area, including the demonstration of several quantum logic gates, the use of feed-forward control, a new source of single photons, and a quantum memory device for single photons. A high-fidelity approach in which the logic gates always produce an output will also be discussed.