Related papers: Universal Procedure for Enforcing Quantum Constrai…
We describe a system of axioms that, on one hand, is sufficient for constructing the standard mathematical formalism of quantum mechanics and, on the other hand, is necessary from the phenomenological standpoint. In the proposed scheme, the…
Although the conditions for performing arbitrary unitary operations to simulate the dynamics of a closed quantum system are well understood, the same is not true of the more general class of quantum operations (also known as superoperators)…
The definition of a quantum system requires a Hilbert space, a way to define the dynamics, and an algebra of observables. The structure of the observable algebra is related to a tensor product decomposition of the Hilbert space and…
Quantum walk has been regarded as a primitive to universal quantum computation. By using the operations required to describe the single particle discrete-time quantum walk on a position space we demonstrate the realization of the universal…
We develop a hybrid qubit-qumode framework for simulating quantum electrodynamics in 2+1 dimensions. In this approach, fermionic matter fields are represented by qubits, while U(1) gauge fields are encoded in continuous-variable bosonic…
The qualitatively new concept of dynamic complexity in quantum mechanics is based on a new paradigm appearing within a nonperturbational analysis of the Schroedinger equation for a generic Hamiltonian system. The unreduced analysis…
In this paper a new formulation of quantum dynamics of totally constrained systems is developed, in which physical quantities representing time are included as observables. In this formulation the hamiltonian constraints are imposed on a…
A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal…
In the absence of a satisfactory interpretation of quantum theory, physical law lacks physical basis. This paper reviews the orthodox, or Dirac-von Neumann interpretation, and makes explicit that Hilbert space describes propositions about…
We introduce a framework for realizing universal fermionic quantum processing with globally controlled itinerant fermionic particles. Our approach is tailored to the example of neutral atoms in optical lattices, but transposes to other…
A formulation of quantum mechanics is introduced based on a $2D$-dimensional phase-space wave function $\text{\reflectbox{\text{p}}}\mkern-3mu\text{p}\left(q,p\right)$ which might be computed from the position-space wave function…
Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure. A possible avenue to derive it is to start from the reduced phase space formulation. In this article we review…
A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed…
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and…
Controlled operations allow for the entanglement of quantum registers. In particular, a controlled-$U$ gate allows an operation, $U$, to be applied to the target register and entangle the results to certain values in the control register.…
The quantum master equation is a widespread approach to describing open quantum system dynamics. In this approach, the effect of the environment on the system evolution is entirely captured by the dynamical generator, providing a compact…
This manuscript gathers and subsumes a long series of works on using QW to simulate transport phenomena. Quantum Walks (QWs) consist of single and isolated quantum systems, evolving in discrete or continuous time steps according to a…
The principle of relativity is extended to accommodate finite-mass observers with quantum properties by introducing two operational requirements: (i) equivalence of observers at the level of transition amplitudes, and (ii) the impossibility…
In the Hamiltonian approach on a single spatial plaquette, we construct a quantum (lattice) gauge theory which incorporates the classical singularities. The reduced phase space is a stratified K\"ahler space, and we make explicit the…
We present a quantum computational framework for SU(2) lattice gauge theory, leveraging continuous variables instead of discrete qubits to represent the infinite-dimensional Hilbert space of the gauge fields. We consider a ladder as well as…