Related papers: Equivalent quantum systems
Some precisions are given about the definition of the Hamiltonian operator H and its transformation properties, for a linear wave equation in a general spacetime. In the presence of time-dependent unitary gauge transformations, H as an…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
Hamiltonian operators are gauge dependent. For overcome this difficulty we reexamined the effect of a gauge transformation on Schr\"odinger and Dirac equations. We show that the gauge invariance of the operator…
Driving a quantum system periodically in time can profoundly alter its long-time dynamics and trigger topological order. Such schemes are particularly promising for generating non-trivial energy bands and gauge structures in quantum-matter…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
When can a quantum system of finite dimension be used to simulate another quantum system of finite dimension? What restricts the capacity of one system to simulate another? In this paper we complete the program of studying what simulations…
We investigate the power of quantum systems for the simulation of Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range…
Understanding which physical processes are symmetric with respect to time inversion is a ubiquitous problem in physics. In quantum physics, effective gauge fields allow emulation of matter under strong magnetic fields, realizing the…
Heisenberg spin chains can act as quantum wires transferring quantum states either perfectly or with high fidelity. Gaussian packets of excitations passing through dual rails can encode the two states of a logical qubit, depending on which…
An effective Hamiltonian describing interaction between generic "fast" and a "slow" systems is obtained in the strong interaction limit. The result is applied for studying the effect of quantum phase transition as a bifurcation of the…
We use the dynamical algebra of a quantum system and its dynamical invariants to inverse engineer feasible Hamiltonians for implementing shortcuts to adiabaticity. These are speeded up processes that end up with the same populations than…
The optimal control of unitary transformations is a fundamental problem in quantum control theory and quantum information processing. The feasibility of performing such optimizations is determined by the computational and control resources…
We consider a general symplectic transformation (also known as linear canonical transformation) of quantum-mechanical observables in a quantized version of a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q}…
A quantum computing system is typically represented by a set of non-interacting (local) two-state systems - qubits. Many physical systems can naturally have more accessible states, both local and non-local. We show that the resulting…
Quantum computation and quantum control operate by building unitary transformations out of sequences of elementary quantum logic operations or applications of control fields. This paper puts upper bounds on the minimum time required to…
We investigate consequences of allowing the Hilbert space of a quantum system to have a time-dependent metric. For a given possibly nonstationary quantum system, we show that the requirement of having a unitary Schreodinger time-evolution…
Space-time in quantum mechanics is about bridging Hilbert and configuration space. Thereby, an entirely new perspective is obtained by replacing the Newtonian space-time theater with the image of a presumably high-dimensional Hilbert space,…
The information of quantum pathways can be extracted in the framework of the Hamiltonian-encoding and Observable-decoding method. For closed quantum systems, only off-diagonal elements of the Hamiltonian in the Hilbert space is required to…
We address the problem of integrating operator equations concomitant with the dynamics of non autonomous quantum systems by taking advantage of the use of time-dependent canonical transformations. In particular, we proceed to a discussion…