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Angewandte Chemie

Estimating Phosphorescent Emission Energies in IrIII Complexes Using Large‐Scale Quantum Computing Simulations**

Scott N. Genin, Ilya G. Ryabinkin, Nathan R. Paisley, Sarah O. Whelan, Michael G. Helander, Zachary M. Hudson

Published Mar 10, 2022• 3 citations
Publisher

Abstract

Abstract Here we calculate T1→S0 transition energies in nine phosphorescent iridium complexes using the iterative qubit coupled cluster (iQCC) method to determine if quantum simulations have any advantages over classical methods. These simulations would require a gate‐based quantum computer with at least 72 fully‐connected logical qubits. Since such devices do not yet exist, we demonstrate the iQCC method using a purpose‐built quantum simulator on classical hardware. The results are compared to a selection of common DFT functionals, ab initio methods, and empirical data. iQCC is found to match the accuracy of the best DFT functionals, but with a better correlation coefficient, demonstrating that it is better at predicting the structure–property relationship. Results indicate that the iQCC method has the required accuracy to design organometallic complexes when deployed on emerging quantum hardware and sets an industrially relevant target for demonstrating quantum advantage.

DOI
10.1002/ange.202116175

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Optimization of the Qubit Coupled Cluster Ansatz on Classical Computers

Ilya G. Ryabinkin, S. M. Hosseini Jenab, Scott N. Genin

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).

arXiv:2502.17587•Journal of Chemical Theory and Computation•Jun 17, 2025•1 citation
Abstract Here we calculate T1→S0 transition energies in nine phosphorescent iridium complexes using the iterative qubit coupled cluster (iQCC) method to determine if quantum simulations have any advantages over classical methods. These simulations would require a gate‐based quantum computer with at least 72 fully‐connected logical qubits. Since such devices do not yet exist, we demonstrate the iQCC method using a purpose‐built quantum simulator on classical hardware. The results are compared to a selection of common DFT functionals, ab initio methods, and empirical data. iQCC is found to match the accuracy of the best DFT functionals, but with a better correlation coefficient, demonstrating that it is better at predicting the structure–property relationship. Results indicate that the iQCC method has the required accuracy to design organometallic complexes when deployed on emerging quantum hardware and sets an industrially relevant target for demonstrating quantum advantage.
transition energies in nine phosphorescent iridium complexes using the iterative qubit coupled cluster (iQCC) method to determine if quantum simulations have any advantages over classical methods. These simulations would require a gate-based quantum computer with at least 72 fully-connected logical qubits. Since such devices do not yet exist, we demonstrate the iQCC method using a purpose-built quantum simulator on classical hardware. The results are compared to a selection of common DFT functionals, ab initio methods, and empirical data. iQCC is found to match the accuracy of the best DFT functionals, but with a better correlation coefficient, demonstrating that it is better at predicting the structure-property relationship. Results indicate that the iQCC method has the required accuracy to design organometallic complexes when deployed on emerging quantum hardware and sets an industrially relevant target for demonstrating quantum advantage.
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_11​) 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 R2^22 (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.
Predicting the phosphorescent emission gaps of heavy-metal complexes is crucial for organic light-emitting diode materials design, yet challenged by the highly entangled nature of their triplet states. Traditional projective single-reference methods like coupled cluster break down for these systems due to severe spin contamination, physically misidentifying the electronic character and yielding red-shifted gaps. The iQCC method executed on a classical computer emulates the fault-tolerant quantum simulation on the ∼200 logical qubit scale, to compute the energies of T1 and S0 for the phosphorescent complexes Ir(III) and Pt(II). iQCC achieves a mean absolute error of 0.05 eV and R2 of 0.94 relative to experiment, surpassing the approaches of DFT, TD-DFT, and coupled cluster. These results establish a high-accuracy performance target that molecular electronic-structure calculations on future fault-tolerant quantum computers should aim to exceed.
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 .
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_44​, H2_22​O, N2_22​, and C2_22​, including strongly correlated geometries, and observe robust convergence of all targeted state energies to chemically meaningful accuracy across their potential energy surfaces.
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).