Related papers: An algorithm for the optical equivalence theorem
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the dimension of the problem space grows exponentially, finding the eigenvalues of certain…
The logarithm-determinant is an widely-present operation in many areas of physics and computer science. Derivatives of the logarithm-determinant compute physically relevant quantities in statistical physics models, quantum field theories,…
Given a nonsingular $n \times n$ matrix of univariate polynomials over a field $\mathbb{K}$, we give fast and deterministic algorithms to compute its determinant and its Hermite normal form. Our algorithms use…
In this paper, by virtue of the entangled state representation we concisely derive some new operator identities regarding to two-variable Hermite polynomial (TVHP). By them and the technique of integration within an ordered product (IWOP)…
We describe a novel analogue algorithm that allows the simultaneous factorization of an exponential number of large integers with a polynomial number of experimental runs. It is the interference-induced periodicity of "factoring"…
We consider performing phase estimation under the following conditions: we are given only one copy of the input state, the input state does not have to be an eigenstate of the unitary, and the state must not be measured. Most quantum…
The expansion of quantum states and operators in terms of Fock states plays a fundamental role in the field of continuous-variable quantum mechanics. In particular, for general single-mode Gaussian operators and Gaussian noisy states, many…
The use of algebraic tools of operational and umbral nature is exploited to develop a new point of view and to extend the theory of Hermite polynomials, with more than one variable also of complex nature. The techniques we adopt includes…
In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing…
Many eigenvalue problems arising in practice are often of the generalized form $A\x=\lambda B\x$. One particularly important case is symmetric, namely $A, B$ are Hermitian and $B$ is positive definite. The standard algorithm for solving…
In this paper the idea of holonomic quantum computation is realized within quantum optics. In a non-linear Kerr medium the degenerate states of laser beams are interpreted as qubits. Displacing devices, squeezing devices and interferometers…
A review of probability representation of quantum states in given for optical and photon number tomography approaches. Explicit connection of photon number tomogram with measurable by homodyne detector optical tomogram is obtained. New…
Quantum signal processing is a powerful framework in quantum algorithms, playing a central role in Hamiltonian simulation and related applications. The sequence of polynomials implemented at each step of this protocol provides a polynomial…
Harrow, Hassidim, and Lloyd showed that for a suitably specified $N \times N$ matrix $A$ and $N$-dimensional vector $\vec{b}$, there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of…
We present a quantum algorithm for combinatorial optimization using the cost structure of the search states. Its behavior is illustrated for overconstrained satisfiability and asymmetric traveling salesman problems. Simulations with…
In [1] Zhu and Rabitz presented a rapidly convergent iterative algorithm for optimal control of the expectation value of a positive definite observable in a pure-state quantum system. In this paper we generalize this algorithm to a quantum…
It is not possible, using standard lattice techniques in Euclidean space, to calculate the complete fermionic spectrum of a quantum field theory. Algorithms running on quantum computers have the potential to access the theory with real-time…
The modes of the electromagnetic field are solutions of Maxwell's equations taking into account the material boundary conditions. The field modes of classical optics - properly normalized - are also the mode functions of quantum optics.…
We investigate the question if quantum algorithms exist that compute the maximum of a set of conjugated elements of a given number field in quantum polynomial time. We will relate the existence of these algorithms for a certain family of…
An efficient quantum algorithm is proposed to solve in polynomial time the parity problem, one of the hardest problems both in conventional quantum computation and in classical computation, on NMR quantum computers. It is based on the…