相关论文: Models of Quantum Turing machines
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
We introduce a minimal set of physically motivated postulates that the Hamiltonian H of a continuous-time quantum walk should satisfy in order to properly represent the quantum counterpart of the classical random walk on a given graph. We…
The overcompleteness of the coherent states basis leads to a multiplicity of representations of Feynman's path integral. These different representations, although equivalent quantum mechanically, lead to different semiclassical limits. Two…
As an alternative but unified and more fundamental description for quantum physics, Feynman path integrals generalize the classical action principle to a probabilistic perspective, under which the physical observables' estimation translates…
The quantum computer is supposed to process information by applying unitary transformations to the complex amplitudes defining the state of N qubits. A useful machine needing N=1000 or more, the number of continuous parameters describing…
The topic of this thesis is the development of a versatile and geometrically motivated differential calculus on non-commutative or quantum spaces, providing powerful but easy-to-use mathematical tools for applications in physics and related…
Quantum computing crucially relies on the ability to efficiently characterize the quantum states output by quantum hardware. Conventional methods which probe these states through direct measurements and classically computed correlations…
We describe a quantum state tomography scheme which is applicable to a system described in a Hilbert space of arbitrary finite dimensionality and is constructed from sequences of two measurements. The scheme consists of measuring the…
Quasi-Hermitian quantum systems, including $\mathcal{PT}$-symmetric ones, can be mapped to equivalent Hermitian systems via a similarity transformation that redefines the inner product with a positive-definite metric operator. Although an…
Studying general quantum many-body systems is one of the major challenges in modern physics because it requires an amount of computational resources that scales exponentially with the size of the system.Simulating the evolution of a state,…
We study the fidelity approach to quantum phase transitions (QPTs) and apply it to general thermal phase transitions (PTs). We analyze two particular cases: the Stoner-Hubbard itinerant electron model of magnetism and the BCS theory of…
Matrix representations of quantum operators are computationally complete but often obscure the structural topology of information flow within a quantum circuit \cite{nielsen2000}. In this paper, we introduce a generalized graph-theoretic…
The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…
The construction of large-scale quantum computers will require modular architectures that allow physical resources to be localized in easy-to-manage packages. In this work, we examine the impact of different graph structures on the…
Continuous-time quantum walks (CTQWs) provide a valuable model for quantum transport, universal quantum computation and quantum spatial search, among others. Recently, the empowering role of new degrees of freedom in the Hamiltonian…
The gate version of quantum computation exploits several quantum key resources as superposition and entanglement to reach an outstanding performance. In the way, this theory was constructed adopting certain supposed processes imitating…
We introduce complex-valued tensor network models for sequence processing motivated by correspondence to probabilistic graphical models, interpretability and resource compression. Inductive bias is introduced to our models via network…
Quantum simulations of many-body systems are among the most promising applications of quantum computers. In particular, models based on strongly-correlated fermions are central to our understanding of quantum chemistry and materials…
In its standard formulation, quantum mechanics presents a very serious inconvenience: given a quantum system, there is no possibility at all to unambiguously (causally) connect a particular feature of its final state with some specific…
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.…