相关论文: Quantum state transformations and the Schubert cal…
We develop a rigorous connection between statistical properties of an interference pattern and the coherence properties of the underlying quantum state. With explicit examples, we demonstrate that even for inaccurate reconstructions of…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
We introduce an approximate description of an $N$-qubit state, which contains sufficient information to estimate the expectation value of any observable with precision independent of $N$. We show, in fact, that the error in the estimation…
Solving linear systems and computing eigenvalues are two fundamental problems in linear algebra. For solving linear systems, many efficient quantum algorithms have been discovered. For computing eigenvalues, currently, we have efficient…
To measure an observable of a quantum mechanical system leaves it in one of its eigenstates and the result of the measurement is one of its eigenvalues. This process is shown to be a computational resource. It allows one, in principle, to…
Since the dawn of quantum theory, coherence was attributed as a key to understand the weirdness of fundamental concepts like the wave-particle duality and the Stern-Gerlach experiment. Recently, based on a resource theory approach, the…
We give a simple demonstration that the Schr\"odinger equation may be recast as a self-contained second-order Newtonian law for a congruence of spacetime trajectories. This provides a pictorial representation of the quantum state as the…
The use of quantum computing to solve a problem in quantum mechanics is illustrated, step by step, by calculating energies and transition amplitudes in a nonrelativistic quark model. The quantum computations feature the use of variational…
The possibilities of curvature of space-time in the metric of quantum states are investigated. The curvature of the metric corresponding to a wave function of Hydrogen atom is determined. Also, Einstein tensor is described for a given…
The notion of quantum information related to the two different perspectives of the global and local states is examined. There is circularity in the definition of quantum information because we can speak only of the information of systems…
We review Schmidt and Kraus decompositions in the form of singular value decomposition using operations of reshaping, vectorization and reshuffling. We use the introduced notation to analyse the correspondence between quantum states and…
We consider the statistics of overlaps between a mixed state and its image under random unitary transformations. Choosing the transformations from the unitary group with its invariant (Haar) measure, the distribution of overlaps depends…
In this paper we bring to light an unprecedented property of the eigenvalues of a matrix A with the eigenvalues and eigenvectors of a submatrix of A. This property can be used, through the technique developed here, to determine some of…
We review recent progress on Horn's problem, which asks for a description of the possible eigenspectra of the sum of two matrices with known eigenvalues. After revisiting the classical case, we consider several generalizations in which the…
The eigenvalue density of a matrix plays an important role in various types of scientific computing such as electronic-structure calculations. In this paper, we propose a quantum algorithm for computing the eigenvalue density in a given…
We define a "nit" as a radix n measure of quantum information which is based on state partitions associated with the outcomes of n-ary observables and which, for n>2, is fundamentally irreducible to a binary coding. Properties of this…
Given an quantum dynamical semigroup expressed as an exponential superoperator acting on a space of N-dimensional density operators, eigenvalue methods are presented by which canonical Kraus and Lindblad operator sum representations can be…
Eigenvalue transformations appear ubiquitously in scientific computation, ranging from matrix polynomials to differential equations, and are beyond the reach of the quantum singular value transformation framework. In this work, we study the…
We extend Einstein's hole argument into the quantum domain, and argue that quantum observables for quasiclassical superpositional states of gravitational fields require additional information to be well-defined, namely, relative positions…
We describe a quantum algorithm for finding the smallest eigenvalue of a Hermitian matrix. This algorithm combines Quantum Phase Estimation and Quantum Amplitude Estimation to achieve a quadratic speedup with respect to the best classical…