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The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick…
We present an algorithm for efficiently approximating of qubit unitaries over gate sets derived from totally definite quaternion algebras. It achieves $\varepsilon$-approximations using circuits of length $O(\log(1/\varepsilon))$, which is…
Classical clustering algorithms typically either lack an underlying probability framework to make them predictive or focus on parameter estimation rather than defining and minimizing a notion of error. Recent work addresses these issues by…
Effective quantum computation relies upon making good use of the exponential information capacity of a quantum machine. A large barrier to designing quantum algorithms for execution on real quantum machines is that, in general, it is…
Quantum circuit simulation is crucial for the development of quantum algorithms, particularly given the high cost and noise limitations of physical quantum hardware. While full-state quantum circuit simulation is commonly employed for…
We present a detailed description of the generalized geometric cluster algorithm for the efficient simulation of continuum fluids. The connection with well-known cluster algorithms for lattice spin models is discussed, and an explicit full…
Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…
Optimizing a high-dimensional non-convex function is, in general, computationally hard and many problems of this type are hard to solve even approximately. Complexity theory characterizes the optimal approximation ratios achievable in…
Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain results that are of interest from both quantum theory and the computational…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
We present improved approximation algorithms in stochastic optimization. We prove that the multi-stage stochastic versions of covering integer programs (such as set cover and vertex cover) admit essentially the same approximation algorithms…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
We give algorithms for approximating the partition function of the ferromagnetic $q$-color Potts model on graphs of maximum degree $d$. Our primary contribution is a fully polynomial-time approximation scheme for $d$-regular graphs with an…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure…
Constraint programming (CP) is a paradigm used to model and solve constraint satisfaction and combinatorial optimization problems. In CP, problems are modeled with constraints that describe acceptable solutions and solved with backtracking…
Amplitude filtering is concerned with identifying basis-states in a superposition whose amplitudes are greater than a specified threshold; probability filtering is defined analogously for probabilities. Given the scarcity of qubits, the…
(Abridged abstract.) In this thesis we introduce new models of quantum computation to study the emergence of quantum speed-up in quantum computer algorithms. Our first contribution is a formalism of restricted quantum operations, named…
In a recent preprint by Deutsch et al. [1995] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on $n$ qubits by 2-qubit unitary operations. We address that comment by proving strong lower…
We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted…