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Quantum machine learning, though in its initial stage, has demonstrated its potential to speed up some of the costly machine learning calculations when compared to the existing classical approaches. Among the challenging subroutines,…
Run-times of quantum algorithms are often studied via an asymptotic, worst-case analysis. Whilst useful, such a comparison can often fall short: it is not uncommon for algorithms with a large worst-case run-time to end up performing well on…
Quantum bits have technological imperfections. Additionally, the capacity of a component that can be implemented feasibly is limited. Therefore, distributed quantum computation is required to scale up quantum computers. This dissertation…
We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known…
The most important computational problem on lattices is the Shortest Vector Problem (SVP). In this paper, we present new algorithms that improve the state-of-the-art for provable classical/quantum algorithms for SVP. We present the…
We study dynamical decoupling in a multi-qubit setting, where it is combined with quantum logic gates. This is illustrated in terms of computation using Heisenberg interactions only, where global decoupling pulses commute with the…
Achieving practical quantum advantage requires a classical decoding algorithm to identify and correct faults during computation. This classical decoding algorithm must deliver both accuracy and speed, but in what combination? When is a…
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…
Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. However, due to the noise and the limited scale of current quantum…
Quantum computers can solve semidefinite programs (SDPs) using resources that scale better than state-of-the-art classical methods as a function of the problem dimension. At the same time, the known quantum algorithms scale very unfavorably…
We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities, thereby demonstrating new connections between quantum codes and classical codes. Using this result --…
We propose a systematic scheme for the construction of graphs associated with binary stabilizer codes. The scheme is characterized by three main steps: first, the stabilizer code is realized as a codeword-stabilized (CWS) quantum code;…
The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
K-nearest neighbor classification algorithm is one of the most basic algorithms in machine learning, which determines the sample's category by the similarity between samples. In this paper, we propose a quantum K-nearest neighbor…
We introduce a novel strategy for cosmological Boltzmann codes leading to an increase in speed by a factor of \sim 30 for small scale Fourier modes. We (re-)investigate the tight coupling approximation and obtain analytic formulae reaching…
Recent works have shown that quantum computers can polynomially speed up certain SAT-solving algorithms even when the number of available qubits is significantly smaller than the number of variables. Here we generalise this approach. We…
The computation of the distance of two time series is time-consuming for any elastic distance function that accounts for misalignments. Among those functions, DTW is the most prominent. However, a recent extensive evaluation has shown that…
Finding the closest separable state to a given target state is a notoriously difficult task, even more difficult than deciding whether a state is entangled or separable. To tackle this task, we parametrize separable states with a neural…
We prove a new version of the quantum threshold theorem that applies to concatenation of a quantum code that corrects only one error, and we use this theorem to derive a rigorous lower bound on the quantum accuracy threshold epsilon_0. Our…