Variational quantum algorithm for molecular geometry optimization

Delgado, Alain; Arrazola, Juan Miguel; Jahangiri, Soran; Niu, Zeyue; Izaac, Josh; Roberts, Chase; Killoran, Nathan

doi:10.1103/physreva.104.052402

Cited by 28 publications

(23 citation statements)

References 30 publications

(25 reference statements)

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“…For example, (|0 0|) ⊗N is used frequently in quantum simulations [17,18]. Hartree-Fock (HF) states [8,10], which are prepared by the tensor product of {|0 , |1 }, serve as good initial states in quantum chemistry tasks [10,11,12,13]. For quantum machine learning (QML) tasks, initial states encode the information of the training data, which could have a complex form.…”

Section: Observables and Input Statesmentioning

confidence: 99%

“…Next, we extend the Gaussian initialization framework to general quantum circuits with correlated parameters and global observables. Quantum circuits with correlated parameters have wide applications in quantum simulations and quantum chemistry [10,11,12,13]. One example is the Givens rotation…”

Section: Correlated Parameters With Global Observablesmentioning

confidence: 99%

“…We follow settings on the ansatz in Refs. [12,13]. For the molecule with n e active electrons and n o free spin orbitals, the corresponding VQA contains N = n o qubits, which employs the HF state [8,10] |φ…”

Section: Quantum Chemistrymentioning

confidence: 99%

“…We construct the parameterized quantum circuit with Givens rotation gates [12], where each gate is implemented on 2 or 4 qubits with one parameter. Specifically, for the LiH molecule, the number of electrons n e = 2, the number of free spin orbitals n o = 10, and the number of different Givens rotations is L = 24 [13]. We follow the molecule Hamiltonian H LiH defined in Ref.…”

Section: Quantum Chemistrymentioning

confidence: 99%

“…Due to mild requirements on the gate noise and the circuit connectivity, variational quantum algorithms (VQAs) [4] become one of the most promising frameworks for achieving practical quantum advantages on NISQ devices. Specifically, different VQAs have been proposed for many topics, e.g., quantum chemistry [5,6,7,8,9,10,11,12,13], quantum simulations [14,15,16,17,18,19,20,21,22,23], machine learning [24,25,26,27,28,29,30,31], numerical analysis [32,33,34,35,36], and linear algebra problems [37,38,39]. Recently, various small-scale VQAs have been implemented on real quantum computers for tasks such as finding the ground state of molecules [8,11,12] and exploring promising applications in supervised learning [25], generative learning [30] and reinforcement learning [29].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Gaussian initializations help deep variational quantum circuits escape from the barren plateau

Zhang¹,

Hsieh²,

Liu³

et al. 2022

Preprint

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Variational quantum circuits have been widely employed in quantum simulation and quantum machine learning in recent years. However, quantum circuits with random structures have poor trainability due to the exponentially vanishing gradient with respect to the circuit depth and the qubit number. This result leads to a general belief that deep quantum circuits will not be feasible for practical tasks. In this work, we propose an initialization strategy with theoretical guarantees for the vanishing gradient problem in general deep circuits. Specifically, we prove that under proper Gaussian initialized parameters, the norm of the gradient decays at most polynomially when the qubit number and the circuit depth increase. Our theoretical results hold for both the local and the global observable cases, where the latter was believed to have vanishing gradients even for shallow circuits. Experimental results verify our theoretical findings in the quantum simulation and quantum chemistry.

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Section: Observables and Input Statesmentioning

confidence: 99%

Section: Correlated Parameters With Global Observablesmentioning

confidence: 99%

Section: Quantum Chemistrymentioning

confidence: 99%

Section: Quantum Chemistrymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Gaussian initializations help deep variational quantum circuits escape from the barren plateau

Zhang¹,

Hsieh²,

Liu³

et al. 2022

Preprint

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show abstract

Open source variational quantum eigensolver extension of the quantum learning machine for quantum chemistry

Haidar

Rančić

Ayral

et al. 2023

WIREs Comput Mol Sci

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Quantum chemistry (QC) is one of the most promising applications of quantum computing. However, present quantum processing units (QPUs) are still subject to large errors. Therefore, noisy intermediate-scale quantum (NISQ) hardware is limited in terms of qubit counts/circuit depths. Variational quantum eigensolver (VQE) algorithms can potentially overcome such issues. Here, we introduce the OpenVQE open-source QC package. It provides tools for using and developing chemically-inspired adaptive methods derived from unitary coupled cluster (UCC). It facilitates the development and testing of VQE algorithms and is able to use the Atos Quantum Learning Machine (QLM), a general quantum programming framework enabling to write/optimize/simulate quantum computing programs. We present a specific, freely available QLM open-source module, myQLM-fermion. We review its key tools for facilitating QC computations (fermionic second quantization, fermion-spin transforms, etc.). OpenVQE largely extends the QLM's QC capabilities by providing:(i) the functions to generate the different types of excitations beyond the commonly used UCCSD ansatz; (ii) a new Python implementation of the "adaptive derivative assembled pseudo-Trotter method" (ADAPT-VQE). Interoperability with other major quantum programming frameworks is ensured thanks to the myQLM-interop package, which allows users to build their own code and easily execute it on existing QPUs. The combined OpenVQE/myQLM-fermion libraries facilitate the implementation, testing and development of variational quantum algorithms, while offering access to large molecules as the noiseless Schrödinger-style dense simulator can reach up to 41 qubits for any circuit.Extensive benchmarks are provided for molecules associated to qubit counts

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A quantum information theoretic analysis of reinforcement learning-assisted quantum architecture search

Sadhu,

Sarkar,

Kundu

2024

Quantum Mach. Intell.

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In the field of quantum computing, variational quantum algorithms (VQAs) represent a pivotal category of quantum solutions across a broad spectrum of applications. These algorithms demonstrate significant potential for realising quantum computational advantage. A fundamental aspect of VQAs involves formulating expressive and efficient quantum circuits (namely ansatz), and automating the search of such ansatz is known as quantum architecture search (QAS). Recently reinforcement learning (RL) techniques is utilized to automate the search for ansatzes, know as RL-QAS. This study investigates RL-QAS for crafting ansatz tailored to the variational quantum state diagonalisation problem. Our investigation includes a comprehensive analysis of various dimensions, such as the entanglement thresholds of the resultant states, the impact of initial conditions on the performance of RL-agent, the phase transition behaviour of correlation in concurrence bounds, and the discrete contributions of qubits in deducing eigenvalues through conditional entropy metrics. We leverage these insights to devise an entanglement-guided admissible ansatz in QAS to diagonalise random quantum states using optimal resources. Furthermore, the methodologies presented herein offer a generalised framework for constructing reward functions within RL-QAS applicable to variational quantum algorithms.

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Variational quantum algorithm for molecular geometry optimization

Cited by 28 publications

References 30 publications

Gaussian initializations help deep variational quantum circuits escape from the barren plateau

Gaussian initializations help deep variational quantum circuits escape from the barren plateau

Open source variational quantum eigensolver extension of the quantum learning machine for quantum chemistry

A quantum information theoretic analysis of reinforcement learning-assisted quantum architecture search

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