Related papers: Factorizing time evolution into elementary steps
Time-driven quantum systems are important in many different fields of physics like cold atoms, solid state, optics, etc. Many of their properties are encoded in the time evolution operator which is calculated by using a time-ordered product…
Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrodinger equations of Lie type and we show how these methods explain…
Quantum speed-ups for dynamical simulation usually demand unitary time-evolution, whereas the large ODE/PDE systems encountered in realistic physical models are generically non-unitary. We present a universal moment-fulfilling dilation that…
In variational quantum algorithms, parameterization is typically applied to single-qubit gates.In this study, we instead parameterize a generalized controlled gate and propose an algorithm to locally minimize the cost function by maximally…
This paper investigates a new formalism to describe real time evolution of quantum systems at finite temperature. A time correlation function among subsystems will be derived which allows for a probabilistic interpretation. Our derivation…
We apply majorization theory to study the quantum algorithms known so far and find that there is a majorization principle underlying the way they operate. Grover's algorithm is a neat instance of this principle where majorization works step…
Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability…
Simulating Hamiltonian dynamics is one of the most fundamental and significant tasks for characterising quantum materials. Recently, a series of quantum algorithms employing block-encoding of Hamiltonians have succeeded in providing…
Diagonalizing a Hamiltonian, which is essential for simulating its long-time dynamics, is a key primitive in quantum computing and has been proven to yield a quantum advantage for several specific families of Hamiltonians. Yet, despite its…
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"…
Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical tradeoff between improved accuracy for finer…
Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…
The solution of pseudo initial value differential equations, either ordinary or partial (including those of fractional nature), requires the development of adequate analytical methods, complementing those well established in the ordinary…
Complex queries for massive data analysis jobs have become increasingly commonplace. Many such queries contain com- mon subexpressions, either within a single query or among multiple queries submitted as a batch. Conventional query…
This work introduces and analyzes a finite element scheme for evolution problems involving fractional-in-time and in-space differentiation operators up to order two. The left-sided fractional-order derivative in time we consider is employed…
In this paper we develop an analogue of Hamilton-Jacobi theory for the time-evolution operator of a quantum many-particle system. The theory offers a useful approach to develop approximations to the time-evolution operator, and also…
Approximate combinatorial optimization is a promising use case for quantum computers. The quantum optimization algorithms often employ a fixed ansatz that evolves an unbiased initial state towards states with better values of the optimand,…
We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number…
Quantum versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times respectively. Non-unitary quantum walks can provide a useful optimisation of these…
We consider filtering for a continuous-time, or asynchronous, stochastic system where the full distribution over states is too large to be stored or calculated. We assume that the rate matrix of the system can be compactly represented and…