Related papers: Solvable Quantum Circuits in Tree+1 Dimensions
Understanding thermalisation in quantum many-body systems is among the most enduring problems in modern physics. A particularly interesting question concerns the role played by quantum mechanics in this process, i.e. whether thermalisation…
A continuous-time quantum walk on a dynamic graph evolves by Schr\"odinger's equation with a sequence of Hamiltonians encoding the edges of the graph. This process is universal for quantum computing, but in general, the dynamic graph that…
Continuous-time quantum walk is one of the alternative approaches to quantum computation, where a universal set of quantum gates can be achieved by scattering a quantum walker on some specially-designed structures embedded in a sparse graph…
Quantum dynamics of strongly correlated systems is a challenging problem. Although the low energy fractional excitations of one dimensional integrable models are often well-understood, exploring quantum dynamics in these systems remains…
Quantum computation is frequently mischaracterized as the simultaneous execution of exponentially many classical computations. This article offers a conceptual clarification of why this ``branchwise parallelism'' picture is misleading,…
We propose a scheme for scalable and robust quantum computing on two-dimensional arrays of qubits with fixed longitudinal coupling. This opens the possibility for bypassing the device complexity associated with tunable couplers required in…
In this thesis we analyze a very simple model of two dimensional quantum gravity based on causal dynamical triangulations (CDT). We present an exactly solvable model which indicates that it is possible to incorporate spatial topology…
Quantum computation is a continuously growing research area which is based on nature and resources of quantum mechanics, as superposition and entanglement. In its quantum circuits version, the use of convenient and appropriate gates is…
Fault tree analysis is a technique widely used in risk and reliability analysis of complex engineering systems given its deductive nature and relatively simple interpretation. In a fault tree, events are usually represented by a binary…
Universality is a cornerstone of theories of critical phenomena. It is well understood in most systems especially in the thermodynamic limit. Finite-size systems present additional challenges. Even in low dimensions, universality of the…
We introduce a geometrical framework to construct a large class of time-dependent quantum systems, in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over…
We introduce a class of quantum adiabatic evolutions that we claim may be interpreted as the equivalents of the unitary gates of the quantum gate model. We argue that these gates form a universal set and may therefore be used as building…
Controlled quantum systems such as ultracold atoms can provide powerful platforms to study non-equilibrium dynamics of closed many-body quantum systems, especially since a complete theoretical description is generally challenging. In this…
Optimal control of closed quantum systems is a well studied geometrically elegant set of computational theory and techniques that have proven pivotal in the implementation and understanding of quantum computers. The design of a circuit…
We introduce an adaptive-weighted tree tensor network, for the study of disordered and inhomogeneous quantum many-body systems. This ansatz is assembled on the basis of the random couplings of the physical system with a procedure that…
Unlike fixed designs, programmable circuit designs support an infinite number of operators. The functionality of a programmable circuit can be altered by simply changing the angle values of the rotation gates in the circuit. Here, we…
We consider a graph with a single quantum system at each node. The entire compound system evolves in discrete time steps by iterating a global evolution $U$. We require that this global evolution $U$ be unitary, in accordance with quantum…
We introduce a concept of tree-graded metric space and we use it to show quasi-isometry invariance of certain classes of relatively hyperbolic groups, to obtain a characterization of relatively hyperbolic groups in terms of their asymptotic…
We consider models of dynamical supersymmetry breaking in which the extremization of a tree-level superpotential conflicts with a quantum constraint. We show that in such models the low-energy effective theory near the origin of moduli…
The quenched unitary Bose gas is a paradigmatic example of a strongly interacting out-of-equilibrium quantum system, whose dynamics become difficult to describe theoretically due to the growth of non-Gaussian quantum correlations. We…