Related papers: Simulating Time-dependent Hamiltonian Based On Hig…
We apply the method of flow equations to describe quantum systems subject to a time-periodic drive with a time-dependent envelope. The driven Hamiltonian is expressed in terms of its constituent Fourier harmonics with amplitudes that may…
Hamiltonian simulation is arguably the most fundamental application of quantum computers. The Magnus operator is a popular method for time-dependent Hamiltonian simulation in computational mathematics, yet its usage requires the…
We present a recursive formula for the computation of the static effective Hamiltonian of a system under a fast-oscillating drive. Our analytical result is well-suited to symbolic calculations performed by a computer and can be implemented…
In this paper, we present a method for the Hamiltonian simulation in the context of eigenvalue estimation problems which improves earlier results dealing with Hamiltonian simulation through the truncated Taylor series. In particular, we…
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…
The capacity for solving eigenstates with a quantum computer is key for ultimately simulating physical systems. Here we propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse…
In this paper we study the evolution operator of a time-dependent Hamiltonian in the three level system. The evolution operator is based on $SU(3)$ and its dimension is $8$, so we obtain three complex Riccati differential equations…
We present a model of discrete quantum evolution based on quantum correlations between the evolving system and a reference quantum clock system. A quantum circuit for the model is provided, which in the case of a constant Hamiltonian is…
We describe an improved version of the quantum simulation method based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an…
In this article we present an effective Hamiltonian approach for Discrete Time Quantum Random Walk. A form of the Hamiltonian for one dimensional quantum walk has been prescribed, utilizing the fact that Hamiltonians are the generators of…
Hamiltonian simulation is one of the most important problems in the field of quantum computing. There have been extended efforts on designing algorithms for faster simulation, and the evolution time $T$ for the simulation turns out to…
Accurately simulating the non-Markovian dynamics of open quantum systems remains a significant challenge. While the recently proposed time-evolving matrix product operator (TEMPO) algorithm based on path integrals successfully circumvents…
We present a C++ implementation of a fifth order semi-implicit Runge-Kutta algorithm for solving Ordinary Differential Equations. This algorithm can be used for studying many different problems and in particular it can be applied for…
We show that the time-dependent variational principle provides a unifying framework for time-evolution methods and optimisation methods in the context of matrix product states. In particular, we introduce a new integration scheme for…
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…
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…
Time-dependent Hamiltonian simulation (TDHS) is a critical task in quantum computing. Existing algorithms are generally biased with a small algorithmic error $\varepsilon$, and the gate complexity scales as $O(\text{poly}(1/\varepsilon))$…
In this thesis we study aspects of Hamiltonian models which can affect the time evolution of transmon systems. We model the time evolution of various systems as a unitary real-time process by numerically solving the time-dependent…
Quantum algorithms for electronic-structure simulations are actively being developed, yet many hybrid quantum-classical approaches are bottlenecked by the measurement overhead associated with large molecular Hamiltonians. Here we introduce…
Quantum imaginary time evolution (QITE) is one of the promising candidates for finding eigenvalues and eigenstates of a Hamiltonian. However, the original QITE proposal [Nat. Phys. 16, 205-210 (2020)], which approximates the imaginary time…