Quantum Simulation of Tunneling in Small Systems

TL;DR

This paper demonstrates a resource-efficient quantum simulation method for tunneling phenomena using minimal ancillary qubits, enabling small-scale quantum computers to simulate complex tunneling dynamics.

Contribution

It introduces a new approach to simulate tunneling without ancillary qubits, reducing gate complexity for small quantum systems.

Findings

Tunneling problems can be simulated with no ancillary qubits.

Simulation of 2-qubit tunneling requires about 40 gates.

3-qubit tunneling simulations need 70-140 gates.

Abstract

A number of quantum algorithms have been performed on small quantum computers; these include Shor's prime factorization algorithm, error correction, Grover's search algorithm and a number of analog and digital quantum simulations. Because of the number of gates and qubits necessary, however, digital quantum particle simulations remain untested. A contributing factor to the system size required is the number of ancillary qubits needed to implement matrix exponentials of the potential operator. Here, we show that a set of tunneling problems may be investigated with no ancillary qubits and a cost of one single-qubit operator per time step for the potential evolution. We show that physically interesting simulations of tunneling using 2 qubits (i.e. on 4 lattice point grids) may be performed with 40 single and two-qubit gates. Approximately 70 to 140 gates are needed to see interesting tunneling dynamics in three-qubit (8 lattice point) simulations.