We introduce the multistate iterative qubit coupled cluster (MS-iQCC) method, a quantum-inspired algorithm that runs efficiently on classical hardware and is designed to predict both ground and excited electronic states of molecules. Accurate excited-state energetics are essential for interpreting spectroscopy and chemical reactivity, but standard electronic structure methods are either too computationally expensive for larger systems or lose reliability in the presence of strong electron correlation. MS-iQCC addresses this challenge by simultaneously optimizing multiple electronic states in a single, state-averaged procedure that treats ground and excited states on equal footing. This removes the energetic bias that is introduced when excited states are computed one at a time and constrained to remain orthogonal to previously optimized states. The approach supports multireference electronic structure by allowing multideterminantal initial guesses and by adaptively building a compact exponential ansatz from a pool of qubit excitation generators. We apply MS-iQCC to H$_4$, H$_2$O, N$_2$, and C$_2$, including strongly correlated geometries, and observe robust convergence of all targeted state energies to chemically meaningful accuracy across their potential energy surfaces.
We introduce the multistate iterative qubit coupled cluster (MS-iQCC) method, a quantum-inspired algorithm that runs efficiently on classical hardware and is designed to predict both ground and excited electronic states of molecules. Accurate excited-state energetics are essential for interpreting spectroscopy and chemical reactivity, but standard electronic structure methods are either too computationally expensive for larger systems or lose reliability in the presence of strong electron correlation. MS-iQCC addresses this challenge by simultaneously optimizing multiple electronic states in a single, state-averaged procedure that treats ground and excited states on equal footing. This removes the energetic bias that is introduced when excited states are computed one at a time and constrained to remain orthogonal to previously optimized states. The approach supports multireference electronic structure by allowing multideterminantal initial guesses and by adaptively building a compact exponential ansatz from a pool of qubit excitation generators. We apply MS-iQCC to H4, H2O, N2, and C2, including strongly correlated geometries, and observe robust convergence of all targeted state energies to chemically meaningful accuracy across their potential energy surfaces.
Ab initio quantum chemistry simulations are crucially useful for the accurate prediction andunderstanding of chemical phenomena. The quality of such simulations rely heavily on precise solutions to the electronic structure problem. To facilitate the approximate yet efficient solving of the electronic structure problem, many methods rely on a set of problem assumptions, such as the validity of truncations of the fermionic excitation hierarchy, or active space selections. In this work, we describe black-box algorithms for the electronic structure problem, namely the iterative qubit coupled cluster (iQCC) algorithm along with a few of its variants and extensions. The iQCC method is a variational adaptive technique, where an iteratively updated effective Hamiltonian directly guides the selection of transformation generators of the next iteration. We describe the algorithm in detail, and introduce variations of the algorithm to alleviate the proliferation of terms in the effective Hamiltonians. Finally, we describe how the algorithm can be modified to perform simultaneuous determination of ground and excited states. These methods are amenable to implementation using near-term quantum computing devices, and with certain restrictions on meta-parameters, can be implemented as fully classical “quantum-inspired” algorithms. ii
Abstract The performance of quantum algorithms for ground-state energy estimation is directly impacted by the quality of the initial state, where quality is traditionally defined in terms of the overlap of the input state with the target state. An ideal state preparation protocol can be characterized by being easily generated classically and can be transformed to a quantum circuit with minimal overhead while having a significant overlap with the targeted eigenstate of a given Hamiltonian. We propose a method that meets these requirements by introducing a variant of the iterative qubit coupled cluster (iQCC) approach, which exclusively uses Clifford circuits. These circuits can be efficiently simulated on a classical computer, with polynomial scaling according to the Gottesman–Knill theorem. Since the iQCC method has been developed as a quantum algorithm firstly, our variant can be mapped naturally to quantum hardware. We additionally implemented several optimizations to the algorithm enhancing its scalability. We demonstrate the algorithm’s correctness in ground-state simulations for small molecules such as H2, LiH, and H2O, and extend our study to complex systems like the titanium-based compound Ti(C5H5)(CH3)3 with a (20, 20) active space, requiring 40 qubits. Results show that the convergence of the algorithm is well-behaved, and the ground state can be represented accurately. Moreover, we show an automated workflow for restricting the qubit active space, thus relieving computational resources by considering only qubits affected by non-trivial operations.
Molecular simulations are widely regarded as leading candidates to demonstrate quantum advantage--defined as the point at which quantum methods surpass classical approaches in either accuracy or scale. Yet the qubit counts and error rates required to realize such an advantage remain uncertain; resource estimates for ground-state electronic structure span orders of magnitude, and no quantum-native method has been validated at a commercially relevant scale. Here we address this uncertainty by executing the iterative qubit coupled-cluster (iQCC) algorithm, designed for fault-tolerant quantum hardware, at unprecedented scale using a quantum solver on classical processors, enabling simulations of transition organo-metallic complexes requiring hundreds of logical qubits and millions of entangling gates. Using this approach, we compute the lowest triplet excited state (T1) energies of Ir(III) and Pt(II) phosphorescent organometallic compounds and show that iQCC achieves the lowest mean absolute error (0.05 eV) and highest R2 (0.94) relative to experiment, outperforming leading classical methods. We find these systems remain classically tractable up to $\sim$200 logical qubits, establishing the threshold at which quantum advantage in computational chemistry may emerge and clarifying resource requirements for future quantum computers.
Immense interest in quantum computing has prompted the development of electronic structure methods that are suitable for quantum hardware. However, the slow pace at which quantum hardware progresses forces researchers to implement their ideas on classical computers despite the obvious loss of any “quantum advantage.” As a result, the so-called q uantum-inspired methods emerge. They allow one to look at the electronic structure problem from a different angle, yet to fully exploit their capacity, efficient implementations are highly desirable. Here, we report two schemes for improving the amplitude optimization in the iterative qubit coupled cluster (iQCC) method: a variational quantum eigensolver-type approach, which is based on the qubit coupled cluster (QCC) Ansatz. Our first scheme approximates the QCC unitary as a sum of symmetrical polynomials of generators up to a given order. The resulting energy expression allows for flexible control of computational complexity via the order parameter. It also guarantees smoothness of trial energies and their derivatives, which is important for gradient-based optimization strategies. The second scheme limits the size of the expansion space in which the QCC unitary is generated. It provides better control of memory requirements but, in general, may lead to the nonsmooth variation of energy estimates upon changes in amplitudes. It can be used, however, to extrapolate energies for a given set of amplitudes toward the exact QCC value. Both schemes allow for a larger number of generators to be included in the QCC form compared to the exact formulation. This reduces the number of iterations in the iQCC method and/or leads to higher accuracy. We assess the capabilities of the new schemes to perform QCC amplitudes optimization for a few molecular systems: dinitrogen (N 2, 16 qubits), water (H 2 O, 36 qubits), and tris(2-(2,4-difluorophenyl)pyridine) iridium(III), (Ir(F 2 ppy) 3, 80 qubits).
Abstract The iterative qubit coupled cluster (iQCC) method is a systematic variational approach to solve the electronic structure problem on universal quantum computers. It is able to use arbitrarily shallow quantum circuits at expense of iterative canonical transformation of the Hamiltonian and rebuilding a circuit. Here we present a variety of a posteriori corrections to the iQCC energies to reduce the number of iterations to achieve the desired accuracy. Our energy corrections are based on a low-order perturbation theory series that can be efficiently evaluated on a classical computer. Moreover, capturing a part of the total energy perturbatively, allows us to formulate the qubit active-space concept, in which only a subset of all qubits is treated variationally. As a result, further reduction of quantum resource requirements is achieved. We demonstrate the utility and efficiency of our approach numerically on the examples of 10-qubit N 2 molecule dissociation, the 24-qubit H 2 O symmetric stretch, and 56-qubit singlet-triplet gap calculations for the technologically important complex, tris-(2-phenylpyridine)iridium(III) Ir(ppy) 3 .
An iterative version of the qubit coupled cluster (QCC) method [I. G. Ryabinkin et al., J. Chem. Theory Comput. 2019, 14, 6317] is proposed. The new method seeks to find ground electronic energies of molecules on noisy intermediate-scale quantum devices. Each iteration involves a canonical transformation of the Hamiltonian and employs constant-size quantum circuits at the expense of increasing the Hamiltonian size. We numerically studied the convergence of the method on ground-state calculations for LiH, H 2 O, and N 2 molecules and found that the exact ground-state energies can be systematically approached only if the generators of the QCC ansatz are sampled from a specific set of operators. We report an algorithm for constructing this set that scales linearly with the size of the Hamiltonian.