Demonstration notebooks of various Quantum Algorithms
In this notebook we construct quantum circuits to simulate quantum dynamics of spin chains. We discuss different variants of the Trotterized time evolution of quantum spin chains in one dimension. We aim to find the shortest depth Trotter circuit that can simulate the time evolution of Haar random quantum states with the best possible fidelity. The reference states at time (t=0) are initialized via random Quantum circuits. Multiple realization of the random circuits are sampled and a measure of average fidelity of the time evolved state is defined to quantify the efficiency of the different Trotter circuits.
This topic is motivated by the ibm open science prize competition 2021 , however in the present notebook the focus is a bit different and that is to study how Quantum Resources scale with number of qubits for different variants of the Trotter circuits. More precisely we consider two kinds of Trotter circuits:
(i) conventional first-order Trotter decomposition of the time evolution operator with the Heisenberg or XXZ Hamiltonian.
(ii)Fast forwarded Trotter Circuit where the XY part of the spin chain Hamiltonian is diagonalized using Givens rotation.
The simulations below can be carried out for an arbitrary number of qubits, in this notebook we have carried out a simulation for num. of qubits=3,4,5,6,7,8. We check the number of CNOT gates required to perform high fidelity quantum dynamics simulation of XXZ spin chains for number of qubits 3,4,5,6,7,8 and for total evolution time of T=70 secs with a average fidelity above 99.9%.