We describe a quantum algorithm to compute the density of states and thermal equilibrium properties of quantum many-body systems. We present results obtained by running this algorithm on a software implementation of a 21-qubit quantum computer for the case of an antiferromagnetic Heisenberg model on triangular lattices of different size.
We outline a proposal to test quantum mechanics in the high-complexity regime using noisy intermediate-scale quantum (NISQ) devices. The procedure involves simulating a non-Clifford random circuit, followed by its inverse, and then checking that the resulting state is the same as the initial state. We are motivated by the hypothesis that quantum mechanics is not fundamental, but instead emerges from a theory with less computational power, such as classical mechanics. This emergent quantum mechanics (EmQM) hypothesis makes the prediction that quantum computers will not be capable of sufficientl…
We investigate superconformal quantum mechanics (SCQM) on a quantum computer. We study the ground state of the mass deformed SCQM on a quantum computed using the Variational Quantum Eigensolver (VQE) using a one boson and one boson - one fermion Hilbert space with and without noise and compare the accuracy of the results. We study the Feynman path integral for SCQM using the Evolution of Hamiltonian (EOH) algorithm on the quantum computer using the Trotter-Suzuki approximation and compare with the exact result. We consider an N boson and N fermion version of SCQM given be the Supersymmetric Ca…
In this paper, we investigate DNA denaturation through Statistical Mechanics and show that exceptional polynomials lead to DNA mutation. We consider a DNA model with two chains connected by Morse potential representing the H bonds, and then we calculate the partition function for this model. The partition function is converted into a Schrödinger like an equation. We exploit the techniques of SUSY quantum mechanics to model DNA mutation. We also compute the thermal denaturation of DNA for each mutated state.
Transformation Relation of Two Descriptive Systems between Quantum Mechanics and Classical Statistical Mechanics and Dynamic Foundation of Classical Statistical Physics
In this paper we discuss the Morse potential on a quantum computer. The Morse potential is useful to describe diatomic molecules and has a finite number of bound states which can be measured through spectroscopy. It is also a example of an exactly soluble potential using supersymmetric quantum mechanics. Using the the supersymmetric quantum mechanics formalism one can derive a heirachy of Hamiltonians such that the ground state of the next rung on the heirarchy yeids the first excited state of the hamiltonian below it. Using this method one can determine all the states of the Morse potential b…
These are the lecture notes for quantum and statistical mechanics courses that are given by DC at Ben-Gurion University. They are complementary to "Lecture Notes in Quantum Mechanics" [arXiv: quant-ph/0605180]. Some additional topics are covered, including: introduction to master equations; non-equilibrium processes; fluctuation theorems; linear response theory; adiabatic transport; the Kubo formalism; and the scattering approach to mesoscopics.
