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The Journal of Chemical Physics

Hybrid mechanics of coupled qubits

Merfat Alzomai, Dmitrii V. Shalashilin

Published Oct 28, 2026• 0 citations
PDF (CC BY)Publisher

Abstract

We find that a technique analogous to hybrid mechanics previously developed for Gaussian coherent states and molecular vibrations, can be extended to SU(2) coherent states describing coupled qubits. This formulation reveals a sparse structure of the propagator, leading to a computationally efficient scheme while maintaining numerical accuracy. As a result, the method enables simulations of larger qubit systems on classical computers. In particular, we demonstrate accurate real-time propagation for systems of up to 21 qubits, which would be computationally demanding using straightforward quantum-dynamics approaches.

DOI
10.1063/5.0349433

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We find that a technique analogous to hybrid mechanics previously developed for Gaussian coherent states and molecular vibrations, can be extended to SU(2) coherent states describing coupled qubits. This formulation reveals a sparse structure of the propagator, leading to a computationally efficient scheme while maintaining numerical accuracy. As a result, the method enables simulations of larger qubit systems on classical computers. In particular, we demonstrate accurate real-time propagation for systems of up to 21 qubits, which would be computationally demanding using straightforward quantum-dynamics approaches.
This paper explores the potential of a hybrid quantum-classical simulation approach to accelerate the simulation of complex molecular systems. Traditional molecular dynamics (MD) simulations are computationally expensive, particularly for large systems and long timescales. This research proposes a novel method that leverages the strengths of both quantum computing and classical computing to address these limitations. The core mechanism involves strategically employing quantum computation to expedite computationally demanding aspects of the MD process, while relying on classical methods for the majority of the simulation. We present a detailed framework for integrating these techniques, demonstrating the benefits of this hybrid approach through simulations of a prototypical molecular system – a small molecule with a defined structure. The results highlight the significant speed-up potential offered by this hybrid system, offering a pathway toward more efficient and comprehensive molecular dynamics studies.
The coupled coherent states method has demonstrated itself as an accurate and efficient method of studying the quantum dynamics of various systems. In recent years, its applicability has been extended by incorporating a number of new numerical expansions and modifications to generate a closely related family of methods. In this thesis, two new augmentations are developed to further broaden the scope of problems that are able to be treated. The first of these is a 2-layer extension of coupled coherent states, capable of providing an increased mathematical description of a degree or degrees of freedom within a quantum mechanical system, as well as beneficial numerical and scalability properties. The newly developed method is tested on a model system-bath Hamiltonian consisting of a tunnelling mode governed by an asymmetric double well potential coupled to a harmonic bath. It is found to compare well to previous methods of studying the Hamiltonian, as well as a benchmark calculation on the system conducted in this thesis, and demonstrate the beneficial numerical and scalability properties expected. The second development is to extend coupled coherent states to treat systems of indistinguishable bosons in the second quantisation representation. The method is tested on the same Hamiltonian as the 2-layer coupled coherent states scheme, where the harmonic bath is second quantised as it is comprised of oscillators of the same frequency, so they may be thought of as indistinguishable. Exploiting this symmetry property is found to be extremely advantageous, with remarkable agreement to the benchmark calculation. The method is then tested on a model Hamiltonian consisting of 100 bosons in a shifted harmonic trap, with oscillations in the 1-body density calculated. The results are found to compare favourably with a multiconfigurational time-dependent Hartree for bosons calculation that is equivalent to the Gross-Pitaevskii equation, providing impetus for future studies on systems of Bose-Einstein condensates. The existing ab initio multiple cloning extension of coupled coherent states for nonadiabatic dynamics is also used to study the ultrafast photodissociation of 2-ethylpyrrole. The results are compared to experimental data, and a novel insight into the dissociation mechanism is obtained, with it shown to be composed of a two step process. Firstly, molecules that are able to dissociate immediately over the barrier along the N-H coordinate do so in < 50 fs, and this is followed by a second slower dissociation process from molecules that must sample the potential energy surface before finding a way around the barrier. This is not observed experimentally due to the temporal widths of the laser pulses obscuring the dynamics in the < 50 fs window.
In a previous paper [J. S. Briggs and A. Eisfeld, Phys. Rev. A 85, 052111 (2012)] we showed that the time development of the complex amplitudes of NNN coupled quantum states can be mapped by the time development of positions and velocities of NNN coupled classical oscillators. Here we examine to what extent this mapping can be realized to simulate the ``quantum,'' properties of entanglement and qubit manipulation. By working through specific examples, e.g., of quantum gate operation, we seek to illuminate quantum and classical differences which hitherto have been treated more mathematically. In addition, we show that important quantum coupled phenomena, such as the Landau-Zener transition and the occurrence of Fano resonances can be simulated by classical oscillators.
Modern computational techniques used to simulate quantum chemistry are on the boundary of tractability due to the exponential growth of the molecular wavefunction, requiring a careful balance between molecule size and simulation accuracy. In recent years, quantum computing has risen in popularity as a potential alternative to conventional (classical) techniques; however, most methods rely on access to "digital" quantum computers composed of qubits and quantum gates, which at present are severely limited by noise. We have developed a real-time, analog approach to simulate vibronic chemical dynamics with existing quantum technology. Our approach uses an intuitive mapping of molecular electronic and vibrational degrees of freedom onto quantum resonators and qudit (d-level system) states, with controllable couplings between degrees of freedom. The measurement output can be mapped onto different time-dependent observables, including the time-domain simulation of vibronic spectra. Our approach can also incorporate controlled sources of noise to simulate system-bath interactions and dissipative dynamics at a minimal cost. We present experimental results using a trapped-ion device, thus showing the potential for near-term simulation of chemical dynamics in complex environments beyond the abilities of classical computers.
Zombie states are a recently introduced formalism to describe coupled coherent fermionic states that address the fermionic sign problem in a computationally tractable manner. Previously, it has been shown that Zombie states with fractional occupations of spin orbitals obeyed the correct fermionic creation and annihilation algebra and presented results for real-time evolution [D. V. Shalashilin, J. Chem. Phys. 148, 194109 (2018)]. In this work, we extend and build on this formalism by developing efficient algorithms for evaluating the Hamiltonian and other operators between Zombie states and address their normalization. We also show how imaginary time propagation can be used to find the ground state of a system. We also present a biasing method, for setting up a basis set of random Zombie states, that allows much smaller basis sizes to be used while still accurately describing the electronic structure Hamiltonian and its ground state and describe a technique of wave function "cleaning" that removes the contributions of configurations with the wrong number of electrons, improving the accuracy further. We also show how low-lying excited states can be calculated efficiently using a Gram-Schmidt orthogonalization procedure. The proposed algorithm of imaginary time propagation on biased random grids of Zombie states may present an alternative to the existing quantum Monte Carlo methods.