Quantum simulation of partially distinguishable boson sampling

Boson Sampling is the problem of sampling from the same output probability distribution as a collection of indistinguishable single photons input into a linear interferometer. It has been shown that, subject to certain computational complexity conjectures, in general the problem is difficult to solve classically, motivating optical experiments aimed at demonstrating quantum computational "supremacy". There are a number of challenges faced by such experiments, including the generation of indistinguishable single photons. We provide a quantum circuit that simulates bosonic sampling with arbitrarily distinguishable particles. This makes clear how distinguishabililty leads to decoherence in the standard quantum circuit model, allowing insight to be gained. At the heart of the circuit is the quantum Schur transform, which follows from a representation theoretic approach to the physics of distinguishable particles in first quantisation. The techniques are quite general and have application beyond boson sampling.Comment: 25 pages, 4 figures, 2 algorithms, comments welcom

Error probability analysis in quantum tomography: a tool for evaluating experiments

We expand the scope of the statistical notion of error probability, i.e., how often large deviations are observed in an experiment, in order to make it directly applicable to quantum tomography. We verify that the error probability can decrease at most exponentially in the number of trials, derive the explicit rate that bounds this decrease, and show that a maximum likelihood estimator achieves this bound. We also show that the statistical notion of identifiability coincides with the tomographic notion of informational completeness. Our result implies that two quantum tomographic apparatuses that have the same risk function, (e.g. variance), can have different error probability, and we give an example in one qubit state tomography. Thus by combining these two approaches we can evaluate, in a reconstruction independent way, the performance of such experiments more discerningly.Comment: 14pages, 2 figures (an analysis of an example is added, and the proof of Lemma 2 is corrected

An input-output based alternative to 'ecological footprints' for tracking pollution generation in a small open economy

The usefulness, rigour and consistency of Input-Output (IO) as an accounting framework is well known. However, there is concern over the appropriateness of the standard IO attribution approach, particularly when applied to environmental issues (Bicknell et al. 1998). It is often argued that the source and responsibility for pollution should be located in human private or public consumption. An example is the "ecological footprint" approach of Wackernagel and Rees (1996). However, in the standard IO procedure, the pollution attributed to consumption, particularly private consumption, can be small or even zero. Here we attempt to retain the consumption-orientation of the "ecological footprint" method within an IO framework by implementing a neo-classical linear attribution system (NCLAS) which endogenises trade flows. We argue that this approach has practical and conceptual advantages over the "ecological footprint". The NCLAS method is then applied to the small, open economy of Jersey

Additional measures of progress for Scotland : an analysis of the issues and problems associated with aggregate/composite measures of sustainability

the purpose of this paper is to consider the broad set of issues and problems associated with adopting aggregate measures of sustainability. We do this by first considering what we mean when we talk about 'sustainable development' in a policy context and the role that we want sustainability indicators to play. Two broad types of sustainability are identified and we argue that the role of sustainability indicators depends on which type we are concerned with. This also proves to have a bearing on many of the problems and issues commonly associated with composite or aggregate indicators. In order to consider these problems and issues systematically we initially abstract from examination of any specific candidate. Of course GDP is an aggregate measure, involving valuing output at prices that, in perfect markets, reflect the valuations of individuals. indicators. However, in the latter stages of the paper we illustrate our analysis with a number of candidate measures of sustainability

Greening the national accounts for Scotland

Our main finding is that according to green accounting measures, Scotland's development over much of the past 20 years has not, on the whole, matched up to the standards of sustainability. However, the national picture seems to have improved in the recent past

Modelling word meaning using efficient tensor representations

Models of word meaning, built from a corpus of text, have demonstrated success in emulating human performance on a number of cognitive tasks. Many of these models use geometric representations of words to store semantic associations between words. Often word order information is not captured in these models. The lack of structural information used by these models has been raised as a weakness when performing cognitive tasks. This paper presents an efficient tensor based approach to modelling word meaning that builds on recent attempts to encode word order information, while providing flexible methods for extracting task specific semantic information

The impact of Scotland’s economy on the environment : a response

This is a short response to the paper by Moffatt et al (2005) which comments on some of our earlier work. Our work uses a specific Input-Output (IO) based technique, labelled a Neo-Classical Linear Attribution System (NCLAS), to measure the impact of domestic consumption on the domestic environment. We have presented this as an alternative to the currently popular Ecological Footprint approach

Generating entanglement with linear optics

Entanglement is the basic building block of linear optical quantum computation, and as such understanding how to generate it in detail is of great importance for optical architectures. We prove that Bell states cannot be generated using only 3 photons in the dual-rail encoding, and give strong numerical evidence for the optimality of the existing 4 photon schemes. In a setup with a single photon in each input mode, we find a fundamental limit on the possible entanglement between a single mode Alice and arbitrary Bob. We investigate and compare other setups aimed at characterizing entanglement in settings more general than dual-rail encoding. The results draw attention to the trade-off between the entanglement a state has and the probability of postselecting that state, which can give surprising constant bounds on entanglement even with increasing numbers of photons.Comment: 13 pages, 10 figures, 1 table, comments welcom

Randomized benchmarking in measurement-based quantum computing

Randomized benchmarking is routinely used as an efficient method for characterizing the performance of sets of elementary logic gates in small quantum devices. In the measurement-based model of quantum computation, logic gates are implemented via single-site measurements on a fixed universal resource state. Here we adapt the randomized benchmarking protocol for a single qubit to a linear cluster state computation, which provides partial, yet efficient characterization of the noise associated with the target gate set. Applying randomized benchmarking to measurement-based quantum computation exhibits an interesting interplay between the inherent randomness associated with logic gates in the measurement-based model and the random gate sequences used in benchmarking. We consider two different approaches: the first makes use of the standard single-qubit Clifford group, while the second uses recently introduced (non-Clifford) measurement-based 2-designs, which harness inherent randomness to implement gate sequences.Comment: 10 pages, 4 figures, comments welcome; v2 published versio