Iterative Qubit Coupled Cluster Approach with Efficient Screening of Generators

Ryabinkin, Ilya G.; Lang, Robert A.; Genin, Scott N.; Izmaylov, Artur F.

doi:10.1021/acs.jctc.9b01084

Cited by 167 publications

(216 citation statements)

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“…Several variants of VQE are available (Parrish et al, 2019b;Chivilikhin et al, 2020), but all build on the variational principle from quantum mechanics, which constrains the quantum states that can satisfy the electronic eigenvalue problem (McClean et al, 2016). While the initial VQE proposal assumes a predefined ansatz, this constraint has been relaxed, opening the door to adaptive approaches (Grimsley et al, 2019;Ryabinkin et al, 2020), by which the preparable quantum states are driven by the problem at hand. In particular, the adaptive derivative-assembled pseudo-trotter (ADAPT) ansatz, which finds support on the recently coined "disentangled" UCC (Evangelista et al, 2019) and starts from an exact UCC representation of the electronic ground state to construct an approximate prepared state based on the dominant contributions.…”

Section: Introductionmentioning

confidence: 99%

Benchmarking Adaptive Variational Quantum Eigensolvers

et al. 2020

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By design, the variational quantum eigensolver (VQE) strives to recover the lowest-energy eigenvalue of a given Hamiltonian by preparing quantum states guided by the variational principle. In practice, the prepared quantum state is indirectly assessed by the value of the associated energy. Novel adaptive derivative-assembled pseudo-trotter (ADAPT) ansatz approaches and recent formal advances now establish a clear connection between the theory of quantum chemistry and the quantum state ansatz used to solve the electronic structure problem. Here we benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves for a few selected diatomic molecules, namely H2, NaH, and KH. Using numerical simulation, we find both methods provide good estimates of the energy and ground state, but only ADAPT-VQE proves to be robust to particularities in optimization methods. Another relevant finding is that gradient-based optimization is overall more economical and delivers superior performance than analogous simulations carried out with gradient-free optimizers. The results also identify small errors in the prepared state fidelity which show an increasing trend with molecular size.

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Section: Introductionmentioning

confidence: 99%

Benchmarking Adaptive Variational Quantum Eigensolvers

et al. 2020

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“…For the embedding Hamiltonians specified by Eq. (C9) and Table II, the DIS is characterized by a single flip index [37] F = {0, 1} that gives rise to a set of two electron correlation generators…”

Section: The Qubit Coupled-cluster Methodsmentioning

confidence: 99%

“…We first consider an ansatz state that is a product state of n q arbitrary single-qubit states, following the method described in the work of Ryabinkin et al [37]. We evaluate the expectation value of the mean-field Hamiltonian with respect to the ansatz state and use VQE, simulated on a classical computer, to minimize the value.…”

mentioning

confidence: 99%

Efficient and Accurate Electronic Structure Simulation Demonstrated on a Trapped-Ion Quantum Computer

Kawashima¹,

Coons²,

Nam

et al. 2021

Preprint

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Quantum computers have the potential to perform accurate and efficient electronic structure calculations, enabling the simulation of properties of materials. However, today’s noisy, intermediate-scale quantum (NISQ) devices have a limited number of qubits and gate operations due to the presence of errors. Here, we propose a systematically improvable end-to-end pipeline to alleviate these limitations. Our proposed resource-efficient pipeline combines problem decomposition techniques for compact molecular representations, circuit optimization methods for compilation, solving the eigenvalue problem on advanced quantum hardware, and error-mitigation techniques in post-processing the results. Using the density matrix embedding theory for compact representation, and an ion-trap quantum computer, we simulate a ring of 10 hydrogen atoms taking into account all electrons equally and explicitly in the electronic structure calculation. In our experiment, we simulated the largest molecular system on a quantum computer within chemical accuracy with respect to total molecular energy calculated by the full CI method. Our methods reduce the number of qubits required for high-accuracy quantum simulations by an order of magnitude in the present work, enabling the simulation of larger, more industrially relevant molecules using NISQ devices. They are further systematically improvable as devices’ computational capacity continues to grow.

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“…4 for a high level overview). These type of algorithms have been successfully applied in different avors like qubit-coupledcluster [67][68][69][70] or adapt-vqe, 35,71 which mostly differ in the way they screen and construct operators. In these approaches, the commutator between the Hamiltonian and the generator of potential excitations is used in the screening process to compute the gradient.…”

Section: Adapt Vqementioning

confidence: 99%