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arXiv:quant-ph/0310188

Simulation of quantum interference by reactions of chemical type

Yuri Ozhigov

Published Oct 31, 2003• 0 citations
arXivHTMLPDF

Abstract

A quantum unitary evolution alternated with measurements is simulated by a bubble filled with fictitious particles called amplitude quanta that move chaotically and can be transformed by the simple rules that look like chemical reactions. A basic state of simulated system is treated as a collision of the two corresponding amplitude quanta, that gives the quantum statistics of measurements. The movement of the external membrane of the bubble corresponds to the classical dynamics of the simulated system. Measurements are treated as the membrane perforations and they are completely determined by initial conditions. An identity of particles and an entanglement is simulated by the membranes touching. The required memory grows linearly where the number of particles increases, but entangled states of the big number of particles can be simulated. The method can be used for a visualization of quantum dynamics.

DOI
10.48550/arxiv.quant-ph/0310188

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A quantum unitary evolution alternated with measurements is simulated by a bubble filled with fictitious particles called amplitude quanta that move chaotically and can be transformed by the simple rules that look like chemical reactions. A basic state of simulated system is treated as a collision of the two corresponding amplitude quanta, that gives the quantum statistics of measurements. The movement of the external membrane of the bubble corresponds to the classical dynamics of the simulated system. Measurements are treated as the membrane perforations and they are completely determined by initial conditions. An identity of particles and an entanglement is simulated by the membranes touching. The required memory grows linearly where the number of particles increases, but entangled states of the big number of particles can be simulated. The method can be used for a visualization of quantum dynamics.
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Simulations of chemical dynamics are a powerful means for understanding chemistry. However, classical computers struggle to simulate many chemical processes, especially non-adiabatic ones, where the Born-Oppenheimer approximation breaks down. Quantum computers could simulate quantum-chemical dynamics more efficiently than classical computers, but there is currently no complete quantum algorithm for calculating dynamical observables to within a known error. Here, we develop an efficient, end-to-end quantum algorithm for simulating chemical dynamics that avoids all uncontrolled approximations (including the Born-Oppenheimer approximation) and whose error is bounded subject to mild assumptions. To do so, we treat the nuclei and the electrons on an equal footing and simulate the full molecular wavefunction on a momentum-space grid in first quantization, including all algorithmic steps: initial-state preparation, time evolution using qubitization, and measurement of chemical observables such as reaction yields and rates. Our work gives the first algorithm for quantum simulation of chemistry whose end-to-end complexity achieves sublinear scaling in the size of the grid. We achieve this by developing an exponentially faster method for initial-state-preparation. Photochemistry is a likely early application of our algorithm and we estimate resources required for end-to-end simulations of non-adiabatic dynamics of atmospherically important molecules. Classically intractable photochemical computations could be performed using resources comparable to those required for other chemical applications of quantum computing.
Quantum computers can potentially simulate quantum-mechanical phenomena, so chemical reactions are a potential application of them. In particular, the time evolution of the wavefunctions should be simulated because chemical reactions are accompanied by structural changes. In this study, to pave the way to achieving such wavefunction simulations, we decompose chemical reactions into their main parts and comprehensively show the minimum essential circuits for simulating each part. An antisymmetrized initial state is constructed using ancillae. Chemical reactions should be simulated in two different ways, where the difference is whether the ancillae are released or not. When they are released, the whole electronic system is simulated. When they are not released, orbital information is obtained. These ways are hence complementary.
This paper explores the potential of quantum computing for simulating complex chemical reactions. Traditional classical computational methods often struggle with the inherent quantum mechanical nature of chemical systems, particularly when dealing with large molecules and intricate reaction pathways. This work proposes a novel quantum algorithm leveraging superposition and entanglement to directly simulate the time evolution of these systems. The core of the algorithm centers on a time-dependent Schrödinger equation (TDSE) implemented on a quantum computer. We outline the key elements, including the encoding of molecular states, the construction of a suitable Hamiltonian operator, and the execution of the quantum algorithm to obtain the final state of the system. The efficiency gains compared to classical methods, particularly for reactions involving significant quantum effects, are discussed. Furthermore, we highlight the potential impact of this technology on accelerating drug discovery, materials science, and fundamental chemical research. The algorithm's core relies on the ability of a quantum computer to perform a vast number of calculations simultaneously, offering a substantial advantage over classical computers when simulating quantum systems.
A simple collision model is employed to introduce elementary concepts of open system dynamics of quantum systems. In particular, within the framework of collision models we introduce the quantum analogue of thermalization process called quantum homogenization and simulate quantum decoherence processes. These dynamics are driven by partial swaps and controlled unitary collisions, respectively. We show that collision models can be used to prepare multipartite entangled states. Partial swap dynamics generates W-type of entanglement saturating the CKW inequalities, whereas the decoherence collision models creates GHZ-type of entangled states. The considered evolution of a system in a sequence of collisions is described by a discrete semigroup E_1,...,E_n. Interpolating this discrete points within the set of quantum channels we derive for both processes the corresponding Lindblad master equations. In particular, we argue that collision models can be used as simulators of arbitrary Markovian dynamics, however, the inverse is not true.