Related papers: The Computational Complexity of Ball Permutations
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum…
Since their appearance in the 1950s, computational models capable of performing probabilistic choices have received wide attention and are nowadays pervasive in almost every areas of computer science. Their development was also inextricably…
We apply the recently developed notion of complexity for field theory to a quantum quench through a critical point in 1+1 dimensions. We begin with a toy model consisting of a quantum harmonic oscillator, and show that complexity exhibits…
This thesis aims to establish notions of symmetry for quantum states and channels as well as describe algorithms to test for these properties on quantum computers. Ideally, the work will serve as a self-contained overview of the subject. We…
A new model of quantum computation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantum computation, e. g.…
This paper studies complexity theoretic aspects of quantum refereed games, which are abstract games between two competing players that send quantum states to a referee, who performs an efficiently implementable joint measurement on the two…
We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state $|0\rangle$ computational basis. In addition, we allow the creation of a one-qubit ancilla in a…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
Classical-quantum computational complexity separations are an important motivation for the long-term development of digital quantum computers, but classical-quantum complexity equivalences are just as important in our present era of noisy…
Entanglement is widely believed to lie at the heart of the advantages offered by a quantum computer. This belief is supported by the discovery that a noiseless (pure) state quantum computer must generate a large amount of entanglement in…
We provide a computational complexity lens to understand the power of machine learning models, particularly their ability to model complex systems. Machine learning models are often trained on data drawn from sampleable or more complex…
We describe a method to axiomatize computations in deterministic Turing machines. When applied to computations in non-deterministic Turing machines, this method may produce contradictory (and therefore trivial) theories, considering…
Quantum computation offers a promising new kind of information processing, where the non-classical features of quantum mechanics can be harnessed and exploited. A number of models of quantum computation exist, including the now well-studied…
Quantum superposition says that any physical system simultaneously exists in all of its possible states, the number of which is exponential in the number of entities composing the system. The strength of presence of each possible state in…
We present a quantum Monte Carlo algorithm for the simulation of general quantum and classical many-body models within a single unifying framework. The algorithm builds on a power series expansion of the quantum partition function in its…
In this paper, the space complexity of nonuniform quantum computations is investigated. The model chosen for this are quantum branching programs, which provide a graphic description of sequential quantum algorithms. In the first part of the…
We study the computational strength of quantum particles (each of finite dimensionality) arranged on a line. First, we prove that it is possible to perform universal adiabatic quantum computation using a one-dimensional quantum system (with…
Quantum Computing offers a potentially powerful new method for performing Machine Learning. However, several Quantum Machine Learning techniques have been shown to exhibit poor generalisation as the number of qubits increases. We address…
The concept of qudit (a d-level system) cluster state is proposed by generalizing the qubit cluster state (Phys. Rev. Lett. \textbf{86}, 910 (2001)) according to the finite dimensional representations of quantum plane algebra. We…
Measurement-based quantum computation (MBQC) represents a powerful and flexible framework for quantum information processing, based on the notion of entangled quantum states as computational resources. The most prominent application is the…