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arXiv:1902.08257 · Scientific Reports

Assessing the quantumness of the annealing dynamics via Leggett Garg’s inequalities: a weak measurement approach

Vittorio Vitale, G. De Filippis, ANTONIO DE CANDIA, A. Tagliacozzo, V. Cataudella, Procolo Lucignano

Published Sep 20, 2019• 3 citations
arXivHTMLPDF

Abstract

Adiabatic quantum computation (AQC) is a promising counterpart of universal quantum computation, based on the key concept of quantum annealing (QA). QA is claimed to be at the basis of commercial quantum computers and benefits from the fact that the detrimental role of decoherence and dephasing seems to have poor impact on the annealing towards the ground state. While many papers show interesting optimization results with a sizable number of qubits, a clear evidence of a full quantum coherent behavior during the whole annealing procedure is still lacking. In this paper we show that quantum non-demolition (weak) measurements of Leggett Garg inequalities can be used to efficiently assess the quantumness of the QA procedure. Numerical simulations based on a weak coupling Lindblad approach are compared with classical Langevin simulations to support our statements.

DOI
10.1038/s41598-019-50081-8

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Adiabatic quantum computation (AQC) is a promising counterpart of universal quantum computation, based on the key concept of quantum annealing (QA). QA is claimed to be at the basis of commercial quantum computers and benefits from the fact that the detrimental role of decoherence and dephasing seems to have poor impact on the annealing towards the ground state. While many papers show interesting optimization results with a sizable number of qubits, a clear evidence of a full quantum coherent behavior during the whole annealing procedure is still lacking. In this paper we show that quantum non-demolition (weak) measurements of Leggett Garg inequalities can be used to efficiently assess the quantumness of the QA procedure. Numerical simulations based on a weak coupling Lindblad approach are compared with classical Langevin simulations to support our statements.
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The realization of quantum adiabatic dynamics is at the core of implementations of adiabatic quantum computers. One major issue is to efficiently compromise between the long time scales required by the adiabatic protocol and the detrimental effects of the environment, which set an upper bound to the time scale of the operation. In this work we propose a protocol which achieves fast adiabatic dynamics by coupling the system to an external environment by the means of a quantum-non-demolition (QND) Hamiltonian. We analyse the infidelity of adiabatic transfer for a Landau-Zener problem in the presence of QND measurement, where the qubit couples to a meter which in turn quickly dissipates. We analyse the protocol's fidelity as a function of the strength of the QND coupling and of the relaxation time of the meter. In the limit where the decay rate of the ancilla is the largest frequency scale of the dynamics, the QND coupling induces an effective dephasing in the adiabatic basis. Optimal conditions for adiabaticity are found when the coupling with the meter induces dissipative dynamics which suppresses unwanted diabatic transitions.
In this dissertation, we explore how quantum annealing (QA) and its applications behave in an open system setting. We give derivations and numerical recipes for effective parallel simulation methods for time-dependent open dynamics of quantum annealing devices. We consider the weak-coupling limit to an environment and also the case of 1/f1/f1/f noise. The stochastic time-dependent quantum trajectories technique can be utilized in studying weak measurements and feedback error correction in quantum annealing. Then we focus on opensystem descriptions of reverse annealing (RA), which is a promising variant and application of quantum annealing. We show that, with various simulation tools, reverse annealing can benefit from the interaction between the annealer and its environment.