Experimental Simulation of Bosonic Creation and Annihilation Operators in a Quantum Processor

TL;DR

This paper introduces a quantum algorithm to simulate bosonic creation and annihilation operators using a two-qubit ancillary system, demonstrated experimentally with high fidelity on an NMR processor, advancing quantum control techniques.

Contribution

It presents a novel quantum algorithm for simultaneously implementing bosonic creation and annihilation operators using linear combinations of unitaries, experimentally validated on a 4-qubit NMR system.

Findings

Achieved creation and annihilation operator realization with over 96% fidelity.

Successfully demonstrated the algorithm via full state tomography.

Enabled quantum random walk with arbitrary initial states.

Abstract

The ability of implementing quantum operations plays fundamental role in manipulating quantum systems. Creation and annihilation operators which transform a quantum state to another by adding or subtracting a particle are crucial of constructing quantum description of many body quantum theory and quantum field theory. Here we present a quantum algorithm to perform them by the linear combination of unitary operations associated with a two-qubit ancillary system. Our method can realize creation and annihilation operators simultaneously in the subspace of the whole system. A prototypical experiment was performed with a 4-qubit Nuclear Magnetic Resonance processor, demonstrating the algorithm via full state tomography. The creation and annihilation operators are realized with a fidelity all above 96% and a probability about 50%. Moreover, our method can be employed to quantum random walk in an arbitrary initial state. With the prosperous development of quantum computing, our work provides a quantum control technology to implement non-unitary evolution in near-term quantum computer.