# Quantum Simulation

Illustrative scheme for a compact mapping.
Quantum Simulations The ability of a quantum computer to be programmed as a universal quantum simulator, that is an efficient simulator for other quantum systems, is definitively one of the main driving forces behind enthusiasm and investments into the quantum computing. The main reason behind efficient simulations is that the number of required qubits grows only linearly with the size (number of particles) of the system to be simulated. We study the possibilities of mapping the fermionic algebra to the Pauli spin algebra in the most efficient way. The standard approach is to utilize the Jordan-Wigner transform which results in a direct mapping, where each qubit represents a fermionic two-valued occupational state. In practice, only a subspace with a fixed number of particles is usually of interest and, consequently, less qubits would suffice for the simulation. Such a compact mapping would allow for relatively meaningful simulations to be brought into the few qubit domain. With success in this direction we would be able to design experiments for 3-4 qubits simulating for example the evolution of two electrons in first few atomic orbitals of Helium atom. In combination with the phase estimation algorithm, the physical quantities that could be extracted include the ground state energy and temporal correlations functions. |