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Iterative qubit coupled cluster method: A systematic approach to the full-CI limit in quantum chemistry calculations on NISQ devices

Ilya G. Ryabinkin, Scott N. Genin

Published Jun 26, 2019• 0 citations
OpenAlex

Abstract

Noisy intermediate-scale quantum (NISQ) devices is the current realm of quantum computing. To exploit their limited powers to full extent it is imperative to develop suitable algorithms. We present the iterative qubit coupled cluster (iQCC) method aimed to perform realistic quantum chemistry calculations on such devices. The iQCC method can use as few as a single generator of entanglement (a single Pauli word) yet is able to reach the full configurational interaction (FCI) limit. The iQCC method is also endowed with a few techniques that allow for relatively large problems to be addressed. We show the capacity of our method on the electronic structure calculations for the LiH (4 qubits), H$_2$O (6 qubits) and N$_2$ (14 qubits) molecules

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Noisy intermediate-scale quantum (NISQ) devices is the current realm of quantum computing. To exploit their limited powers to full extent it is imperative to develop suitable algorithms. We present the iterative qubit coupled cluster (iQCC) method aimed to perform realistic quantum chemistry calculations on such devices. The iQCC method can use as few as a single generator of entanglement (a single Pauli word) yet is able to reach the full configurational interaction (FCI) limit. The iQCC method is also endowed with a few techniques that allow for relatively large problems to be addressed. We show the capacity of our method on the electronic structure calculations for the LiH (4 qubits), H2_22​O (6 qubits) and N2_22​ (14 qubits) molecules
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.
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
We introduce a parallel, GPU-accelerated implementation of the iterative qubit coupled cluster (iQCC) method that overcomes the exponential growth of the transformed Hamiltonian -- the principal bottleneck for classical emulation of quantum chemistry circuits. By distributing Hamiltonian terms across compute nodes via bit-wise partitioning and offloading Pauli contractions to GPUs, we achieve speedups exceeding two orders of magnitude over the serial CPU approach. Crucially, iQCC confines the variational evolution to a classically simulable operator subspace by selecting entanglers exclusively from the Direct Interaction Space, which guarantees non-vanishing energy gradients at every iteration and thereby naturally avoids the barren-plateau phenomenon that renders highly expressive quantum circuits untrainable. Leveraging these algorithmic and hardware advances, we simulate electronic-structure Hamiltonians for industrially relevant ruthenium catalysts in the 100--124 qubit regime, completing full ground-state calculations on NVIDIA GPUs in the ranges of 1.2 - 45 hrs and surpassing the accuracy of Density Matrix Renormalization Group. These results effectively de-quantize a significant portion of the NISQ roadmap: quantum advantage for chemistry is often assumed to emerge beyond ∼50{\sim}50∼50 qubits, yet our work demonstrates that this frontier lies significantly further -- potentially past 200 qubits -- reshaping expectations for where genuine quantum advantage may first appear.
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 .
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.
The Variational Quantum Eigensolver (VQE) is a promising algorithm for future Noisy Intermediate-Scale Quantum (NISQ) devices to simulate chemical systems. In this paper, we consider the classical simulation of the iterative Qubit Coupled Cluster (iQCC) ansatz. To this end, we implement a multi-threaded sparse wave function simulator and simulate iQCC circuits with up to 80 qubits and 980 entanglers to compare our results to experimental values and previous approximate simulations. In contrast to previous iQCC simulations, e.g., for computing the emission spectra of a phosphorescent emitting material, our approach features a variational guarantee, such that the resulting energies are true upper bounds on the exact energies. Additionally, our method is two orders of magnitude more memory efficient because it does not store the transformed Hamiltonians. Our theoretical analysis also enables the construction of ansätze with a limited number of nonzero amplitudes, for which our simulator can obtain exact results.This will allow one to generate complex benchmarking instances for future NISQ devices and simulators.