We present the first quantum computing simulation of wavepacket dynamics in an HO 2 –water cluster. These systems are of great interest in atmospheric chemistry and, due to anharmonicity, can display multidimensional quantum nuclear effects arising from delocalized hydrogen bond networks. Here, we utilize the Quantum Shannon Decomposition (QSD) method to represent a quantum propagator for the nuclear degrees of freedom of the HO 2 radical interacting with one and two water molecules, in the presence of an electronic potential energy surface, and in terms of the R y, R z, and CNOT quantum gates. The resultant time evolution of the quantum wavepacket, constructed by using the Qiskit quantum simulation tool, with a Python driver, yields a vibrational spectrum that is in very good agreement with the classically obtained result. The numerical demonstration here is restricted to one- and two-nuclear dimensions and hence is a proof of principle, but future implementations will include novel tensor network strategies to reduce quantum circuit depth and expand to higher dimensions.
We present the first quantum computing simulation of wavepacket dynamics in an HO 2 –water cluster. These systems are of great interest in atmospheric chemistry and, due to anharmonicity, can display multidimensional quantum nuclear effects arising from delocalized hydrogen bond networks. Here, we utilize the Quantum Shannon Decomposition (QSD) method to represent a quantum propagator for the nuclear degrees of freedom of the HO 2 radical interacting with one and two water molecules, in the presence of an electronic potential energy surface, and in terms of the R y, R z, and CNOT quantum gates. The resultant time evolution of the quantum wavepacket, constructed by using the Qiskit quantum simulation tool, with a Python driver, yields a vibrational spectrum that is in very good agreement with the classically obtained result. The numerical demonstration here is restricted to one- and two-nuclear dimensions and hence is a proof of principle, but future implementations will include novel tensor network strategies to reduce quantum circuit depth and expand to higher dimensions.
The accurate computational study of wavepacket nuclear dynamics is considered to be a classically intractable problem, particularly with increasing dimensions. Here, we present two algorithms that, in conjunction with other methods developed by us, may result in one set of contributions for performing quantum nuclear dynamics in arbitrary dimensions. For one of the two algorithms discussed here, we present a direct map between the Born-Oppenheimer Hamiltonian describing the nuclear wavepacket time evolution and the control parameters of a spin-lattice Hamiltonian that describes the dynamics of qubit states in an ion-trap quantum computer. This map is exact for three qubits, and when implemented, the dynamics of the spin states emulates those of the nuclear wavepacket in a continuous representation. However, this map becomes approximate as the number of qubits grows. In a second algorithm, we present a general quantum circuit decomposition formalism for such problems using a method called the Quantum Shannon Decomposition. This algorithm is more robust and is exact for any number of qubits at the cost of increased circuit complexity. The resultant circuit is implemented on IBM's quantum simulator (QASM) for 3-7 qubits, without using a noise model so as to test the intrinsic accuracy of the method. In both cases, the wavepacket dynamics is found to be in good agreement with the classical propagation result and the corresponding vibrational frequencies obtained from the wavepacket density time evolution are in agreement to within a few tenths of a wavenumber.
We present an approach based on tensor networks for distributed quantum computing simulation of chemical wavepacket dynamics in a continuous variable representation. The central idea is that the tensor-network representation of the multidimensional time-evolution operator naturally induces an elevated Hilbert space where the dynamics decomposes into a set of independent lower-dimensional propagations. This transformation converts an entangled quantum evolution into a set of parallel computational tasks that can be executed asynchronously across heterogeneous quantum and classical computing architectures. The resulting formalism establishes a direct connection between tensor-network decompositions, uniformly controlled quantum circuits, and asynchronous distributed quantum computing. The approach is developed with a goal towards hybrid quantum/classical implementation, and is appropriate for a general heterogeneous mixture of quantum hardware systems. The experimental realization of the asynchronously distributed quantum processes that arise from the tensor-network decomposition are carried out on the Sandia National Laboratories' trapped-ion quantum computer, where the circuits are compiled using native partial-entangling XX(θ) gates, reducing the expected two-qubit gate infidelity by more than 30\% relative to conventional fully entangling decompositions. We demonstrate the methodology by quantum computing the vibrational spectra of a small protonated water cluster that shows critical quantum nuclear behavior. Such water cluster systems have been found to be challenging for experimental action spectroscopy and for theory, and here, for the first time, we provide results for vibrational spectroscopy that are in agreement with the respective classical results to within 4cm−1, thus allowing for the potential for spectroscopic accuracy from quantum computations.
Quantum nuclear dynamics with wavepacket time evolution is classically intractable and viewed as a promising avenue for quantum information processing. Here, we use IonQ, Inc.'s 11-qubit trapped-ion quantum computer, Harmony, to study the quantum wavepacket dynamics of a shared-proton within a short-strong hydrogen-bonded system. We also provide the first application of distributed quantum computing for chemical dynamics problems, where a distributed set of quantum processes is constructed using a tensor network formalism. For a range of initial states, we experimentally drive the ion-trap system to emulate the quantum nuclear wavepacket as it evolves along the potential surface generated from the electronic structure. Following the experimental creation of the nuclear wavepacket, we extract measurement observables such as its time-dependent spatial projection and its characteristic vibrational frequencies to good agreement with classical results. Vibrational eigenenergies obtained from quantum computation are in agreement with those obtained from classical simulations to within a fraction of a kilocalorie per mole, thus suggesting chemical accuracy. Our approach opens a new paradigm for studying the quantum chemical dynamics and vibrational spectra of molecules and also provides the first demonstration of parallel quantum computation on a distributed set of ion-trap quantum computers.
ConspectusSimulating molecular dynamics (MD) within a comprehensive quantum framework has been a long-standing challenge in computational chemistry. An exponential scaling of computational cost renders solving the time dependent Schrödinger equation (TDSE) of a molecular Hamiltonian, including both electronic and nuclear degrees of freedom (DOFs), as well as their couplings, infeasible for more than a few DOFs. In the Born-Oppenheimer (BO), or adiabatic, picture, electronic and nuclear parts of the wave function are decoupled and treated separately. Within this framework, the nuclear wave function evolves along potential energy surfaces (PESs) computed as solutions to the electronic Schrödinger equation parametrized in the nuclear DOFs. This approximation, together with increasingly elaborate numerical approaches to solve the nuclear time dependent Schrödinger equation (TDSE), enabled the treatment of up to a few dozens of degrees of freedom (DOFs). However, for particular applications, such as photochemistry, the BO approximation breaks down. In this regime of non-adiabatic dynamics, solving the full molecular problem including electron-nuclear couplings becomes essential, further increasing the complexity of the numerical solution. Although valuable methods such as multiconfigurational time-dependent Hartree (MCTDH) have been proposed for the solution of the coupled electron-nuclear dynamics, they remain hampered by an exponential scaling in the number of nuclear DOFs and by the difficulty of finding universal variational forms.In this Account, we present a perspective on novel quantum computational algorithms, aiming to alleviate the exponential scaling inherent to the simulation of many-body quantum dynamics. In particular, we focus on the derivation and application of quantum algorithms for adiabatic and non-adiabatic quantum dynamics, which include efficient approaches for the calculation of the BO potential energy surfaces (PESs). Thereafter, we study the time-evolution of a model system consisting of two coupled PESs in first and second quantization. In a first application, we discuss a recently introduced quantum algorithm for the evolution of a wavepacket in first quantization and exploit the potential quantum advantage of mapping its spatial grid representation to logarithmically many qubits. For the second demonstration, we move to the second quantization framework and review the scaling properties of two alternative time-evolution algorithms, namely, a variational quantum algorithm (VQA) (based on the McLachlan variational principle) and conventional Trotter-type evolution (based on a Lie-Trotter-Suzuki formula). Both methods clearly demonstrate the potential of quantum algorithms and their favorable scaling compared to the available classical approaches. However, a clear demonstration of quantum advantage in the context of molecular quantum dynamics may require the implementation of these algorithms in fault-tolerant quantum computers, while their application in near-term, noisy quantum devices is still unclear and deserves further investigation.
Calculating observable properties of chemical systems is often classically intractable and widely viewed as a promising application of quantum information processing. Here, we introduce a new framework for solving generic quantum chemical dynamics problems using quantum logic. We experimentally demonstrate a proof-of-principle instance of our method using the QSCOUT ion-trap quantum computer, where we experimentally drive the ion-trap system to emulate the quantum wavepacket dynamics corresponding to the shared-proton within an anharmonic hydrogen bonded system. Following the experimental creation and propagation of the shared-proton wavepacket on the ion-trap, we extract measurement observables such as its time-dependent spatial projection and its characteristic vibrational frequencies to spectroscopic accuracy (3.3 cm –1 wavenumbers, corresponding to >99.9% fidelity). Our approach introduces a new paradigm for studying the chemical dynamics and vibrational spectra of molecules and opens the possibility to describe the behavior of complex molecular processes with unprecedented accuracy.
The exponential scaling of the quantum degrees of freedom with the size of the system is one of the biggest challenges in computational chemistry and particularly in quantum dynamics. We present a tensor network approach for the time-evolution of the nuclear degrees of freedom of multiconfigurational chemical systems at a reduced storage and computational complexity. We also present quantum algorithms for the resultant dynamics. To preserve the compression advantage achieved via tensor network decompositions, we present an adaptive algorithm for the regularization of nonphysical bond dimensions, preventing the potentially exponential growth of these with time. While applicable to any quantum dynamical problem, our method is particularly valuable for dynamical simulations of nuclear chemical systems. Our algorithm is demonstrated using ab initio potentials obtained for a symmetric hydrogen-bonded system, namely, the protonated 2,2'-bipyridine, and compared to exact diagonalization numerical results.