Related papers: Quantum codes give counterexamples to the unique p…
We propose a hybrid quantum-classical algorithm for approximating the ground state and ground state energy of a Hamiltonian. Once the Ansatz has been decided, the quantum part of the algorithm involves the calculation of two overlap…
We assess the probability of resonances between sufficiently distant states in a combinatorial graph serving as the configuration space of an N-particle disordered quantum system. This includes the cases where the transition "shuffles" the…
We study the question of what kind of a macroscopic superposition can(not) naturally exist as a ground state of some gapped local many-body Hamiltonian. We derive an upper bound on the energy gap of an arbitrary physical Hamiltonian…
Approximate analytical energy formulas for N-body relativistic Hamiltonians with one- and two-body interactions are obtained within the framework of the auxiliary field method. This method has already been proved to be a powerful technique…
Quantum Mechanical ground states of many-body systems can be important resources for various investigations: for quantum sensing, as the initial state for nonequilibrium quantum dynamics following quenches, and the simulation of quantum…
We present an approximative simulation method for quantum many-body systems based on coarse graining the space of the momentum transferred between interacting particles, which leads to effective Hamiltonians of reduced size with the…
The general problem of finding the ground state energy of lattice Hamiltonians is known to be very hard, even for a quantum computer. We show here that this is the case even for translationally invariant systems. We also show that a quantum…
Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by…
A method of representing probabilistic aspects of quantum systems is introduced by means of a density function on the space of pure quantum states. In particular, a maximum entropy argument allows us to obtain a natural density function…
We consider the problem of reconstructing global quantum states from local data. Because the reconstruction problem has many solutions in general, we consider the reconstructed state of maximum global entropy consistent with the local data.…
The question of whether given density operators for subsystems of a multipartite quantum system are compatible to one common total density operator is known as the quantum marginal problem. We briefly review the solution of a subclass of…
Two-body scattering and other discreteness effects are unimportant in cosmological gravitational clustering in most scenarios, since the dark matter has a small particle mass. The collective field should determine evolution: Two-body…
We discuss the problem of constructing self-adjoint and lower bounded Hamiltonians for a system of $n>2$ non-relativistic quantum particles in dimension three with contact (or zero-range or $\delta$) interactions. Such interactions are…
Variational calculation of the ground state energy and its properties using the second-order reduced density matrix (2-RDM) is a promising approach for quantum chemistry. A major obstacle with this approach is that the $N$-representability…
We obtain the exact ground state for the Calogero-Sutherland problem in arbitrary dimensions. In the special case of two dimensions, we show that the problem is connected to the random matrix problem for complex matrices, provided the…
Entanglement in the ground state of a many-body quantum system may arise when the local terms in the system Hamiltonian fail to commute with the interaction terms in the Hamiltonian. We quantify this phenomenon, demonstrating an analogy…
Molecular simulations generally require fermionic encoding in which fermion statistics are encoded into the qubit representation of the wave function. Recent calculations suggest that fermionic encoding of the wave function can be bypassed,…
Neural-network-based variational quantum states in general, and more recently autoregressive models in particular, have proven to be powerful tools to describe complex many-body wave functions. However, their performance crucially depends…
Much evidence has been collected to date which shows that repulsive electron-electron interaction can lead to the formation of particle pairs in a one-dimensional random energy landscape. The localization length \lambda_2 of these pair…
We study the quantization of three-dimensional many-body systems in rotating coordinate frames defined implicitly by frame conditions. We carry out the elimination of orientational degrees of freedom in general, giving the Hamiltonian for…