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  • 1. Acín, Antonio
    et al.
    Pironio, Stefano
    Vértesi, Tamás
    Wittek, Peter
    University of Borås, Faculty of Librarianship, Information, Education and IT.
    Optimal randomness certification from one entangled bit2016In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 93, no 4Article in journal (Refereed)
    Abstract [en]

    By performing local projective measurements on a two-qubit entangled state one can certify in a device-independent way up to one bit of randomness. We show here that general measurements, defined by positive-operator-valued measures, can certify up to two bits of randomness, which is the optimal amount of randomness that can be certified from an entangled bit. General measurements thus provide an advantage over projective ones for device-independent randomness certification.

  • 2. Baccari, Flavio
    et al.
    Cavalcanti, Daniel
    Wittek, Peter
    University of Borås, Faculty of Librarianship, Information, Education and IT.
    Acín, Antonio
    Efficient device-independent entanglement detection for multipartite systems2016In: arXiv, article id 1612.08551Article in journal (Other academic)
    Abstract [en]

    Entanglement is one of the most studied properties of quantum mechanics for its application in quantum information protocols. Nevertheless, detecting the presence of entanglement in large multipartite sates keeps being a great challenge both from the theoretical and the experimental point of view. Most of the known methods either have computational costs that scale inefficiently with the number of parties or require more information on the state than what is attainable in every-day experiments. We introduce a new technique for entanglement detection that provides several important advantages in these respects. First, its scales efficiently with the number of parties, thus allowing for application to systems composed by up to few tens of parties. Second, it needs only the knowledge of a subset of all possible measurements on the state, therefore being apt for experimental implementation. Moreover, since it is based on the detection of nonlocality, our method is device-independent. We report several examples of its implementation for well-known multipartite states, showing that the introduced technique has a promising range of applications.

  • 3.
    Bengtsson, Anders
    University of Borås, School of Engineering.
    An Abstract Interface to Higher Spin Field Theory2005In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 46, no 4Article in journal (Refereed)
  • 4.
    Bengtsson, Anders
    University of Borås, School of Engineering.
    Mechanical Models for Higher Gauge Fields2009In: Fortschritte der Physik, ISSN 0015-8208, E-ISSN 1521-3978, Vol. 57, no 5-7, p. 499-504Article in journal (Refereed)
  • 5.
    Bengtsson, Anders
    et al.
    University of Borås, School of Engineering.
    Brink, Lars
    Kim, Sung-Soo
    Counterterms in gravity in the light-front formulation and a D = 2 conformal-like symmetry in gravity2013In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 118, no 3Article in journal (Refereed)
    Abstract [en]

    In this paper we discuss gravity in the light-front formulation (light-cone gauge) and show how possible counterterms arise. We find that Poincaré invariance is not enough to find the three-point counterterms uniquely. Higher-spin fields can intrude and mimic three-point higher derivative gravity terms. To select the correct term we have to use the remaining reparametrization invariance that exists after the gauge choice. We finally sketch how the corresponding programme for N = 8 Supergravity should work.

  • 6. Biamonte, Jacob
    et al.
    Wittek, Peter
    University of Borås, Faculty of Librarianship, Information, Education and IT.
    Pancotti, Nicola
    Rebentrost, Patrick
    Wiebe, Nathan
    Lloyd, Seth
    Quantum Machine Learning2016In: arXiv, article id 1611.09347Article in journal (Other academic)
    Abstract [en]

    Recent progress implies that a crossover between machine learning and quantum information processing benefits both fields. Traditional machine learning has dramatically improved the benchmarking and control of experimental quantum computing systems, including adaptive quantum phase estimation and designing quantum computing gates. On the other hand, quantum mechanics offers tantalizing prospects to enhance machine learning, ranging from reduced computational complexity to improved generalization performance. The most notable examples include quantum enhanced algorithms for principal component analysis, quantum support vector machines, and quantum Boltzmann machines. Progress has been rapid, fostered by demonstrations of midsized quantum optimizers which are predicted to soon outperform their classical counterparts. Further, we are witnessing the emergence of a physical theory pinpointing the fundamental and natural limitations of learning. Here we survey the cutting edge of this merger and list several open problems.

  • 7. Calderaro, Luca
    et al.
    Fetter, Alexander L.
    Massignan, Pietro
    Wittek, Peter
    University of Borås, Faculty of Librarianship, Information, Education and IT.
    Vortex dynamics in coherently coupled Bose-Einstein condensates2017In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 95, no 2, article id 023605Article in journal (Other academic)
    Abstract [en]

    In classical hydrodynamics with uniform density, vortices move with the local fluid velocity. This description is rewritten in terms of forces arising from the interaction with other vortices. Two such positive straight vortices experience a repulsive interaction and precess in a positive (anticlockwise) sense around their common centroid. A similar picture applies to vortices in a two-component two-dimensional uniform Bose-Einstein condensate (BEC) coherently coupled through rf Rabi fields. Unlike the classical case, however, the rf Rabi coupling induces an attractive interaction and two such vortices with positive signs now rotate in the negative (clockwise) sense. Pairs of counter-rotating vortices are instead found to translate with uniform velocity perpendicular to the line joining their cores. This picture is extended to a single vortex in a two-component trapped BEC. Although two uniform vortex-free components experience familiar Rabi oscillations of particle-number difference, such behavior is absent for a vortex in one component because of the nonuniform vortex phase. Instead the coherent Rabi coupling induces a periodic vorticity transfer between the two components.

  • 8. Curchod, Florian J.
    et al.
    Johansson, Markus
    Augusiak, Remigiusz
    Hoban, Matthew J.
    Wittek, Peter
    Acín, Antonio
    Unbounded randomness certification using sequences of measurements2015In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 95, no 2Article in journal (Refereed)
  • 9. Monràs, Alex
    et al.
    Sentís, Gael
    Wittek, Peter
    University of Borås, Faculty of Librarianship, Information, Education and IT.
    Inductive quantum learning: Why you are doing it almost right2016In: arXiv, article id 1605.07541Article in journal (Refereed)
    Abstract [en]

    In supervised learning, an inductive learning algorithm extracts general rules from observed training instances, then the rules are applied to test instances. We show that this splitting of training and application arises naturally, in the classical setting, from a simple independence requirement with a physical interpretation of being non-signalling. Thus, two seemingly different definitions of inductive learning happen to coincide. This follows from very specific properties of classical information, which break down in the quantum setup. We prove a quantum de Finetti theorem for quantum channels, which shows that in the quantum case, the equivalence holds in the asymptotic setting (for large number of test instances). This reveals a natural analogy between classical learning protocols and their quantum counterparts, thus allowing to naturally enquire about standard elements in computational learning theory, such as structural risk minimization, model and sample complexity.

  • 10. Oszmaniec, Michał
    et al.
    Guerini, Leonardo
    Wittek, Peter
    University of Borås, Faculty of Librarianship, Information, Education and IT.
    Acín, Antonio
    Simulating positive-operator-valued measures with projective measurements2016In: arXiv, article id 1609.06139Article in journal (Refereed)
    Abstract [en]

    Standard projective measurements represent a subset of all possible measurements in quantum physics. In fact, non-projective measurements are relevant for many applications, e.g. for estimation problems or transformations among entangled states. In this work we study what quantum measurements can be simulated by using only projective measurements and classical randomness. We first prove that every measurement on a given quantum system can be realised by a projective-simulable measurement on a system enlarged by an ancilla of the same dimension. Then, given a general measurement in dimension two or three, we show that deciding whether it is projective-simulable can be solved by means of semi-definite programming. We also establish conditions for the simulation of measurements using projective ones valid for any dimension. As an application of our formalism, we improve the range of visibilities for which two-qubit Werner states do not violate any Bell inequality for all measurements. From an implementation point of view, our results provide bounds on the amount of noise a general measurement tolerates before losing any advantage over projective ones.

  • 11. Palittapongarnpim, Pantita
    et al.
    Wittek, Peter
    University of Borås, Faculty of Librarianship, Information, Education and IT.
    Sanders, Barry C.
    Controlling adaptive quantum phase estimation with scalable reinforcement learning2016In: Proceedings of ESANN-16, 24th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, 2016, p. 327-332Conference paper (Refereed)
    Abstract [en]

    We develop a reinforcement-learning algorithm to construct a feedback policy that delivers quantum-enhanced interferometric-phase estimation up to 100 photons in a noisy environment. We ensure scalability of the calculations by distributing the workload in a cluster and by vectorizing time-critical operations. We also improve running time by introducing accept-reject criteria to terminate calculation when a successful result is reached. Furthermore, we make the learning algorithm robust to noise by fine-tuning how the objective function is evaluated. The results show the importance and relevance of well-designed classical machine learning algorithms in quantum physics problems.

  • 12. Palittapongarnpim, Pantita
    et al.
    Wittek, Peter
    University of Borås, Faculty of Librarianship, Information, Education and IT.
    Sanders, Barry C.
    Single-shot adaptive measurement for quantum-enhanced metrology2016In: Quantum Communications and Quantum Imaging XIV, 2016, Vol. 9980, article id 99800HConference paper (Refereed)
    Abstract [en]

    Quantum-enhanced metrology aims to estimate an unknown parameter such that the precision scales better than the shot-noise bound. Single-shot adaptive quantum-enhanced metrology (AQEM) is a promising approach that uses feedback to tweak the quantum process according to previous measurement outcomes. Techniques and formalism for the adaptive case are quite different from the usual non-adaptive quantum metrology approach due to the causal relationship between measurements and outcomes. We construct a formal framework for AQEM by modeling the procedure as a decision-making process, and we derive the imprecision and the Cram´er- Rao lower bound with explicit dependence on the feedback policy. We also explain the reinforcement learning approach for generating quantum control policies, which is adopted due to the optimal policy being non-trivial to devise. Applying a learning algorithm based on differential evolution enables us to attain imprecision for adaptive interferometric phase estimation, which turns out to be SQL when non-entangled particles are used in the scheme.

  • 13. Palittapongarnpim, Pantita
    et al.
    Wittek, Peter
    University of Borås, Faculty of Librarianship, Information, Education and IT.
    Zahedinejad, Ehsan
    Vedaie, Shakib
    Sanders, Barry C.
    Learning in Quantum Control: High-Dimensional Global Optimization for Noisy Quantum Dynamics2016In: arXiv, article id 1607.03428Article in journal (Refereed)
    Abstract [en]

    Quantum control is valuable for various quantum technologies such as high-fidelity gates for universal quantum computing, adaptive quantum-enhanced metrology, and ultra-cold atom manipulation. Although supervised machine learning and reinforcement learning are widely used for optimizing control parameters in classical systems, quantum control for parameter optimization is mainly pursued via gradient-based greedy algorithms. Although the quantum fitness landscape is often compatible for greedy algorithms, sometimes greedy algorithms yield poor results, especially for large-dimensional quantum systems. We employ differential evolution algorithms to circumvent the stagnation problem of non-convex optimization, and we average over the objective function to improve quantum control fidelity for noisy systems. To reduce computational cost, we introduce heuristics for early termination of runs and for adaptive selection of search subspaces. Our implementation is massively parallel and vectorized to reduce run time even further. We demonstrate our methods with two examples, namely quantum phase estimation and quantum gate design, for which we achieve superior fidelity and scalability than obtained using greedy algorithms.

  • 14. Salavrakos, Alexia
    et al.
    Augusiak, Remigiusz
    Tura, Jordi
    Wittek, Peter
    University of Borås, Faculty of Librarianship, Information, Education and IT.
    Acín, Antonio
    Pironio, Stefano
    Bell inequalities for maximally entangled states2016In: arXiv, article id 1607.04578Article in journal (Other academic)
    Abstract [en]

    Bell inequalities have traditionally been used to demonstrate that quantum theory is nonlocal, in the sense that there exist correlations generated from composite quantum states that cannot be explained by means of local hidden variables. With the advent of device-independent quantum information processing, Bell inequalities have gained an additional role as certificates of relevant quantum properties. In this work we consider the problem of designing Bell inequalities that are tailored to detect the presence of maximally entangled states. We introduce a class of Bell inequalities valid for an arbitrary number of measurements and results, derive analytically their maximal violation and prove that it is attained by maximally entangled states. Our inequalities can therefore find an application in device-independent protocols requiring maximally entangled states.

  • 15.
    Wittek, Peter
    et al.
    University of Borås, Faculty of Librarianship, Information, Education and IT.
    Calderaro, Luca
    Extended computational kernels in a massively parallel implementation of the Trotter–Suzuki approximation2015In: Computer Physics Communications, ISSN 0010-4655, E-ISSN 1879-2944, Vol. 197, p. 339-340Article in journal (Other academic)
    Abstract [en]

    We extended a parallel and distributed implementation of the Trotter-Suzuki algorithm for simulating quantum systems to study a wider range of physical problems and to make the library easier to use. The new release allows periodic boundary conditions, many-body simulations of non-interacting particles, arbitrary stationary potential functions, and imaginary time evolution to approximate the ground state energy. The new release is more resilient to the computational environment: a wider range of compiler chains and more platforms are supported. To ease development, we provide a more extensive command-line interface, an application programming interface, and wrappers from high-level languages.

  • 16.
    Wittek, Peter
    et al.
    University of Borås, Faculty of Librarianship, Information, Education and IT.
    Gogolin, Christian
    Quantum Enhanced Inference in Markov Logic Networks2016In: arXiv, article id 1611.08104Article in journal (Other academic)
    Abstract [en]

    Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is essentially a first-order logic template to generate Markov networks. Inference in MLNs is probabilistic and it is often performed by approximate methods such as Markov chain Monte Carlo (MCMC) Gibbs sampling. An MLN has many regular, symmetric structures that can be exploited at both first-order level and in the generated Markov network. We analyze the graph structures that are produced by various lifting methods and investigate the extent to which quantum protocols can be used to speed up Gibbs sampling with state preparation and measurement schemes. We review different such approaches, discuss their advantages, theoretical limitations, and their appeal to implementations. We find that a straightforward application of a recent result yields exponential speedup compared to classical heuristics in approximate probabilistic inference, thereby demonstrating another example where advanced quantum resources can potentially prove useful in machine learning.

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