Δ-Quantum machine learning for medicinal chemistry

Many molecular design tasks benefit from fast and accurate calculations of quantum-mechanical (QM) properties. However, the computational cost of QM methods applied to drug-like molecules currently renders large-scale applications of quantum chemistry challenging. Aiming to mitigate this problem, we developed DelFTa, an open-source toolbox for the prediction of electronic properties of drug-like molecules at the density functional (DFT) level of theory, using Δ-machine-learning. Δ-Learning corrects the prediction error (Δ) of a fast but inaccurate property calculation. DelFTa employs state-of-the-art three-dimensional message-passing neural networks trained on a large dataset of QM properties. It provides access to a wide array of quantum observables on the molecular, atomic and bond levels by predicting approximations to DFT values from a low-cost semiempirical baseline. Δ-Learning outperformed its direct-learning counterpart for most of the considered QM endpoints. The results suggest that predictions for non-covalent intra- and intermolecular interactions can be extrapolated to larger biomolecular systems. The software is fully open-sourced and features documented command-line and Python APIs.

Error mitigation with Clifford quantum-circuit data

Achieving near-term quantum advantage will require accurate estimation of quantum observables despite significant hardware noise. For this purpose, we propose a novel, scalable error-mitigation method that applies to gate-based quantum computers. The method generates training data {Xinoisy,Xiexact} via quantum circuits composed largely of Clifford gates, which can be efficiently simulated classically, where Xinoisy and Xiexact are noisy and noiseless observables respectively. Fitting a linear ansatz to this data then allows for the prediction of noise-free observables for arbitrary circuits. We analyze the performance of our method versus the number of qubits, circuit depth, and number of non-Clifford gates. We obtain an order-of-magnitude error reduction for a ground-state energy problem on 16 qubits in an IBMQ quantum computer and on a 64-qubit noisy simulator.

Open-source Δ-quantum machine learning for medicinal chemistry

Certain molecular design tasks benefit from fast and accurate calculations of quantum-mechanical (QM) properties. However, the computational cost of QM methods applied to drug-like compounds currently makes large-scale applications of quantum chemistry challenging. In order to mitigate this problem, we developed DelFTa, an open-source toolbox for predicting small-molecule electronic properties at the density functional (DFT) level of theory, using the Δ-machine learning principle. DelFTa employs state-of-the-art E(3)-equivariant graph neural networks that were trained on the QMugs dataset of QM properties. It provides access to a wide array of quantum observables by predicting approximations to ωB97X-D/def2-SVP values from a GFN2-xTB semiempirical baseline. Δ-learning with DelFTa was shown to outperform direct DFT learning for most of the considered QM endpoints. The software is provided as open-source code with fully-documented command-line and Python APIs.

Classical Limit of Quantum Mechanics for Damped Driven Oscillatory Systems: Quantum–Classical Correspondence

The investigation of quantum–classical correspondence may lead to gaining a deeper understanding of the classical limit of quantum theory. I have developed a quantum formalism on the basis of a linear invariant theorem, which gives an exact quantum–classical correspondence for damped oscillatory systems perturbed by an arbitrary force. Within my formalism, the quantum trajectory and expectation values of quantum observables precisely coincide with their classical counterparts in the case where the global quantum constant ℏ has been removed from their quantum results. In particular, I have illustrated the correspondence of the quantum energy with the classical one in detail.

General Non-Markovian Quantum Dynamics

A general approach to the construction of non-Markovian quantum theory is proposed. Non-Markovian equations for quantum observables and states are suggested by using general fractional calculus. In the proposed approach, the non-locality in time is represented by operator kernels of the Sonin type. A wide class of the exactly solvable models of non-Markovian quantum dynamics is suggested. These models describe open (non-Hamiltonian) quantum systems with general form of nonlocality in time. To describe these systems, the Lindblad equations for quantum observable and states are generalized by taking into account a general form of nonlocality. The non-Markovian quantum dynamics is described by using integro-differential equations with general fractional derivatives and integrals with respect to time. The exact solutions of these equations are derived by using the operational calculus that is proposed by Yu. Luchko for general fractional differential equations. Properties of bi-positivity, complete positivity, dissipativity, and generalized dissipativity in general non-Markovian quantum dynamics are discussed. Examples of a quantum oscillator and two-level quantum system with a general form of nonlocality in time are suggested.

Quantum Violation of the Suppes-Zanotti Inequalities and “Contextuality”

The Suppes-Zanotti inequalities involving the joint expectations of just three binary quantum observables are (re-)derived by the hull computation of the respective correlation polytope. A min-max calculation reveals its maximal quantum violations correspond to a generalized Tsirelson bound. Notions of “contextuality” motivated by such violations are critically reviewed.

The Phase Space Model of Nonrelativistic Quantum Mechanics

We focus on several questions arising during the modelling of quantum systems on a phase space. First, we discuss the choice of phase space and its structure. We include an interesting case of discrete phase space. Then, we introduce the respective algebras of functions containing quantum observables. We also consider the possibility of performing strict calculations and indicate cases where only formal considerations can be performed. We analyse alternative realisations of strict and formal calculi, which are determined by different kernels. Finally, two classes of Wigner functions as representations of states are investigated.