Accurate quantum chemical calculations are critical for understanding molecular properties, yet their computational cost remains a major challenge. Full Configuration Interaction (FCI) provides exact solutions but is prohibitively expensive for large systems. To address this, quantum computers are expected to be useful, but developing practical quantum computers is still ongoing. Here we introduce an efficient Configuration Interaction (CI) computation algorithm based on classical mechanics, which we call Simulated Bifurcation-based CI (SBCI), because we derive this algorithm from a quantum inspired algorithm for combinatorial optimization called Simulated Bifurcation. Applying it to FCI computations of representative molecular systems and comparing the results with those by a standard method, we demonstrate that SBCI can reduce computation costs such as computation times and/or required memory sizes, while keeping high accuracy comparable to the standard method. Thus, SBCI will be promising for accelerating high-precision electronic structure calculations without compromising reliability.
Four decades after Richard Feynman's famous remark, we have reached a stage at which nature can be simulated quantum mechanically. Quantum simulation is among the most promising applications of quantum computing. However, like many quantum algorithms, it is severely constrained by noise in near-term hardware. Quantum-inspired algorithms provide an attractive alternative by avoiding the need for error-prone quantum devices. In this study, we demonstrate that the coherent Ising machine and simulated bifurcation algorithms can accurately reproduce the electronic energy profiles of H_2 and H_2O, capturing their essential energetic features. Notably, we obtain computational times of 1.2 s and 2.4 s for the H_2 and H_2O profiles, respectively, representing a substantial speed-up compared to gate-based quantum computing approaches, which typically require at least 6 s to compute a single molecular geometry with comparable accuracy. These results highlight the potential of quantum-inspired approaches for scaling to larger molecular systems and for future applications in chemistry and materials science.
Full configuration interaction (FCI) provides exact electronic structure within a given atomic basis, but its computational cost grows exponentially with the number of spin orbitals. Selected configuration interaction (SCI) methods alleviate this limitation by retaining only the most important Slater determinants. However, the repeated identification of important determinants remains a major computational bottleneck. We present a quantum assisted selected configuration interaction (QASCI) method that combines SCI with graph based block diagonalization (GBBD) of FCI Hamiltonian. The GBBD method partitions FCI Hamiltonian into independent blocks, within which determinant selection problem is formulated as a quadratic unconstrained binary optimization (QUBO) problem. The QUBO problems for selecting determinants to construct SCI space are iteratively solved using a fast annealing approach. We benchmark method on H8-H18 hydrogen chains and Li2S in STO3G basis. For Hn chains, chemical accuracy is achieved while retaining only a small fraction of Slater determinants, and this fraction decreases with increasing n, despite the exponential growth of the FCI Hilbert space. For Li2S, QASCI results remain within chemical accuracy while retaining substantially fewer determinants than the full FCI space. We apply QASCI to N2 using the 631G basis, considering both active orbital and full orbital treatments. The full orbital QASCI calculation, using 50000 determinants, yields a lower ground state energy than an FCI calculation within an active space comprising 12 spin orbitals and 12 electrons. These results demonstrate that the combination of QASCI and the GBBD approach can substantially reduce computational cost of determinant selection while maintaining the accuracy of FCI based electronic structure calculations, thereby enabling accurate calculations in larger orbital spaces.
This work presents the implementation of a fragment-based, quantum-centric supercomputing workflow for computing molecular electronic structure using quantum hardware. The workflow is applied to predict the relative energies of two conformers of the 300-atom Trp-cage miniprotein. The methodology employs wave function-based embedding (EWF) as the underlying fragmentation framework, in which all atoms in the system are explicitly included in the CI treatment. CI calculations for individual fragments are performed using either sample-based quantum diagonalization (SQD) for challenging fragments or full configuration interaction (FCI) for trivial fragments. To assess the accuracy of SQD for fragment CI calculations, EWF-(FCI,SQD) results are compared against EWF-MP2 and EWF-CCSD benchmarks. Overall, the results demonstrate that large-scale electronic configuration interaction (CI) simulations of protein systems containing hundreds or even thousands of atoms can be realized through the combined use of quantum and classical computing resources.
Quantum chemistry and materials science are among the most promising areas for demonstrating algorithmic quantum advantage and quantum utility due to their inherent quantum mechanical nature. Still, large-scale simulations of quantum circuits are essential for determining the problem size at which quantum solutions outperform classical methods. In this work, we present a novel hybrid simulation approach, forming a hybrid of a fullstate and a Clifford simulator, specifically designed to address the computational challenges associated with the time evolution of quantum chemistry Hamiltonians. Our method focuses on the efficient emulation of multi-qubit rotations, a critical component of Trotterized Hamiltonian evolution. By optimizing the representation and execution of multi-qubit operations leveraging the Pauli frame, our approach significantly reduces the computational cost of simulating quantum circuits, enabling more efficient simulations. Beyond its impact on chemistry applications, our emulation strategy has broad implications for any computational workload that relies heavily on multi-qubit rotations. By increasing the efficiency of quantum simulations, our method facilitates more accurate and cost-effective studies of complex quantum systems. We quantify the performance improvements and computational savings for this emulation strategy, and we obtain a speedup of a factor
≈18 (
≈22 with MPI) for our evaluated chemistry Hamiltonians with 24 qubits. Thus, we evaluate our integration of this emulation strategy into the Intel Quantum SDK, further bridging the gap between theoretical algorithm development and practical quantum software implementations.
In quantum chemistry, the "electronic structure problem" refers to the process of numerically solving Schrodinger's equation for a given molecular system. These calculations rank among the most CPU-intensive computations that are performed nowadays, yet they are also crucial to the design of new drugs and materials. The idea behind quantum simulation of quantum chemistry is that a quantum computer could perform such calculations in a manner that is exponentially more efficient than what a classical computer could accomplish. In fact, quantum simulation is quite possibly the application most naturally suited to a quantum computer. In this work we introduce novel algorithms for the simulation of quantum chemistry, algorithms that are exponentially more precise than previous algorithms in the literature. Previous algorithms are based on the Trotter-Suzuki decomposition and scale like the inverse of the desired precision, while our algorithms represent the first practical application of the recently developed truncated Taylor series approach, and they achieve scaling that is logarithmic in the inverse of the precision. We explore algorithms for both second-quantized and first-quantized encodings of the chemistry Hamiltonian, where the second-quantized encoding requires
mathcalO(N) qubits for an
N spin-orbital system, and the highly compressed first-quantized encoding requires
mathcalO(eta) qubits, where
eta<<N is the number of electrons in the system. We first introduce a second-quantized algorithm that uses pre-computed molecular integrals, resulting in a gate count that scales like
widetildecalO(N8t). Next we introduce algorithms that compute molecular integrals on the fly by carefully discretizing these integrals. Indeed, figuring out how to evaluate the integrals in an efficient manner is one of the main challenges of applying the truncated Taylor series approach to the chemistry problem: the complexity of a general quantum algorithm is traditionally formulated in terms of the number of queries made to an oracle whose assumption we just assume, but in this case, we actually construct the oracle for our specific problem. The evaluation of the oracle itself requires evaluating molecular integrals, which adds additional complexity to an algorithm. We find that the gate count of the second-quantized on-the-fly algorithm scales like
widetildecalO(N5t). We also find that the first-quantized on-the-fly algorithm, which uses the configuration interaction (CI) matrix representation of the Hamiltonian, requires at most
widetildecalO(eta2N3t) gates. In general, the discovery of exponentially more precise algorithms will allow for the simulation of larger molecular systems than was previously possible under Trotter-based methods. In addition, the results here can be generalized to the simulation of other fermionic systems beyond the electronic structure problem.
This thesis explores the use of computational methods in quantum chemistry, focusing on the challenge of accurately computing full configuration interaction (FCI) energies. While FCI represents the exact solution to the electronic Schrödinger equation, its exponential scaling limits applications to small systems. To address this, machine learning–based correction methods are developed to improve the extrapolation of coupled cluster results toward the FCI limit. These approaches are benchmarked against standard extrapolation techniques and demonstrate superior accuracy and efficiency. The applicability of these methods is further examined through the study of ground-state dissociation energies of 1-naphthol complexes, in collaboration with experimental efforts. Together, these results highlight the potential of combining data-driven techniques with traditional quantum chemical methods to expand their reach toward larger and more realistic chemical systems.