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The decoherence effect on Grover algorithm has been studied numerically through a noise modelled by a depolarizing channel. Two types of error are introduced characterizing the qubit time evolution and gate application, so the noise is…
The problem to express a natural number N as a product of natural numbers without regard to order corresponds to a thermally isolated non-interacting Bose gas in a one-dimensional potential with logarithmic energy eigenvalues. This…
In theory, quantum computers can efficiently simulate quantum physics, factor large numbers and estimate integrals, thus solving otherwise intractable computational problems. In practice, quantum computers must operate with noisy devices…
We use trajectory calculations to successfully explain two-photon "ghost" diffraction, a phenomenon previously explained via quantum mechanical entanglement. The diffraction patterns are accumulated one photon pair at a time. The…
Shor's algorithm can find prime factors of a large number more efficiently than any known classical algorithm. Understanding the properties that gives the speedup is essential for a general and scalable construction. Here we present a…
We show that the ability to probe primordial non-Gaussianity with cluster counts is drastically improved by adding the excess variance of counts which contains information on the clustering. The conflicting dependences of changing the mass…
This note introduces a new class of integer factoring algorithms. Two versions of this method will be described, deterministic and probabilistic. These algorithms are practical, and can factor large classes of balanced integers N = pq, p <…
We develop a factor analysis for mixed continuous and binary observed variables. To this end, we utilized a recently developed multivariate probability distribution for mixed-type random variables, the Gaussian-Grassmann distribution. In…
We present a non-parametric Bayesian approach to structure learning with hidden causes. Previous Bayesian treatments of this problem define a prior over the number of hidden causes and use algorithms such as reversible jump Markov chain…
We consider Shor's quantum factoring algorithm in the setting of noisy quantum gates. Under a generic model of random noise for (controlled) rotation gates, we prove that the algorithm does not factor integers of the form $pq$ when the…
Factoring large integers using a quantum computer is an outstanding research problem that can illustrate true quantum advantage over classical computers. Exponential time order is required in order to find the prime factors of an integer by…
Shor's quantum factoring algorithm finds the prime factors of a large number exponentially faster than any other known method a task that lies at the heart of modern information security, particularly on the internet. This algorithm…
Properties of Shor's algorithm and the related period-finding algorithm could serve as benchmarks for the operation of a quantum computer. Distinctive universal behaviour is expected for the probability for success of the period-finding…
Suprema of random processes appear naturally in a plethora of disciplines, and Talagrand's majorizing theorem yields a geometric interpretation for them: for a centered Gaussian random process $(X_t)_{t \in T},$ $\mathbb{E}[\sup_{t \in…
Variational autoencoders often assume isotropic Gaussian priors and mean-field posteriors, hence do not exploit structure in scenarios where we may expect similarity or consistency across latent variables. Gaussian process variational…
We present a path integral calculation of the probability distribution associated with the time-integrated moments of the Ornstein-Uhlenbeck process that includes the Gaussian prefactor in addition to the dominant path or instanton term…
Bayesian optimisation requires fitting a Gaussian process model, which in turn requires specifying prior on the unknown black-box function -- most of the theoretical literature assumes this prior is known. However, it is common to have more…
We report the observation of $g$-factors of natural paramagnetic impurities in a pure synthetic quartz crystal at milli-Kelvin temperatures. Measurements are made by performing spectroscopy using multiple high-$Q$ Whispering Gallery Modes…
The problem of finding a nontrivial factor of a polynomial f(x) over a finite field F_q has many known efficient, but randomized, algorithms. The deterministic complexity of this problem is a famous open question even assuming the…
Various noise models have been developed in quantum computing study to describe the propagation and effect of the noise which is caused by imperfect implementation of hardware. Identifying parameters such as gate and readout error rates are…