Related papers: SymPT: a comprehensive tool for automating effecti…
Hamiltonian simulation is known to be one of the fundamental building blocks of a variety of quantum algorithms such as its most immediate application, that of simulating many-body systems to extract their physical properties. In this work,…
Many significant quantum physical systems are characterized by Hamiltonians expressible as a linear combination of time-independent generators of a closed Lie algebra, $\hat{H}(t)=\sum_{l=1}^{L}\eta_{l}(t)\hat{g}_{l}$. The Wei-Norman method…
Combining non-hermiticity and interactions yields novel effects in open quantum many-body systems. Here, we develop the generalized Schrieffer-Wolff transformation and derive the effective Hamiltonian suitable for various quasi-degenerate…
Building on recent results for adiabatic gauge potentials, we propose a variational approach for computing the generator of Schrieffer-Wolff transformations. These transformations consist of block diagonalizing a Hamiltonian through a…
We present a formalized perturbation theory for Markovian open systems in the language of a generalized Schrieffer-Wolff (SW) transformation. A non-unitary rotation decouples the unper- turbed steady states from all fast degrees of freedom,…
This work develops a symplectic framework for quantum computing to be applied to classical Hamiltonian systems, exploiting the intrinsic geometric compatibility between unitary quantum evolution and symplectic phase-space dynamics in a…
Modern quantum physics is very modular: we first understand basic building blocks (``XXZ Hamiltonian'' ``Jaynes-Cummings'' etc.) and then combine them to explore novel effects. A typical example is placing known systems inside an optical…
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…
A practical automatic textual math word problems (MWPs) solver should be able to solve various textual MWPs while most existing works only focused on one-unknown linear MWPs. Herein, we propose a simple but efficient method called Universal…
Schrieffer-Wolff transformation is a very important transformation in Quantum Many Body physics. Yet, there isn't an explicit method in the literature to calculate the generator of this unitary transformation directly from the hamiltonian.…
We derive recursive relations for the Schrieffer--Wolff (SW) transformation applied to the half-filled Hubbard dimer. While the standard SW transformation is set to block-diagonalize the transformed Hamiltonian solely at the first order of…
A quantum algorithm for approximating efficiently 3--manifold topological invariants in the framework of SU(2) Chern-Simons-Witten (CSW) topological quantum field theory at finite values of the coupling constant k is provided. The model of…
We provide a new approach for compiling quantum simulation circuits that appear in Trotter, qDRIFT and multi-product formulas to Clifford and non-Clifford operations that can reduce the number of non-Clifford operations by a factor of up to…
We present and analyze a framework for designing symplectic neural networks (SympNets) based on geometric integrators for Hamiltonian differential equations. The SympNets are universal approximators in the space of Hamiltonian…
The Wigner Transform (WT) has been extensively used in the formulation of phase-space models for a variety of wave propagation problems including high-frequency limits, nonlinear and random waves. It is well known that the WT features…
This paper proposes a numerical method for solving time-dependent Schrodinger equations with finite spectral bandwidth, which applies to both periodic and non-periodic cases. We introduce the concept of Pulse Width Modulation (PWM), which…
The special affine Fourier transform (SAFT) is a promising tool for analyzing non-stationary signals with more degrees of freedom. However, the SAFT fails in obtaining the local features of non-transient signals due to its global kernel and…
Reinforcement learning (RL) has demonstrated great potential in robotic operations. However, its data-intensive nature and reliance on the Markov Decision Process (MDP) assumption limit its practical deployment in real-world scenarios…
Simple families of quantum Hamiltonians can simulate general many-body systems at arbitrary precision through the use of perturbative gadgets, however this generally requires interaction strengths spanning many orders of magnitude which…
We introduce HAML (Hamiltonian Adaptation via Meta-Learning), a framework for fast online adaptation of effective Hamiltonian models of superconducting quantum processors. HAML proceeds in two phases. A supervised training phase uses an…