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arXiv:2610.02916

Quasiparticle quantum simulation of materials with the Bethe-Salpeter equation

Jielun Chen, Jiace Sun, Garnet Kin-Lic Chan

quant-phphysics.chem-phSubmitted Oct 2, 2026• Announced Oct 5, 2026• 0 citations
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Abstract

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 $\widetilde{O}(N)$ Toffoli gates and $O(\log N)$ logical qubits, or, using space-time tradeoffs, $\widetilde{O}(\sqrt{N})$ Toffoli gates and $\widetilde{O}(\sqrt{N})$ 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 $O(10^3)$ atoms, show that our Toffoli-optimized implementation reduces the Toffoli count by $10^6-10^7$ 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.

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31 pages, 9 figures

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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 NNN, and a fixed number of quasiparticles, the resulting algorithms require O~(N)\widetilde{O}(N)O(N) Toffoli gates and O(log⁡N)O(\log N)O(logN) logical qubits, or, using space-time tradeoffs, O~(N)\widetilde{O}(\sqrt{N})O(N​) Toffoli gates and O~(N)\widetilde{O}(\sqrt{N})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)O(10^3)O(103) atoms, show that our Toffoli-optimized implementation reduces the Toffoli count by 106−10710^6-10^7106−107 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.
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We present a comprehensive end-to-end framework for simulating the real-time dynamics of chemical systems on a fault-tolerant quantum computer, incorporating both electronic and nuclear quantum degrees of freedom. An all-particle simulation is nominally efficient on a quantum computer, but practically infeasible. Hence, central to our approach is the construction of a first-quantized plane-wave algorithm making use of pseudoions. The latter consolidate chemically inactive electrons and the nucleus into a single effective dynamical ionic entity, extending the well-established concept of pseudopotentials in quantum chemistry to a two-body interaction. We explicitly describe efficient quantum circuits for initial state preparation across all degrees of freedom, as well as for block-encoding the Hamiltonian describing interacting pseudoions and chemically active electrons, by leveraging recent advances in quantum rejection sampling to optimize the implementations. To extract useful chemical information, we first design molecular fingerprints by combining density-functional calculations with machine learning techniques, and subsequently validate them through surrogate classical molecular dynamics simulations. These fingerprints are then coherently encoded on a quantum computer for efficient molecular identification via amplitude estimation. We provide an extensive analysis of the cost of running the algorithm on a fault-tolerant quantum computer for several chemically interesting systems. As an illustration, simulating the interaction between NH3\mathrm{NH_3}NH3​ and BF3\mathrm{BF_3}BF3​ (a 40-particle system) requires 808 logical qubits to encode the problem, and approximately 101110^{11}1011 Toffoli gates per femtosecond of time evolution. Our results establish a foundation for further quantum algorithm development targeting chemical and material dynamics.
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