相关论文: Implementing unitary operators in quantum computat…
Feynman, in 1982, proposed the idea of using a quantum simulator to perform quantum simulations. A quantum simulator is basically a controllable quantum system that can mimic the dynamics of other quantum systems we wish to study. In this…
Quantum signal processing combined with quantum eigenvalue transformation has recently emerged as a unifying framework for several quantum algorithms. In its standard form, it consists of two separate routines: block encoding, which encodes…
The spinor representation of the quantum group $U_q(su(N))$ is given in terms of a set of fermion creation and annihilation operators. It is shown that the $q$-fermion operators introduced earlier can be identifi ed with the conventional…
Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement "quantum simulators". Quantum…
Point splitting has been suggested as a way to deal with anomalous commutators in quantum field theory. It has been pointed out by D.G. Boulware[4] that in order to obtain a mathematically consistent theory the Hamiltonian operator must be…
The variational quantum eigensolver is one of the most promising algorithms for near-term quantum computers. It has the potential to solve quantum chemistry problems involving strongly correlated electrons, which are otherwise difficult to…
Simulating plasma physics on quantum computers is difficult because most problems of interest are nonlinear, but quantum computers are not naturally suitable for nonlinear operations. In weakly nonlinear regimes, plasma problems can be…
The article surveys quantization schemes for metric graphs with spin. Typically quantum graphs are defined with the Laplace or Schrodinger operator which describe particles whose intrinsic angular momentum (spin) is zero. However, in many…
While quantum devices rely on interactions between constituent subsystems and with their environment to operate, native interactions alone often fail to deliver targeted performance. Coherent pulsed control provides the ability to tailor…
We describe a quantum computer based upon the coherent manipulation of two-level atoms between discrete one-dimensional momentum states. Combinations of short laser pulses with kinetic energy dependent free phase evolution can perform the…
In recent work, we initiated a research program aimed at the systematic investigation of quantum superintegrable systems describing the interaction of two non-relativistic spin-$1/2$ particles in three-dimensional Euclidean space. In that…
A possibility of performing the C-NOT gate operation at the ground and the first excited states of two harmonic oscillators interacting via a two-level system subject to complete control is demonstrated. The system resembles Turing machine,…
For a (classically) integrable quantum mechanical system with two degrees of freedom, the functional dependence $\hat{H}=H_Q(\hat{J}_1,\hat{J}_2)$ of the Hamiltonian operator on the action operators is analyzed and compared with the…
We treat the ultraviolet problem for polaron-type models in nonrelativistic quantum field theory. Assuming that the dispersion relations of particles and the field have the same growth at infinity, we cover all subcritical…
To find the discrete symmetries of a Hamilton operator $\hat H$ is of central importance in quantum theory. Here we describe and implement a brute force method to determine the discrete symmetries given by permutation matrices for Hamilton…
Unitary operators are essential to quantum mechanics, however for discrete systems larger than a qubit, it is difficult to express them in a self-contained way. This report presents just such a description, providing a compact, useful…
The improved quantum scheduling algorithm proposed by Grover has been generalized using the generalized quantum search algorithm, in which a unitary operator replaces the Walsh-Hadamard transform, and $\pi/2$ phase rotations replace the…
The effect of noise on a quantum system can be described by a set of operators obtained from the interaction Hamiltonian. Recently it has been shown that generalized quantum error correcting codes can be derived by studying the algebra of…
Implementing general functions of operators is a powerful tool in quantum computation. It can be used as the basis for a variety of quantum algorithms including matrix inversion, real and imaginary-time evolution, and matrix powers. Quantum…
We study a sequence of quantum gates in finite-dimensional Hilbert spaces given by the normalized eigenvectors of the unitary operators. The corresponding sequence of the Hamilton operators is also given. From the Hamilton operators we…