Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions

Barkoutsos, Panagiotis Kl.; Gonthier, Jérôme F.; Sokolov, Igor O.; Moll, Nikolaj; Salis, G.; Fuhrer, Andreas; Ganzhorn, Marc; Egger, Daniel; Troyer, Matthias; Mezzacapo, Antonio; Filipp, Stefan; Tavernelli, Ivano

doi:10.1103/physreva.98.022322

Cited by 322 publications

(361 citation statements)

References 46 publications

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“…In fact, it was demonstrated that the single Trotter step ansatz of uCCSD gave nearly identical variational energies to the original uCCSD ansatz for a H 2 molecule. 43 Hereafter, the Trotter n-step ansatz is denoted by a superscript 'circ/n' to the corresponding original ansatz, e.g. the energy of the k-CJF circ/n ansatzs are evaluated by performing the n-times symmetric Trotter steps with the k-CJF ansatz, respectively.…”

Section: Some Consideratins For Implementation Of the Exponential mentioning

confidence: 99%

Jastrow-type Decomposition in Quantum Chemistry for Low-Depth Quantum Circuits

Matsuzawa

Kurashige

2020

J. Chem. Theory Comput.

123

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We propose an efficient O(N 2 )-parameter ansatz that consists of a sequence of exponential operators, each of which is a unitary variant of Neuscamman's cluster Jastrow operator. The ansatz can also be derived as a decomposition of T2 amplitudes of the unitary coupled cluster with generalized singles and doubles, which gives a near full-CI energy, and reproduces it by extending the exponential operator sequence. Because the cluster Jastrow operators are expressed by a product of number operators and the derived Pauli operator products, namely the Jordan-Wigner strings, are all commutative, it does not require the Trotter approximation to implement to a quantum circuit and should be a good candidate for the variational quantum eigensolver algorithm by a near-term quantum computer. The accuracy of the ansatz was examined for dissociation of a nitrogen dimer, and compared with other existing O(N 2 )-parameter ansatzs. Not only the original ansatzs defined in the second-quantization form but also their Trotterized variants, in which the cluster amplitudes are optimized to minimize the energy obtained with a few, typically single, Trotter steps, were examined by quantum circuit simulators.

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Section: Some Consideratins For Implementation Of the Exponential mentioning

confidence: 99%

Jastrow-type Decomposition in Quantum Chemistry for Low-Depth Quantum Circuits

Matsuzawa

Kurashige

2020

J. Chem. Theory Comput.

123

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“…Interestingly, the unitary variant of CC (UCC) [21][22][23][24] can naturally be mapped as a quantum circuit for preparing the corresponding wavefunction in a digital quantum computer. [25][26][27][28][29][30] Moreover, variational approaches and in particular the Variational Quantum Eigensolver (VQE) algorithm 25 appear as the most promising way to leverage the exponentially growing Hilbert space of the qubits in near-term quantum hardware. [31][32][33][34][35] Hence, in this work we study the performance of the variational implementation of UCC as a quantum algorithm (q-UCC) 25 in computing the ground state of molecules and lattice models for which the classical CC formulation is known to break.…”

Section: Introductionmentioning

confidence: 99%

Quantum orbital-optimized unitary coupled cluster methods in the strongly correlated regime: Can quantum algorithms outperform their classical equivalents?

Sokolov

Barkoutsos

Ollitrault

et al. 2020

The Journal of Chemical Physics

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157

149

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The Coupled Cluster (CC) method is used to compute the electronic correlation energy in atoms and molecules and often leads to highly accurate results. However, its usual implementation in the projected form becomes nonvariational when the excitations are truncated and therefore fails to describe quantum states characterized by strong electronic correlations. Thanks to its exponential form, CC can be naturally adapted to quantum algorithms. In particular, the quantum unitary CC (q-UCC) is a popular wavefunction Ansatz for the Variational Quantum Eigensolver (VQE). The variational nature of this approach can lead to significant advantages compared to its classical equivalent (in the projected form), in particular for the description of strong electronic correlation. However, due to the large number of gate operations required in q-UCC, approximations need to be introduced in order to make this approach implementable in a stateof-the-art quantum computer. In this work, we propose several variants of the standard q-UCCSD Ansatz in which only a subset of excitations is included. In particular, we investigate the singlet and pair q-UCCD approaches combined with orbital optimization. We show that these approaches can capture the dissociation/distortion profiles of challenging systems such as H 4 , H 2 O and N 2 molecules, as well as the one-dimensional periodic Fermi-Hubbard chain. The results, which are in good agreement with the exact solutions, promote the future use of q-UCC methods for the solution of challenging electronic structure problems in quantum chemistry.

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“…However, this comes at the cost of an increased number of measurements, and the introduction of a wavefunction ansatz that can limit the accuracy of the simulation (although our recent approach, ADAPT-VQE, can remove the ansatz error). 8 The initial demonstration of VQE 7 was followed by several theoretical studies [9][10][11][12][13][14][15] and demonstrations on other hardware such as superconducting qubits 10,14,16 and trapped ions. 17,18 A key ingredient in VQE is the ansatz, which is implemented as a quantum circuit which constructs trial wavefunctions that are measured and then updated in a classical optimization loop.…”

Section: Introductionmentioning

confidence: 99%

Is the Trotterized UCCSD Ansatz Chemically Well-Defined?

Grimsley

Claudino

Economou

et al. 2019

J. Chem. Theory Comput.

139

148

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The variational quantum eigensolver (VQE) has emerged as one of the most promising near-term quantum algorithms that can be used to simulate many-body systems such as molecular electronic structures. Serving as an attractive ansatz in the VQE algorithm, unitary coupled cluster (UCC) theory has seen a renewed interest in recent literature. However, unlike the original classical UCC theory, implementation on a quantum computer requires a finite-order Suzuki-Trotter decomposition to separate the exponentials of the large sum of Pauli operators. While previous literature has recognized the non-uniqueness of different orderings of the operators in the Trotterized form of UCC methods, the question of whether or not different orderings matter at the chemical scale has not been addressed. In this letter, we explore the effect of operator ordering on the Trotterized UCCSD ansatz, as well as the much more compact k-UpCCGSD ansatz recently proposed by Lee et al. We observe a significant, system-dependent variation in the energies of Trotterizations with different operator orderings. The energy variations occur on a chemical scale, sometimes on the order of hundreds of kcal/mol. This letter establishes the need to define not only the operators present in the ansatz, but also the order in which they appear. This is necessary for adhering to the quantum chemical notion of a "model chemistry", in addition to the general importance of scientific reproducibility. As a final note, we suggest a useful strategy to select out of the combinatorial number of possibilities, a single well-defined and effective ordering of the operators.

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Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions

Cited by 322 publications

References 46 publications

Jastrow-type Decomposition in Quantum Chemistry for Low-Depth Quantum Circuits

Jastrow-type Decomposition in Quantum Chemistry for Low-Depth Quantum Circuits

Quantum orbital-optimized unitary coupled cluster methods in the strongly correlated regime: Can quantum algorithms outperform their classical equivalents?

Is the Trotterized UCCSD Ansatz Chemically Well-Defined?

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