Simulating open quantum dynamics on an NMR quantum processor using the Sz.-Nagy dilation algorithm

Abstract

We experimentally implement the Sz.-Nagy dilation algorithm to simulate open quantum dynamics on an nuclear magnetic resonance (NMR) quantum processor. The Sz.-Nagy algorithm enables the simulation of the dynamics of arbitrary-dimensional open quantum systems, using only a single ancilla qubit. We experimentally simulate the action of two non-unitary processes, namely, a phase damping channel acting independently on two qubits and a magnetic field gradient pulse (MFGP) acting on an ensemble of two coupled nuclear spin-1/2 particles. To evaluate the quality of the experimentally simulated quantum process, we perform convex optimization-based full quantum process tomography to reconstruct the quantum process from the experimental data and compare it with the target quantum process to be simulated.

Quantum State Preparation and Non-Unitary Evolution with Diagonal Operators

“…Current quantum devices are typically unitary-gate-based, so non-unitary operators must be cast as unitary in order to be practically implementable. There are a variety of algorithms which have been developed to bypass this obstacle, including explicit mathematical dilations [8][9][10][11][12][13][14], quantum imaginary time evolution [15], duality [16,17], the variational principal [18], collision models [19], analog simulation [20], and others [21][22][23][24][25][26][27][28][29][30][31][32]. The majority of these algorithms rely on some form of dilation, either mapping the operator to a larger Hilbert space, or adding ancilla qubits.…”