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Open AccessOpen Access JUSTC Chemistry 18 January 2023

Q2Chemistry: A quantum computation platform for quantum chemistry

  • Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China

Cite this:
https://doi.org/10.52396/JUSTC-2022-0118
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  • Author Bio:

    Yi Fan received his B.S. degree in Chemistry from the University of Science and Technology of China (USTC) in 2017 and is currently a Ph.D. candidate at USTC. His research interests include quantum chemistry methods and quantum computing algorithms for solid materials

    Zhenyu Li is a Professor of chemistry at the University of Science and Technology of China (USTC). He received his Ph.D. degree in Physical Chemistry from USTC in 2004. Since then, he worked as a postdoctoral researcher at the University of Maryland, College Park, and the University of California, Irvine. In 2007, he joined USTC as a faculty member. His research interests focus on using or developing electronic structure and molecular simulation methods to study chemical systems

  • Corresponding author: E-mail: zyli@ustc.edu.cn
  • Received Date: 29 August 2022
  • Accepted Date: 03 November 2022
    • Available Online: 18 January 2023
    Abstract

  • Abstract

    Quantum computers provide new opportunities for quantum chemistry. In this article,we present a versatile, extensible, and efficient software package, named Q2Chemistry, for developing quantum algorithms and quantum inspired classical algorithms in the field of quantum chemistry. In Q2Chemistry, the wave function and Hamiltonian can be conveniently mapped into the qubit space, then quantum circuits can be generated corresponding to a specific quantum algorithm already implemented in the package or newly developed by the users. The generated circuits can be dispatched to either a physical quantum computer, if available, or to the internal virtual quantum computer realized by simulating quantum circuits on classical computers. As demonstrated by our benchmark simulations, Q2Chemistry achieves excellent performance in simulating medium scale quantum circuits using the matrix product state algorithm. Applications of Q2Chemistry to simulate molecules and periodic systems are given with performance analysis.

    Graphical abstract

    The main framework of our newly developed quantum computation software package.

    Abstract

    Quantum computers provide new opportunities for quantum chemistry. In this article,we present a versatile, extensible, and efficient software package, named Q2Chemistry, for developing quantum algorithms and quantum inspired classical algorithms in the field of quantum chemistry. In Q2Chemistry, the wave function and Hamiltonian can be conveniently mapped into the qubit space, then quantum circuits can be generated corresponding to a specific quantum algorithm already implemented in the package or newly developed by the users. The generated circuits can be dispatched to either a physical quantum computer, if available, or to the internal virtual quantum computer realized by simulating quantum circuits on classical computers. As demonstrated by our benchmark simulations, Q2Chemistry achieves excellent performance in simulating medium scale quantum circuits using the matrix product state algorithm. Applications of Q2Chemistry to simulate molecules and periodic systems are given with performance analysis.

    • Public Summary

    • We developed a quantum computation platform for quantum chemistry applications.
    • A modular structure was implemented with a mixed-language programming model for easy extension and high performance.
    • Excellent performance is achieved as demonstrated by simulating medium-scale quantum circuits up to 72 qubits.

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    • References(79)
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    Figure  1.  (a) The framework of Q2Chemistry. (b) A typical workflow of solving a chemical problem using a quantum algorithm.

    Figure  2.  (a) Applying a single qubit gate on the MPS quantum state is simulated by simply a local contraction. (b) Applying a two-qubit gate on neighboring qubits generally has 2 steps: (i) reshape the two-qubit gate into a 4-dimensional tensor and contract with the qubits to form a two-qubit tensor; (ii) perform a singular value decomposition to restore the two-qubit tensor back to the MPS formulation. Postprocessing is usually required to maintain normalization or canonicalization of MPS tensors. (c) Auxiliary matrices that contain truncated and normalized singular values are used to normalize the quantum state.

    Figure  3.  (a) The quantum circuit corresponding to the operator $ \exp{({\rm{i}}\theta \hat{\sigma^{x}} \hat{\sigma^{y}} \hat{\sigma^{z}} \hat{\sigma^{x}})} $ and (b) the two-layer HEA circuit that entangles all neighboring qubits using the controlled-U gate. Blue squares represent nonparametric gates, while green squares represent parametric quantum gates such as Rz and the three-parameter (controlled-)U gate.

    Figure  4.  Evaluating the expectation value of a linear combination of Pauli strings using multiple quantum devices or simulator processes. $ |0_{N}\rangle $ represents an $ N $-qubit quantum register with all qubits initialized to $ |0\rangle $. In this example, the measurement parts are the Hadamard test circuits.

    Figure  5.  Simulating the Cr$ _2 $ molecule using the MPS backend. The STO-3G basis set and the symmetry-reduced UCCSD ansatz are used, where the qubit Hamiltonian contains 305041 Pauli strings. The time cost refers to one VQE iteration (including evolution of the quantum circuit and calculation of energy) being tested. The distributed parallelization is implemented using OpenMPI and Python’s $\mathtt{mpi4py}$ package.

    Figure  6.  (a) The VQE optimized potential energy curve of H$ _2 $ calculated by the MPS backend using the ccJ-pVDZ basis set. The VQE results are calculated by interfacing with the external Julia-implemented MPS simulator. (b) Energy difference between EOM-ADAPT-C and classical EOM-CCSD band structures for Si. Inset gives the EOM-ADAPT-C band structure calculated using Q2Chemistry. The FCI and EOM-CCSD energies are obtained using the PySCF code.

    Figure  .  Code Example 1. Interface to quantum devices in the qcircuit module.

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    [15]
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    Higgott O, Wang D, Brierley S. Variational quantum computation of excited states. Quantum, 2019, 3: 156. doi: 10.22331/q-2019-07-01-156
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    [20]
    Liu J, Fan Y, Li Z, et al. Quantum algorithms for electronic structures: basis sets and boundary conditions. Chem. Soc. Rev., 2022, 51: 3263–3279. doi: 10.1039/D1CS01184G
    [21]
    McClean J R, Boixo S, Smelyanskiy V N, et al. Barren plateaus in quantum neural network training landscapes. Nat. Commun., 2018, 9 (1): 4812. doi: 10.1038/s41467-018-07090-4
    [22]
    Napp J. Quantifying the barren plateau phenomenon for a model of unstructured variational ansätze. 2022. https://arxiv.org/abs/2203.06174. Accessed August 1, 2022.
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