Orders of magnitude increased accuracy for quantum many-body problems on quantum computers via an exact transcorrelated method

Quantum orders in an exact soluble model.

We find all the exact eigenstates and eigenvalues of a spin-1/2 model on square lattice: H=16g Sum S(y)(i)S(x)(i + empty set x)S(y)(i + empty set x + empty set y)S(x)(i + empty set y). We show that the ground states for g < 0 and g > 0 have different quantum orders described by Z2A and Z2B projective symmetry groups. The phase transition at g = 0 represents a new kind of phase transition that c...

Quantum Many–Body Problems and Perturbation Theory

We show that the existence of algebraic forms of exactly-solvable A−B− C−D and G2, F4 Olshanetsky-Perelomov Hamiltonians allow to develop the algebraic perturbation theory, where corrections are computed by pure algebraic means. A classification of perturbations leading to such a perturbation theory based on representation theory of Lie algebras is given. In particular, this scheme admits an ex...

Exact Quantum Solutions of Extraordinary N-body Problems

The wave functions of Boson and Fermion gases are known even when the particles have harmonic interactions. Here we generalise these results by solving exactly the N-body Schrödinger equation for potentials V that can be any function of the sum of the squares of the distances of the particles from one another in 3 dimensions. For the harmonic case that function is linear in r2. Explicit N-body ...

Estimation of many-body quantum Hamiltonians via compressive sensing

A. Shabani,1 M. Mohseni,2 S. Lloyd,2,3 R. L. Kosut,4 and H. Rabitz1 1Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA 2Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 3Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 4SC Solutions, Sunnyva...

Many-body studies on atomic quantum systems