Ionic pseudopotentials are widely used in classical simulations of materials to model the effective potential due to the nucleus and the core electrons. Modeling fewer electrons explicitly results in a reduction in the number of plane waves needed to accurately represent the states of a system. In this work, we introduce a quantum algorithm that uses pseudopotentials to reduce the cost of simulating periodic materials on a quantum computer. We use a qubitization-based quantum phase estimation algorithm that employs a first-quantization representation of the Hamiltonian in a plane-wave basis. We address the challenge of incorporating the complexity of pseudopotentials into quantum simulations by developing highly-optimized compilation strategies for the qubitization of the Hamiltonian. This includes a linear combination of unitaries decomposition that leverages the form of separable pseudopotentials. Our strategies make use of quantum read-only memory subroutines as a more efficient alternative to quantum arithmetic. We estimate the computational cost of applying our algorithm to simulating lithium-excess cathode materials for batteries, where more accurate simulations are needed to inform strategies for gaining reversible access to the excess capacity they offer. We estimate the number of qubits and Toffoli gates required to perform sufficiently accurate simulations with our algorithm for three materials: lithium manganese oxide, lithium nickel-manganese oxide, and lithium manganese oxyfluoride. Our optimized compilation strategies result in a pseudopotential-based quantum algorithm with a total Toffoli cost four orders of magnitude lower than the previous state of the art for a fixed target accuracy.
Ionic pseudopotentials are widely used in classical simulations of materials to model the effective potential due to the nucleus and the core electrons. Modeling fewer electrons explicitly results in a reduction in the number of plane waves needed to accurately represent the states of a system. In this work, we introduce a quantum algorithm that uses pseudopotentials to reduce the cost of simulating periodic materials on a quantum computer. We use a qubitization-based quantum phase estimation algorithm that employs a first-quantization representation of the Hamiltonian in a plane-wave basis. We address the challenge of incorporating the complexity of pseudopotentials into quantum simulations by developing highly-optimized compilation strategies for the qubitization of the Hamiltonian. This includes a linear combination of unitaries decomposition that leverages the form of separable pseudopotentials. Our strategies make use of quantum read-only memory subroutines as a more efficient alternative to quantum arithmetic. We estimate the computational cost of applying our algorithm to simulating lithium-excess cathode materials for batteries, where more accurate simulations are needed to inform strategies for gaining reversible access to the excess capacity they offer. We estimate the number of qubits and Toffoli gates required to perform sufficiently accurate simulations with our algorithm for three materials: lithium manganese oxide, lithium nickel-manganese oxide, and lithium manganese oxyfluoride. Our optimized compilation strategies result in a pseudopotential-based quantum algorithm with a total Toffoli cost four orders of magnitude lower than the previous state of the art for a fixed target accuracy.
The first-principles quantum simulation of the full electronic Hamiltonian of a material model of realistic size appears daunting even in a future era of fully fault-tolerant quantum computers. In contrast, classical simulations of material excited states rely on heuristic quasiparticle frameworks, such as the GW approximation and Bethe-Salpeter equation, where only a few quasiparticles are explicitly considered. Here we give a detailed description of quasiparticle quantum simulation for multi-excitonic states within the BSE. We develop an explicit first-quantized, orbital-based block encoding of the multi-exciton BSE Hamiltonian for qubitization, and reduce its cost using integral factorization and crystal symmetries. For a materials model of size N, and a fixed number of quasiparticles, the resulting algorithms require O(N) Toffoli gates and O(logN) logical qubits, or, using space-time tradeoffs, O(N) Toffoli gates and O(N) logical qubits, achieving up to a sixth power reduction in Toffoli count, or up to exponential reduction in qubit count, versus standard full Hamiltonian simulation techniques that have been explored in materials simulation. Resource estimates for the classically challenging problem of triexcitonic eigenvalue estimation across a range of semiconductor models of a realistic physical size of O(103) atoms, show that our Toffoli-optimized implementation reduces the Toffoli count by 106−107 relative to full Hamiltonian simulation estimates, while a qubit-optimized implementation requires only a few hundred logical qubits. More broadly, these results show that classical heuristic frameworks will be essential in the design of future fault-tolerant quantum algorithms for materials.
There is a pressing need to develop new rechargeable battery technologies that can offer higher energy storage, faster charging, and lower costs. Despite the success of existing methods for the simulation of battery materials, they can sometimes fall short of delivering accurate and reliable results. Quantum computing has been discussed as an avenue to overcome these issues, but only limited work has been done to outline how it may impact battery simulations. In this work, we provide a detailed answer to the following question: how can a quantum computer be used to simulate key properties of a lithium-ion battery? Based on recently introduced first-quantization techniques, we lay out an end-to-end quantum algorithm for calculating equilibrium cell voltages, ionic mobility, and thermal stability. These can be obtained from ground-state energies of materials, which are the core calculations executed by the quantum computer using qubitization-based quantum phase estimation. The algorithm includes explicit methods for preparing approximate ground states of periodic materials in first quantization. We bring these insights together to estimate the resources required to implement a quantum algorithm for simulating a realistic cathode material, dilithium iron silicate.
This paper improves and demonstrates the usefulness of the first quantized plane-wave algorithms for the quantum simulation of electronic structure. We describe our quantum algorithm for first quantized simulation that accurately includes pseudopotentials. We focus on the Goedecker-Tetter-Hutter pseudopotential, and despite its complicated form, we block encode the associated operator without significantly increasing the overall cost of quantum simulation. This is surprising since simulating the nuclear potential is much simpler without pseudopotentials, yet is still the bottleneck. We also generalize prior methods to enable the simulation of materials with non-cubic unit cells, which requires nontrivial modifications. Finally, we combine these techniques to estimate block-encoding costs for commercially relevant instances of heterogeneous catalysis (e.g. carbon monoxide adsorption) and compare to the quantum resources needed to simulate materials in second quantization. We conclude that for computational cells with many particles, first quantization often requires meaningfully less spacetime volume.
Advancing battery materials is crucial for sustainable infrastructure, EVs and renewable energy storage. By achieving polynomial scaling for exact electronic structure simulations of materials, quantum computing could emerge as an invaluable tool in this field. In this work, we address two fundamental aspects related to the application of quantum algorithms to lithium diffusion in solid state electrolytes, which have the potential to significantly improve safety and performance of current battery technologies. First of all, we discuss the need for the higher level of accuracy provided by quantum computing. Classical computational methods routinely applied to compute the properties of solid state electrolytes are based on semi-local approximations of density functional theory (DFT). Considering cluster models representative of the properties of the bulk Li10GeP2S12(LGPS) electrolyte, we benchmark several functionals, including state-of-the-art hybrid approximations and compare the results to high-level wavefunction methods. The classical results for lithium diffusion barriers exhibit a variability exceeding the chemical accuracy threshold required for experimentally relevant precision, underscoring the necessity for exact quantum solutions as a reference. Secondly, we perform quantum simulations for lithium diffusion barriers using small active spaces of the cluster models and use those results to extrapolate the minimal resources required for a full simulation of bulk LGPS. Specifically, the variational quantum eigensolver (VQE) with a quantum number preserving ansatz and the quantum Krylov (qK) method are considered. The resource estimations for VQE show that a few hundred qubits and less than one million two-qubit gates could be sufficient to simulate LGPS. For qK the number of required two-qubit gates increases by orders of magnitude. However, for large models it should also be considered that qK avoids the complex non-linear optimization problem involved in VQE. Future advancements in quantum algorithms will be essential for bringing simulations of materials closer to realization.
X-ray absorption spectroscopy (XAS) is a leading technique for understanding structural changes in advanced battery materials such as lithium-excess cathodes. However, extracting critical information like oxidation states from the experimental spectra requires expensive and time-consuming simulations. Building upon a recent proposal to simulate XAS using quantum computers, this work proposes a highly-optimized implementation of the time-domain algorithm for X-ray absorption. Among a host of improvements to Hamiltonian representation, circuit implementation, and measurement strategies, three optimizations are key to the efficiency of the algorithm. The first is the use of product formulas with the compressed double factorized form of the Hamiltonian. The second is recognizing that for spectroscopy applications, it is sufficient to control the error in the eigenvalues of the (approximate) Hamiltonian being implemented by the product formula, rather than the generic error on the full time evolution operator. Using perturbation theory to estimate this eigenvalue error, we find that significantly fewer Trotter steps are needed than expected from the time evolution error bound. The third is the choice of an optimized distribution of samples that takes advantage of the exponentially decaying Lorentzian kernel. Through constant factor resource estimates, we show that a challenging model Li4Mn2O cluster system with 18 spatial orbitals and 22 electrons in the active space can be simulated with 100 logical qubits and less than 4×108 T gates per circuit. Finally, the algorithm is implemented on a simulator, and the reconstructed spectrum is verified against a classical computational reference. The low cost of our algorithm makes it attractive to use on fault-tolerant quantum devices to accelerate the development and commercialization of high-capacity battery cathodes.
Resonant inelastic X-ray scattering (RIXS) is the workhorse experimental technique for probing the structural degradation of higher-capacity cathode materials. However, the interpretation of experimental spectra is challenging due to the lack of accurate simulations. In this work, we propose a quantum algorithm for simulating the RIXS spectrum of molecular clusters hypothesized to form in Li-excess cathodes. The algorithm uses quantum phase estimation to sample the spectrum from a state encoding the scattering transition amplitudes of the cluster valence excitations. We prepare this state in the quantum computer using a block-encoding of the dipole operator and quantum signal processing to implement the Green's function propagator over intermediate core-excited states. To showcase the algorithm, we use a model cluster proposed in recent experimental works consisting of an oxygen dimer bonded to a manganese atom. Using the PennyLane software platform, we report resource estimation for simulating RIXS spectra for chemically motivated active spaces of increasing sizes. For a classically challenging active space with 20 orbitals, the algorithm requires 2.0×1010 Toffoli gates and 414 logical qubits.