Related papers: On the Efficiency of Quantum Algorithms for Hamilt…
Principal component analysis is an important dimension reduction technique in machine learning. In [S. Lloyd, M. Mohseni and P. Rebentrost, Nature Physics 10, 631-633, (2014)], a quantum algorithm to implement principal component analysis…
Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this paper, we propose quantum algorithms capable of testing whether a Hamiltonian…
Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we consider the application of quantum computers to scientific computing and…
Conventional methods of quantum simulation involve trade-offs that limit their applicability to specific contexts where their use is optimal. In particular, the interaction picture simulation has been found to provide substantial asymptotic…
The simulation of electronic properties is a pivotal issue in modern electronic structure theory, driving significant efforts over the past decades to develop protocols for computing energy derivatives. In this work, we address this problem…
Simulating quantum circuits (QC) on high-performance computing (HPC) systems has become an essential method to benchmark algorithms and probe the potential of large-scale quantum computation despite the limitations of current quantum…
The accuracy of quantum dynamics simulation is usually measured by the error of the unitary evolution operator in the operator norm, which in turn depends on certain norm of the Hamiltonian. For unbounded operators, after suitable…
Efficient quantum circuit optimization schemes are central to quantum simulation of strongly interacting quantum many body systems. Here, we present an optimization algorithm which combines machine learning techniques and tensor network…
We present a quantum algorithm for approximating the real time evolution $e^{-iHt}$ of an arbitrary $d$-sparse Hamiltonian to error $\epsilon$, given black-box access to the positions and $b$-bit values of its non-zero matrix entries. The…
Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient…
Classical simulators play a major role in the development and benchmark of quantum algorithms and practically any software framework for quantum computation provides the option of running the algorithms on simulators. However, the…
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…
Hamiltonian simulation is believed to be one of the first tasks where quantum computers can yield a quantum advantage. One of the most popular methods of Hamiltonian simulation is Trotterization, which makes use of the approximation…
We present a quantum algorithm for the simulation of molecular systems that is asymptotically more efficient than all previous algorithms in the literature in terms of the main problem parameters. As in previous work [Babbush et al., New…
A central challenge in quantum computing is to identify more computational problems for which utilization of quantum resources can offer significant speedup. Here, we propose a hybrid quantum-classical scheme to tackle the quantum optimal…
We investigate the sample complexity of Hamiltonian simulation: how many copies of an unknown quantum state are required to simulate a Hamiltonian encoded by the density matrix of that state? We show that the procedure proposed by Lloyd,…
This paper explores the use of quantum computing, specifically the use of HHL and VQLS algorithms, to solve optimal power flow problem in electrical grids. We investigate the effectiveness of these quantum algorithms in comparison to…
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
An observer-based Hamiltonian identification algorithm for quantum systems is proposed. For the 2-level case an exponential convergence result based on averaging arguments and some relevant transformations is provided. The convergence for…