Related papers: Universal algorithm for transforming Hamiltonian e…
We present a procedure for averaging one-parameter random unitary groups and random self-adjoint groups. Central to this is a generalization of the notion of weak convergence of a sequence of measures and the corresponding generalization of…
In this work we extend the notion of universal quantum Hamiltonians to the setting of translationally-invariant systems. We present a construction that allows a two-dimensional spin lattice with nearest-neighbour interactions, open…
Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyse a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent…
Adaptive resolution schemes allow the simulation of a molecular fluid treating simultaneously different subregions of the system at different levels of resolution. In this work we present a new scheme formulated in terms of a global…
We use the dynamical algebra of a quantum system and its dynamical invariants to inverse engineer feasible Hamiltonians for implementing shortcuts to adiabaticity. These are speeded up processes that end up with the same populations than…
Solving Hamiltonian matrix is a central task in quantum many-body physics and quantum chemistry. Here we propose a novel quantum algorithm named as a quantum Heaviside eigen solver to calculate both the eigen values and eigen states of the…
Quasi-degenerate eigenvalue problems are central to quantum chemistry and condensed-matter physics, where low-energy spectra often form manifolds of nearly degenerate states that determine physical properties. Standard quantum algorithms,…
Hamiltonian simulation is a promising application for quantum computers to achieve a quantum advantage. We present classical algorithms based on tensor network methods to optimize quantum circuits for this task. We show that, compared to…
The hidden shift problem is a natural place to look for new separations between classical and quantum models of computation. One advantage of this problem is its flexibility, since it can be defined for a whole range of functions and a…
Implementing the time evolution under a desired target Hamiltonian is critical for various applications in quantum science. Due to the exponential increase in the number of parameters with system size and experimental imperfections, this…
Completely integrable Hamiltonian systems look promising for controllability since their first integrals are stable under an internal evolution, and one may hope to find a perturbation of a Hamiltonian which drives the first integrals at…
The ability to characterise a Hamiltonian with high precision is crucial for the implementation of quantum technologies. In addition to the well-developed approaches utilising optimal probe states and optimal measurements, the method of…
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…
Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…
One of the key challenges in quantum machine learning is finding relevant machine learning tasks with a provable quantum advantage. A natural candidate for this is learning unknown Hamiltonian dynamics. Here, we tackle the supervised…
The Rodeo Algorithm is a quantum computing method for computing the energy spectrum of a Hamiltonian and preparing its energy eigenstates. We discuss how to improve the performance of the rodeo algorithm for each of these two applications.…
We calculate the eigenvalues of some two-dimensional non-Hermitian Hamiltonians by means of a pseudospectral method and straightforward diagonalization of the Hamiltonian matrix in a suitable basis set. Both sets of results agree remarkably…
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…
We consider a bipartite quantum object, composed of a quantum system and a quantum actuator which is periodically reset. We show that the reduced dynamics of the system approaches unitarity as the reset frequency of the actuator is…
Parity-time ($PT$)-symmetric Hamiltonians exhibit non-unitary dynamical evolution while maintaining real spectra, and offer unique approaches to quantum sensing and entanglement generation. Here we present a method for simulating the…