Related papers: Exponential improvement in precision for Hamiltoni…
The paper introduces new corrections of different orders of smallness to the D-MORPH method by using the full form of the derivative of the exponential map, defined on a Lie algebra, to search for the optimal control of a quantum system…
We present a new primitive for quantum algorithms that implements a discrete Hermite transform efficiently, in time that depends logarithmically in both the dimension and the inverse of the allowable error. This transform, which maps basis…
The work here enables linear cost-scaling with evolution time $t$ while keeping ${\rm polylog} (1/\epsilon)$ scaling and no extra block-encoding qubits, where $\epsilon$ is the algorithmic error. This is achieved through product formulas,…
We propose a variational alternative to the Trotter-Suzuki decomposition that provides greater control over errors while preserving the unitary structure of time evolution. The variational parameters in our ansatz are derived from a global…
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 propose an effective and flexible scheme for reverse engineering of a Hamiltonian by designing the evolution operators to eliminate the terms of Hamiltonian which are hard to be realized in practice. Different from transitionless quantum…
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…
The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly…
Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value…
Imaginary time evolution is a powerful technique for computing the ground state of quantum Hamiltonians, where the convergence to ground state in asymptotic imaginary time is guaranteed. However, implementing this method on quantum…
We present a novel, computationally efficient approach to accelerate quantum optimal control calculations of large multi-qubit systems used in a variety of quantum computing applications. By leveraging the intrinsic symmetry of finite…
Simulating time evolution of quantum systems is one of the most promising applications of quantum computing and also appears as a subroutine in many applications such as Green's function methods. In the current era of NISQ machines we…
Quantum simulation using time evolution in phase estimation-based quantum algorithms can yield unbiased solutions of classically intractable models. However, long runtimes open such algorithms to decoherence. We show how measurement-based…
We investigate the problem of fast-forwarding quantum evolution, whereby the dynamics of certain quantum systems can be simulated with gate complexity that is sublinear in the evolution time. We provide a definition of fast-forwarding that…
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…
We introduce a numerical algorithm to simulate the time evolution of a matrix product state under a long-ranged Hamiltonian. In the effectively one-dimensional representation of a system by matrix product states, long-ranged interactions…
We study how parallelism can speed up quantum simulation. A parallel quantum algorithm is proposed for simulating the dynamics of a large class of Hamiltonians with good sparse structures, called uniform-structured Hamiltonians, including…
Recent work has shown that it can be advantageous to implement a composite channel that partitions the Hamiltonian $H$ for a given simulation problem into subsets $A$ and $B$ such that $H=A+B$, where the terms in $A$ are simulated with a…
In this paper, we consider the task of efficiently computing the numerical solution of evolutionary complex Ginzburg--Landau equations on Cartesian product domains with homogeneous Dirichlet/Neumann or periodic boundary conditions. To this…
A novel scheme to simulate the evolution of a restricted set of observables of a quantum system is proposed. The set comprises the spectrum-generating algebra of the Hamiltonian. The idea is to consider a certain open-system evolution,…