Related papers: Engineering Effective Hamiltonians
Effective Hamiltonians are usually constructed by using canonical transformations or projection techniques. In contrast to this, we present a method for systems with arbitrary Hilbert space based on the introduction of cumulants. Cumulants…
We present a systematic scheme for optimization of quantum simulations. Specifically, we show how polychromatic driving can be used to significantly improve the driving of Raman transitions in the Lambda system, which opens new…
A powerful control method in experimental quantum computing is the use of spin echoes, employed to select a desired term in the system's internal Hamiltonian, while refocusing others. Here we address a more general problem, describing a…
We develop a systematic perturbative framework to engineer an arbitrary target Hamiltonian in the Floquet phase space of a periodically driven oscillator based on Floquet-Magnus expansion. The high-order errors in the engineered Floquet…
Digital quantum simulation of many-body dynamics relies on Trotterization to decompose the target time evolution into elementary quantum gates operating at a fixed equidistant time discretization. Recent advances have outlined protocols…
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 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…
Electric fields, applied to insulators, cause transitions between valence and conduction bands, giving rise to current. Adjustments of the Hamiltonian can perfect the quality of the insulator, shutting down transitions whilst fully…
Quantum metrology leverages quantum resources such as entanglement and squeezing to enhance parameter estimation precision beyond classical limits. While optimal quantum control strategies can assist to reach or even surpass the Heisenberg…
Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant input/output maps are unitary transformations, and the fundamental challenge…
This paper is concerned with variational methods for nonlinear open quantum systems with Markovian dynamics governed by Hudson-Parthasarathy quantum stochastic differential equations. The latter are driven by quantum Wiener processes of the…
An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this…
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…
Time-driven quantum systems are important in many different fields of physics like cold atoms, solid state, optics, etc. Many of their properties are encoded in the time evolution operator which is calculated by using a time-ordered product…
Hamiltonian simulation, i.e., simulating the real time evolution of a target quantum system, is a natural application of quantum computing. Trotter-Suzuki splitting methods can generate corresponding quantum circuits; however, a faithful…
Perturbation theory with respect to the kinetic energy of the heavy component of a two-component quantum system is introduced. An effective Hamiltonian that is accurate to second order in the inverse heavy mass is derived. It contains a new…
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…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
Initially introduced in the framework of quantum control, the so-called "monotonic algorithms" have demonstrated excellent numerical performance when dealing with bilinear optimal control problems. This paper presents a unified formulation…
We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…