Exact Ising model simulation on a quantum computer

Abstract

We present an exact simulation of a onedimensional transverse Ising spin chain with a quantum computer. We construct an efficient quantum circuit that diagonalizes the Ising Hamiltonian and allows to obtain all eigenstates of the model by just preparing the computational basis states. With an explicit example of that circuit for n = 4 spins, we compute the expected value of the ground state transverse magnetization, the time evolution simulation and provide a method to also simulate thermal evolution. All circuits are run in IBM and Rigetti quantum devices to test and compare them qualitatively.Accepted in Quantum 2018-12-18, click title to verify arXiv:1807.07112v3 [quant-ph]

Variational Quantum Fidelity Estimation

“…where the right inequality follows from Lemma 3. Inserting (33) and summing the two resulting inequalities gives:…”

“…j the spin components at site j, h the magnetic field, and J the exchange coupling strength. While this model is exactly solvable, it remains of interest as its thermal states can be exactly prepared on a quantum computer [32,33]. Figure 4 shows the fidelity spectrum for this example.…”

Quantum isomer search

“…Since gate-based quantum computers can also solve the Ising Problem [2], in addition to using D-Wave 2000Q, we explored the possibility of using IBM Q's Qiskit software on the available QASM simulator [50] . A QUBO can be expanded into the Pauli basis, and when this is done, it can then be solved using methods such as variational quantum eigensolver (VQE) [51] or quantum approximate optimization algorithm (QAOA) [52].…”

Quantum Computers as Universal Quantum Simulators: State‐of‐the‐Art and Perspectives

“…Following this route, a plethora of analog quantum simulators have been proposed and developed, in which the physical properties of a targeted model are reproduced on a physical setup under externally controlled conditions. On the other hand, digital quantum simulators are programmable and general purpose quantum devices, which promise a larger flexibility on the models to be solved . In this respect, digital quantum simulators are quantum computing machines not restricted to emulate the dynamics of targeted models, but satisfying DiVincenzo criteria for quantum computation.…”

“…On the other hand, digital quantum simulators are programmable and general purpose quantum devices, which promise a larger flexibility on the models to be solved. [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] In this respect, digital quantum simulators are quantum computing machines not restricted to emulate the dynamics of targeted models, but satisfying DiVincenzo criteria [48] for quantum computation. Here we will consider such digital quantum computers as universal quantum simulators (UQS), [31] meaning that they are able, in principle, to reproduce with arbitrary precision the dynamics of any Hamiltonian model that can be suitably encoded on a given quantum register and translated into a sequence of gate operations, as schematically illustrated in Figure 1.…”