Related papers: Quantum Spin Chains and Symmetric Functions
When initially introduced, a Hamiltonian that realises perfect transfer of a quantum state was found to be analogous to an x-rotation of a large spin. In this paper we extend the analogy further to demonstrate geometric effects by…
The information in quantum computers is often stored in identical two-level systems (spins or pseudo-spins) that are separated by a distance shorter than the characteristic wavelength of a reservoir which is responsible for decoherence. In…
The relation between supersymmetric gauge theories in four dimensions and quantum spin systems is exploited to find an explicit formula for the Jost function of the $N$ site $\mathfrak{sl}_{2}$ $XXX$ spin chain (for infinite dimensional…
Quantum computers are expected to become a powerful tool for studying physical quantum systems. Consequently, a number of quantum algorithms for studying the physical properties of such systems have been developed. While qubit-based quantum…
In this paper we consider systems of quantum particles in the $4d$ Euclidean space which enjoy conformal symmetry. The algebraic relations for conformal-invariant combinations of positions and momenta are used to construct a solution of the…
The adaptation of Wigner's induced representation for a relativistic quantum theory making possible the construction of wavepackets and admitting covariant expectation values for the coordinate operator x^\mu introduces a foliation on the…
We provide a mathematical framework for PT-symmetric quantum theory, which is applicable irrespective of whether a system is defined on R or a complex contour, whether PT symmetry is unbroken, and so on. The linear space in which…
We argue that the Hamiltonians for A_{2n}^(2) open quantum spin chains corresponding to two choices of integrable boundary conditions have the symmetries U_q(B_n) and U_q(C_n), respectively. We find a formula for the Dynkin labels of the…
PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside of the conventional equilibrium…
We introduce a transformation which allows the fermionization of operators of any one-dimensional spin-chain. This fermionization procedure is independent of any eventual integrable structure and is compatible with it. We illustrate this…
Using the Algebraic Bethe Ansatz we consider the correlation functions of the integrable higher spin chains. We apply a method recently developed for the spin $\frac 12$ Heisenberg chain, based on the solution of the quantum inverse…
In a quantum computer the hardware and software are intrinsically connected because the quantum Hamiltonian (or more precisely its time development) is the code that runs the computer. We demonstrate this subtle and crucial relationship by…
We survey recent work on designing and evaluating quantum computing implementations based on nuclear or bound-electron spins in semiconductor heterostructures at low temperatures and in high magnetic fields. General overview is followed by…
Symmetry is a fundamentally important concept in many branches of physics. In this work, we discuss two types of symmetries, external symmetry and internal symmetry, which appear frequently in controlled quantum spin chains and apply them…
In physical experiments, reference frames are standardly modelled through a specific choice of coordinates used to describe the physical systems, but they themselves are not considered as such. However, any reference frame is a physical…
Interacting spin networks are fundamental to quantum computing. Data-based tomography of time-independent spin networks has been achieved, but an open challenge is to ascertain the structures of time-dependent spin networks using time…
Classical nonlinear theories are highly successful in describing far-from-equilibrium dynamics of magnets, encompassing phenomena such as parametric resonance, ultrafast switching, and even chaos. However, at ultrashort length and time…
Quantum simulators are engineered devices controllably designed to emulate complex and classically intractable quantum systems. A key challenge is to certify whether the simulator truly mimics the Hamiltonian of interest. This certification…
A simple probabilistic cellular automaton is shown to be equivalent to a relativistic fermionic quantum field theory with interactions. Occupation numbers for fermions are classical bits or Ising spins. The automaton acts deterministically…
The universal quantum computation is obtained when there exists asymmetric anisotropic exchange between electron spins in coupled semiconductor quantum dots. The asymmetric Heisenberg model can be transformed into the isotropic model…