Related papers: Hamiltonian Complexity in the Thermodynamic Limit
Product states, unentangled tensor products of single qubits, are a ubiquitous ansatz in quantum computation, including for state-of-the-art Hamiltonian approximation algorithms. A natural question is whether we should expect to efficiently…
Quantum thermodynamics is a research field that aims at fleshing out the ultimate limits of thermodynamic processes in the deep quantum regime. A complete picture of quantum thermodynamics allows for catalysts, i.e., systems facilitating…
Ground states of local Hamiltonians can be generally highly entangled: any quantum circuit that generates them (even approximately) must be sufficiently deep to allow coupling (entanglement) between any pair of qubits. Until now this…
We describe a method to compute thermodynamic quantities in the harmonic approximation for identical bosons and fermions in an external confining field. We use the canonical partition function where only energies and their degeneracies…
A novel approach to the Hamiltonian formulation of quantum field theory at finite temperature is presented. The temperature is introduced by compactification of a spatial dimension. The whole finite-temperature theory is encoded in the…
Density functional theory is a successful branch of numerical simulations of quantum systems. While the foundations are rigorously defined, the universal functional must be approximated resulting in a `semi'-ab initio approach. The search…
Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. We seek to…
We use density-matrix renormalization group, applied to a one-dimensional model of continuum Hamiltonians, to accurately solve chains of hydrogen atoms of various separations and numbers of atoms. We train and test a machine-learned…
A systematic formalism for quantum electrodynamics in a classical uniform magnetic field is discussed. The first order radiative correction to the ground state energy of an electron is calculated. This then leads to the anomalous magnetic…
We study the computational complexity of the Guided Local Hamiltonian problem: given a local Hamiltonian $H$ together with a classical description of a guiding state that has non-negligible overlap with the ground state of $H$, estimate the…
In this work, we study a variant of the local Hamiltonian problem where we restrict to Hamiltonians that live on a lattice and are invariant under translations and rotations of the lattice. In the one-dimensional case this problem is known…
The third law of thermodynamics forbids cooling a physical system to absolute zero in a finite number of operational steps. Although this unattainability principle has been quantified for specific state-to-state transitions, a universal,…
Can the properties of the thermodynamic limit of a many-body quantum system be extrapolated by analysing a sequence of finite-size cases? We present a model for which such an approach gives completely misleading results: a translationally…
We devise a hierarchy of computational algorithms to enumerate the microstates of a system comprising N independent, distinguishable particles. An important challenge is to cope with integers that increase exponentially with system size,…
State transformation problems such as compressing quantum information or breaking quantum commitments are fundamental quantum tasks. However, their computational difficulty cannot easily be characterized using traditional complexity theory,…
Enhancing the precision of a thermodynamic process inevitably necessitates a thermodynamic cost. This notion was recently formulated as the thermodynamic uncertainty relation, which states that the lower bound on the relative variance of…
Describing matter at near absolute zero temperature requires understanding a system's quantum ground state and the low energy excitations around it, the quasiparticles, which are thermally populated by the system's contact to a heat bath.…
Simulations of quantum transport in coherent conductors have evolved into mature techniques that are used in fields of physics ranging from electrical engineering to quantum nanoelectronics and material science. The most efficient…
The Hamiltonian constraint remains an elusive object in loop quantum gravity because its action on spinnetworks leads to changes in their corresponding graphs. As a result, calculations in loop quantum gravity are often considered…
Finding the ground energy of a quantum system is a fundamental problem in condensed matter physics and quantum chemistry. Existing classical algorithms for tackling this problem often assume that the ground state has a succinct classical…