Browsing by Author "Sanders, Barry C."
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Item Open Access A fully epistemic hidden variable model for emulating quantum dynamics(2007) Skotiniotis, Michael; Sanders, Barry C.Item Open Access Algorithmic Quantum Channel Simulation(2015-09-18) Wang, Dongsheng; Sanders, Barry C.Quantum simulation, which is generically the task to employ quantum computers to simulate quantum physical models, has been one of the most significant motivations of quantum computing. Quantum dynamics, unitary or nonunitary Markovian dynamics driven by local interactions, has been proved to be efficiently simulatable on quantum computers. Extending the underlying models from unitary to nonunitary evolution, and from continuous-time to discrete-time evolution is essential not only for quantum simulation of more general processes, e.g., dissipative processes with evident non-Markovian effects, but also for developing alternative quantum computing models and algorithms. In this thesis, we explore quantum simulation problems mainly from the following three themes. First, we extend quantum simulation framework of Hamiltonian-driven evolution to quantum simulation of quantum channels, combined with the scheme of algorithmic simulation that accepts a promised simulation accuracy, hence algorithmic quantum channel simulation. Our simulation scheme contains a classical preprocessing part, i.e. a classical algorithm for quantum-circuit design, and a quantum part that is the execution of a quantum circuit for the quantum channel simulator. Second, we employ simulation algorithms for arbitrary quantum channels beyond the dilation method. We explore channel decomposition in terms of convex combination of smaller channels, known as generalized extreme channels, which is known as a nontrivial open problem. To attack this problem, we develop an optimization algorithm for approximate decomposition into a convex sum of generalized extreme channels. We provide an ansatz that proves to be able to yield arbitrary generalized extreme channels and allows a precise quantum circuit description. Furthermore, our numerical simulation has demonstrated the validity of our optimization algorithm for low-dimensional quantum channels. Third, by considering quantum simulation problems beyond the rough distinction between digital and analog simulations, and beyond the quantum-state generation problem, we define uniform, strong, and weak quantum simulations from the point view of operator topology. Besides strong simulation of quantum channels, we define a general weak quantum simulation problem, which simulates observable effects instead of the effects on state generation. Also we study the channel simulation problem in the quantum query model, and provide the query complexity by employing uniform quantum simulation method.Item Open Access Algorithmic Quantum-State Generation for Simulating Quantum Field Theories on a Quantum Computer(2022-01) Bagherimehrab, Mohsen; Sanders, Barry C.; Lamoureux, Michael P.; Gour, Gilad; Eberly, Wayne M.; Somma, RolandoSimulating a quantum field theory (QFT) on a quantum computer comprises three steps: generating an initial state, simulating time evolution and measuring observables, with the initial-state generation being the most expensive step for the entire simulation. In this thesis, we introduce a general framework for simulating a QFT on a quantum computer, build a foundation for developing high-level quantum algorithms, and employ wavelet representations as a tool for constructing the first two quantum algorithms for initial-state generation in simulating a QFT. We show that our two quantum algorithms are nearly optimal and compare them for two cases: simulating theories with a broken translational invariance and preparing particle states above the ground state at variable length scales. Moreover, we construct two quantum algorithms for preparing one-dimensional Gaussian states, which have applications beyond QFT simulation. Our first algorithm uses a standard state-preparation method, which requires costly arithmetic. We employ novel techniques in our second algorithm to significantly reduce arithmetic operations. In addition to employing wavelets for state generation, we formulate subsystem entanglement entropy for free bosonic and fermionic QFTs in a wavelet basis. We verify the consistency of the wavelet-based formulation for analyzing ground state entanglement in these theories with the conventional lattice-based formulation developed by Calabrese and Cardy. By showing that lattice-based results can hold true in wavelet-based representations of QFTs, we bolster the case for wavelet-based representations as a key tool for analyzing the physics of quantum fields. The last step of a full quantum simulation is to extract simulation outputs by measuring observables on a quantum computer. We build on a reformulation of the standard amplitude estimation and quantum walks for unitary implementation of observables to develop a new approach for estimating expectation values of an observable. Furthermore, we establish a tight lower bound, with respect to a given accuracy, on the query complexity for computing expectation values. Our approach for expectation-value estimation results in an optimal quantum algorithm for measuring observables and is applicable to the last part of a full QFT simulation.Item Open Access Analysing SLOCC-equivalence of graph states and arbitrary pure quantum states(2008) D'Souza, Adam; Feder, David L.; Sanders, Barry C.Item Open Access Characterization of multipartite squeezed states by su(1,1) symmetry(2007) Shaterzadeh Yazdi, Zahra; Sanders, Barry C.Item Open Access Characterization of Surface-Plasmon Polaritons and Electromagnetic Waveguides With Positive, Negative and Near-Zero Permittivity and Permeability(2017) Sang-Nourpour, Nafiseh; Sanders, Barry C.; Kheradmand, Reza; Hobill, David Wesley; Potter, Mike; Braverman, Elena; Sipe, John E.This thesis reports advances in characterization of electromagnetic waveguides and surface-plasmon polaritons. I advance the applications of electromagnetic waveguides through investigations of electromagnetic duality in waveguides and the tunability of particular waveguide modes. Moreover, an accurate and precise procedure is devised for characterizing surface-plasmon polaritons at lossy planar and curved interfaces. The explanations of each step in this work are summarized as follows. A description of waveguides that respects the duality of electromagnetism, namely the symmetry of the equations arising through the inclusion of magnetic monopoles in addition to electrons, is presented in the thesis. To ensure manifest electromagnetic duality in waveguides, I employ generic electromagnetic susceptibilities that are dual in both electric charges and magnetic monopoles using the generalized Drude-Lorentz model. Our description accommodates exotic media, such as double-negative, near-zero and zero-index materials. I consider metamaterials and metamaterial waveguides, as well as metal waveguides, as examples of waveguides constructed of electromagnetic materials. In particular, in the slab and cylindrical waveguides, exchanging electric and magnetic material properties leads to the exchange of transverse magnetic and transverse electric modes and dispersion equations, which suggests a good test of the potential duality of waveguides. Our advances establish an intuitive microscopic-level understanding of the electromagnetic duality in waveguides and its applications. The properties of metamaterials are then employed to tailor the modes of metamaterial-dielectric waveguides operating at optical frequencies. I survey the effects of 3D isotropic metamaterial structural parameters on the refractive index of metamaterials and on the modes in slab metamaterial-dielectric waveguides. Hybrid modes refer to hybrid ordinary-surface-plasmon polariton modes in the waveguide structures. I investigate how robust metamaterials are to fluctuations in their structural parameters; specifically, the effects of Gaussian errors are examined on the metamaterials EM behaviour. Our survey enables us to determine the allowable fluctuation limits and from this to identify appropriate unit-cell structure for further applications of metamaterials in waveguides technologies. I also characterize surface-plasmon polaritons at lossy planar interfaces between one dispersive and one nondispersive linear isotropic homogeneous media, i.e., materials or metamaterials. Specifically, Maxwell's equations are solved to obtain strict bounds for the permittivity and permeability of these media such that satisfying these bounds implies surface-plasmon polaritons successfully propagate at the interface, and violation of the bounds signifies propagation is impeded, i.e., the field delocalizes from the surface into the bulk. Our characterization of surface-plasmon polaritons is valuable for checking viability of a proposed application, and, as an example, our method is employed to falsify a previous prediction that surface-plasmon propagation through a surface of a double-negative refractive index medium occurs for any permittivity and permeability; instead our results show that propagation can occur only for certain medium parameters. Finally, a theoretical study of surface-plasmon polaritons propagation along lossy curved interfaces is presented here. Specifically, conformal transformation is employed to map the curved interface between one lossy dispersive and one nondispersive linear isotropic homogeneous material to a planar interface between inhomogeneous materials. My characterization of surface-plasmon polaritons is valuable for checking the viability of a proposed application.Item Open Access Conic Linear Programming in Quantum Information(2022-01) Zafar, Fasiha Binat; Gour, Gilad; Scandolo, Carlo Maria; Sanders, Barry C.; Barclay, PaulA frequently studied problem in quantum resource theories (QRTs) is converting one resource state into another by applying free operations. If convexity arises in QRTs, convex analysis tools can be utilized in the analysis of these problems. The separating hyperplane theorem ensures the existence of at least one witness for each resource state in convex QRTs. By using this idea, necessary and sufficient conditions in terms of resource monotones are derived for generic convex static QRTs. We use this result to derive the complete family of conversion resource monotones for majorization as a subset of f-divergences. For classical conditional majorization, necessary and sufficient conditions for state conversion are derived in the form of a homogeneous convex function. We unified the pre-existing results under the umbrella of the resource-theoretic framework. The new approach helps in the significant simplification of the proofs. Furthermore, we extend the work to derive a new complete family of conversion monotones for quantum conditional majorization in terms of min-entropy using the same techniques and procedures. We expect the quantum conditional majorization will find operational applications in future work similar to its classical counterpart.Item Open Access Continuous-Variable Ramp Quantum Secret Sharing with Gaussian States and Operations(2019-04-26) Habibi Davijani, Masoud; Sanders, Barry C.; Feder, David L.; Simon, Ch M.; Safavi-Naini, Reihaneh S.Our aim is to formulate continuous-variable quantum secret-sharing as a continuous-variable ramp quantum secret-sharing protocol, provide a certification procedure for it and explain the criteria for the certification. Here we introduce a technique for certifying continuous-variable ramp quantum secret-sharing schemes in the framework of quantum interactive-proof systems. We devise pseudocodes in order to represent the sequence of steps taken to solve the certification problem. Furthermore, we derive the expression for quantum mutual information between the quantum secret extracted by any multi-player structure and the share held by the referee corresponding to the Tyc-Rowe-Sanders continuous-variable quantum secret-sharing scheme. We solve by converting the Tyc-Rowe-Sanders position representation for the state into a Wigner function from which the covariance matrix can be found, then insert the covariance matrix into the standard formula for continuous-variable quantum mutual information to obtain quantum mutual information in terms of squeezing. Our quantum mutual information result quantifies the leakage of the ramp quantum secret-sharing schemes.Item Open Access Design and application of small-scale quantum information processors(2022-07-22) Dalal, Archismita; Sanders, Barry C.; Denzinger, Jorg; Simon, Christoph; Salahub, Dennis R.; Petrosyan, DavidThe field of quantum computing is developing rapidly, with extensive research being undertaken in several topics ranging from designing novel computing architectures to developing algorithms for achieving quantum advantage. I address two research directions from this wide spectrum of topics and define my PhD research goals. My first objective is to design high-fidelity controlled-Z (CZ) gates for neutral atoms, and my second objective is to construct a quantum-assisted machine-learning model for solving non-linear regression problems. The potential of neutral-atom quantum computer stems from its unique ability to coherently control several stable qubits with the possibility of strong, long-range interactions between qubits; however the fidelity of a native two-qubit entangling gate on this platform lags behind competing platforms of superconducting systems and trapped ions. We propose gate procedures that rely on simultaneous driving of a pair of Caesium (Cs) atoms using broadband laser pulses and predict high-fidelity CZ gates. Using smooth and globally-optimized adiabatic pulse shapes, our simulations predict fidelities exceeding 0.997 in the presence of spontaneous emission from excited energy levels of Cs. By transitionless quantum driving of each Cs atom, we yield a CZ gate with fidelity 0.9985 over an operation time of 0.12 μs in the presence of spontaneous emission and major technical imperfections. The support vector regression (SVR) is a widely-used classical machine-learning model for regression tasks, including prediction of weather, stock market and real-estate pricing; yet, a currently-feasible quantum SVR model is missing from literature. We formulate quantum-assisted SVR based on quantum annealing, and compare its empirical performance against classical models for the task of detecting facial landmarks. By training the quantum-assisted model using the state-of-the-art quantum annealer, we demonstrate comparable performance of this model and two classical models for the landmark-detection task.Our results on high-fidelity CZ gates show that our gate procedures carry significant potential for achieving scalable quantum computing using atoms. On the other hand, our quantum-assisted SVR acts as a feasible quantum alternative for non-linear regression tasks.Item Open Access Distinguishability of tripartite unextendible product basis using local operations and classical communication(2008) Durocher, Michael; Sanders, Barry C.Item Open Access Dynamical Bell Nonlocality(2020-09-12) Sengupta, Kuntal; Gour, Gilad; Cunningham, Clifton L. R.; Sanders, Barry C.Quantum mechanics is a highly nonlocal theory of nature. Quantum systems exhibit correlations which cannot be described by any classical theory of locality. We develop the resource theory of dynamical Bell nonlocality, which includes bipartite states, classical channels, quantum channels and measurements. In the state scenario, all separable states are Bell local. However, there exist mixed bipartite entangled states which also admit Bell local behaviour. To address this anomaly, we introduce the notion of fully Bell locality and show that all entangled states are Bell nonlocal, in the sense that they can be used to simulate at least one nonlocal bipartite Positive Operator Valued Measure (POVM) channel. We take a step further and generalise this result to bipartite entangled quantum channels. We then generalize the CHSH inequality from bipartite classical channels to bipartite POVM channels and devise a technique to check if a given bipartite POVM channel is nonlocal or not. Finally we provide a systematic method to quantify Bell nonlocality of bipartite quantum channels by extending any monotone for Bell nonlocality of classical channels to quantum channels and also introduce the precise definition of relative entropy of Bell nonlocality. We leave some open problems in the way.Item Open Access Entaglement sharing protocol via quantum error correcting code(2012) Choi, Ran Hee; Sanders, Barry C.; Gour, GiladQuantum secret sharing concerns secure and reliable distribution of classical or quantum information by a dealer to a set of "players" such that authorized subsets of players can access full information and unauthorized subsets are denied any information whatsoever. Exploiting quantum secret sharing concepts and techniques, I introduce a new protocol of "entanglement sharing" wherein half of maximally entangled bipartite states arc encrypted into multipartitc states in such a way that unauthorized players can only establish shared separable (not entangled) states with the dealer. Only authorized subsets of players obtain entangled states, which enable quantum information tasks such as quantum teleportation. Entanglement sharing can reduce the size of shares to individual players by half depending on the choice of encoding operation, as I show with the [[4, 2, 2]] stabilizer code. In fact, the [[4, 2, 2]] stabilizer code induces an optimal and threshold entanglement sharing scheme. Furthermore, I propose a new secrecy condition of quantum ramp secret sharing based on the bipartite setting of entanglement sharing. Ramp secret sharing relieves the bandwidth requirement of a protocol by reducing the size of shares at a cost of information leakage. Although quantum ramp secret sharing has been studied, to date it has been a challenge to classify leaked information. In this thesis, I define classical and quantum information with respect to the channels through which information is transmitted, and determine whether the information leakage is classical or quantum. Finally, I establish hybrid entanglement sharing by introducing classical shares in non-perfect entanglement sharing schemes. Hybrid entanglement sharing exploits a technique of locking entanglement with classical information, and can be devised from any quantum error correcting code.Item Open Access Entaglement swapping with imperfect sources and detectors(2009) Howard, Regina B.; Sanders, Barry C.; Tittel, WolfgangItem Open Access Estimating imprecision lower bound in a neighbourhood of a known Cramér-Rao lower bound(2024-09-20) Salimi Moghadam, Mahkame; Sanders, Barry C.; de Guise, Hubert; Oblak, Daniel; Shahbazi, Mozhdeh; Friesen, TimothyThe ultimate metrology limit, classical or quantum, for estimating an unknown parameter defining a distribution of measurement outcomes, is determined by the Cramér-Rao lower bound (CRLB). However, which distribution pertains to the measurement setup can itself fluctuate for running each trial of the experiment or even within one run, meaning that we are estimating the distribution parameter in the case that we have a distribution of distributions. Our aim is to estimate the imprecision CRLB for the parameter of a distribution but in a small neighbourhood of this distribution rather than precisely at this parameter. We determine this CRLB in a neighbourhood by calculating a Taylor expansion of the Fisher information for the distribution in a neighbourhood of its defining parameter, obtain the expression for the CRLB for each distribution in this neighbourhood and then calculate the average CRLB over this neighbourhood. We illustrate our result for the case of two-parameter estimation in SU(2) interferometry for which singularities of the CRLB arise, making this averaging not just illustrative but also needed to circumvent the singularity.Item Open Access Evolutionary Algorithm for Adaptive Quantum-Channel Control(2019-01-23) Palittapongarnpim, Pantita; Sanders, Barry C.; Wiseman, Howard M.; Simon, Ch; Hobill, David W.; Denzinger, JörgThe key to successful implementations of quantum technologies is quantum control, whose aim is to steer quantum dynamics such that the desired outcome is achieved. Quantum control techniques rely on models of the quantum dynamics to generate control policies that attain the control targets. In a practical situation, the dynamic model may not match the dynamic in the implementation, and this mismatch can lead to reduced performance or even a failed control procedure. Data-driven control has been proposed as an alternative to model-based control design. In this approach, measurement outcomes from the system are used to generate a policy, which enables robust control without the need for a noise model. The potential for data-driven quantum control has been demonstrated in the problem of quantum-enhanced adaptive phase estimation. However, the performance and robustness of data-driven policies have never been compared with performance and robustness of model-based control techniques. In this thesis, we aim to determine the advantages and disadvantages of model-based and data-driven policy generation using a simulated quantum-enhanced adaptive phase estimation as an example of a quantum control task. In the process, we explore the connection between an adaptive quantum-enhanced metrological procedure to a decision-making process, which is an alternative model of the dynamic during the control task. We also devise a robust search algorithm based on an evolutionary algorithm that is ignorant of the properties of the phase noise but is still able to deliver quantum-enhanced precision. We then compare the performances of feedback control policies designed using Bayesian inference, which is a model-based technique, to policies generated using this robust evolutionary algorithm on their performance in both noisy and noiseless interferometers. We also assess the resources used in generating and implementing a control policy and use the complexities of the time and space costs as parts of selecting a practical control procedure.Item Open Access Framework for Learning and Control in the Classical and Quantum Domains(2024-06-20) Vedaie, Seyed Shakib; Sanders, Barry C.; Hobill, David W.; Oblak, Daniel; Far, Behrouz H.; Haljan, Paul C.Control and learning are essential to technological advancement, both in the classical and quantum domains, yet their interrelationship is insufficiently clear in the literature, especially between classical and quantum definitions of control and learning. In this thesis, we aim to construct a framework that formally relates learning and control, both classical and quantum, to each other, with this formalism showing how learning can aid control. We formulate new versions of quantum learning and control that essentially quantise classical learning and control, respectively. Furthermore, our framework helps identify interesting unsolved problems in the nexus of classical and quantum control and learning and helps choose tools to solve problems. Our unification of these fields relies on diagrammatically representing the state of knowledge, which elegantly summarises existing knowledge and exposes knowledge gaps. As use cases, we cast the well-studied problem of adaptive quantum-enhanced interferometric phase estimation as a supervised learning problem for devising feasible control policies and develop effective quantum control for two-qubit gate design with trapped ions. Informed by the knowledge that the plant, i.e.~ion trap, is a channel, we develop a comprehensive model of controlled open-system dynamics described by a quantum master equation and validate our model based on empirical data gathered from a control system for preparing Bell states. We then employ global optimisation to design pulse sequences for achieving a robust, rapid two-qubit gate for a chain of seven trapped $^{171}$Yb$^{+}$ ions by optimising over numerically integrated quantum master equation solutions. We further explore the nexus of classical and quantum learning through hybrid classical-quantum learning algorithms. We introduce the ``analogue-quantum kitchen sinks'' algorithm, a quantum extension of the classical "random kitchen sinks," which employs an analogue-quantum computer for mapping data features into new features in a non-linear manner. A classical algorithm can then perform machine learning tasks using the new features. We show the effectiveness of our algorithm for performing binary classification on both a synthetic and a real-world data set through computer simulation of a quantum annealer's operation.Item Open Access The Hubbard Model for Universal Quantum Computation(2019-01-24) Ji, Jiawei; Feder, David L.; Davidsen, Jörn; Høyer, Peter; Sanders, Barry C.Quantum circuits based only on matchgates are able to perform non-trivial (but not universal) quantum algorithms. Because matchgates can be mapped to non-interacting fermions, these circuits can be efficiently simulated on a classical computer. One can perform universal quantum computation by adding any non-matchgate parity-preserving gate, implying that interacting fermions are natural candidates for universal quantum computation. Most work to date has focused on Majorana fermions, which are difficult to realize and manipulate in the laboratory, despite the advantage of topologically protecting quantum information. We instead show that universal quantum computation can be implemented using interacting spinless (spin-polarized) fermions and further propose a scheme for achieving universal quantum computation with the Hubbard model, which may be realized in the laboratory based on current experimental techniques.Item Open Access Large cross phase modulation using double electromagnetically induced transparency(2009) Wang, Zeng-Bin; Sanders, Barry C.; Marzlin, Karl-PeterItem Open Access Long-distance practical quantum key distribution by entanglement swapping(Optical Society of America, 2011-02-14) Scherer, Artur; Sanders, Barry C.; Tittel, WolfgangItem Open Access Machine Learning Assisted Quantum State Tomography(2020-09-08) Kurmapu, Murali Krishna; Lvovsky, Alexander; Sanders, Barry C.; Simon, Christoph; Oblak, DanielQuantum state tomography (QST) can be posed as an optimization problem, where the goal is to find the quantum state ρ that makes the observed data more likely. Obtaining the complete description of a quantum state is crucial for many quantum informational and computing tasks, and various approaches have been proposed to solve this fundamental problem. This thesis aims at presenting two models based on feedforward neural network architecture for QST. The first model is based on a multi-layer perceptron network, while the second one is based on autoregressive neural networks. We show that the perceptron model demonstrates less overfit compared to the standard iterative maximum likelihood model, however, the number of parameters in the network increases exponentially with respect to the system size. In contrast to the perceptron model, we show that the autoregressive model scales efficiently since the number of parameters grows polynomially instead of exponentially, making it suitable for QST of many-qubit systems. For the perceptron model, we presented a reconstruction of an engineered 4-qubit W state and an arbitrary optical superposition of up to 2 photons. On the other hand, using the autoregressive model, we performed QST of a 20-qubit engineered quantum state of trapped ions observed in an experiment. To the best of our knowledge, our results are the first of its kind in performing QST of complex and highly entangled out-of-equilibrium states produced by dynamics of an Ising-type Hamiltonian, engineered via laser fields on 1D trapped ion systems