Related papers: Quantum Algorithm for Simulating Hamiltonian Dynam…
We construct a Hamiltonian whose dynamics simulate the dynamics of every other Hamiltonian up to exponentially long times in the system size. The Hamiltonian is time-independent, local, one-dimensional, and translation invariant. As a…
The efficient simulation of quantum dynamics and ground states is a central challenge in physics and a key frontier for quantum advantage. While short-time evolution in one-dimensional systems can often be simulated classically, extending…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
Manipulating Hamiltonians governing physical systems has found a broad range of applications, from quantum chemistry to semiconductor design. In this work, we provide a new way of manipulating Hamiltonians, by transforming their eigenvalues…
We provide a quantum algorithm for simulating the dynamics of sparse Hamiltonians with complexity sublogarithmic in the inverse error, an exponential improvement over previous methods. Specifically, we show that a $d$-sparse Hamiltonian $H$…
We introduce an algorithm to compute Hamiltonian dynamics on digital quantum computers that requires only a finite circuit depth to reach an arbitrary precision, i.e. achieves zero discretization error with finite depth. This finite number…
With a focus on universal quantum computing for quantum simulation, and through the example of lattice gauge theories, we introduce rather general quantum algorithms that can efficiently simulate certain classes of interactions consisting…
The simulation of quantum systems has been a key aim of quantum technologies for decades, and the generalisation to open systems is necessary to include physically realistic systems. We introduce an approach for quantum simulations of open…
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…
The exponential speedups promised by Hamiltonian simulation on a quantum computer depends crucially on structure in both the Hamiltonian $\hat{H}$, and the quantum circuit $\hat{U}$ that encodes its description. In the quest to better…
Quantum process characterization is a fundamental task in quantum information processing, yet conventional methods, such as quantum process tomography, require prohibitive resources and lack scalability. Here, we introduce an efficient…
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process.…
Dynamical quantum simulation may be one of the first applications to see quantum advantage. However, the circuit depth of standard Trotterization methods can rapidly exceed the coherence time of noisy quantum computers. This has led to…
Quantum computing employs controllable interactions to perform sequences of logical gates and entire algorithms on quantum registers. This paradigm has been widely explored, e.g., for simulating dynamics of manybody systems by decomposing…
What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? We provide an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling n-qubit…
We consider the task of simulating time evolution under a Hamiltonian $H$ within its low-energy subspace. Assuming access to a block-encoding of $H'=(H-E)/\lambda$ for some $E \in \mathbb R$, the goal is to implement an…
The controls enacting logical operations on quantum systems are described by time-dependent Hamiltonians that often include rapid oscillations. In order to accurately capture the resulting time dynamics in numerical simulations, a very…
We present a quantum algorithm that analyzes time series data simulated by a quantum differential equation solver. The proposed algorithm is a quantum version of the dynamic mode decomposition algorithm used in diverse fields such as fluid…
How well can quantum computers simulate classical dynamical systems? There is increasing effort in developing quantum algorithms to efficiently simulate dynamics beyond Hamiltonian simulation, but so far exact resource estimates are not…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…