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Register a new userOn continuous variable quantum algorithms for oracle identification problems
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We establish a framework for oracle identification problems in the continuous variable setting, where the stated problem necessarily is the same as in the discrete variable case, and continuous variables are manifested through a continuous representation in an infinite-dimensional Hilbert space. We apply this formalism to the Deutsch-Jozsa problem and show that, due to an uncertainty relation between the continuous representation and its Fourier-transform dual representation, the corresponding Deutsch-Jozsa algorithm is probabilistic hence forbids an exponential speed-up, contrary to a previous claim in the literature.
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We study a simple-harmonic-oscillator quantum computer solving oracle decision problems. We show that such computers can perform better by using nonorthogonal Gaussian wave functions rather than orthogonal top-hat wave functions as input to the information encoding process. Using the Deutsch-Jozsa problem as an example, we demonstrate that Gaussian modulation with optimized width parameter results in a lower error rate than for the top-hat encoding. We conclude that Gaussian modulation can allow for an improved trade-off between encoding, processing and measurement of the information.
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A novel quantum switch for continuous variables teleportation is proposed. Two pairs of EPR beams with identical frequency and constant phase relation are composed on two beamsplitters to produce two pairs of conditional entangled beams, two of which are sent to two sending stations(Alices) and others to two receiving stations(bobs). The EPR entanglement initionally results from two-mode quadrature squeezed state light. Converting the squeezed component of one of EPR sources between amplitude and phase, the input quantum state at a sender will be reproduced at two receivers in turn. The switching system manipulated by squeezed state light might be developed as a practical quantum switch device for the communication and teleportation of quantum information.
We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat nonlinearities efficiently and by introducing tensor networks as a programming paradigm. The key concepts of the algorithm are demonstrated for the nonlinear Schr{o}dinger equation as a canonical example. We numerically show that the variational quantum ansatz can be exponentially more efficient than matrix product states and present experimental proof-of-principle results obtained on an IBM Q device.
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