量子計算機上におけるグリーン関数計算：分子系における準粒子スペクトル

概要

Quantum chemistry calculations [1] as a kind of quantum
simulation [2] have been drawing attention increasingly since
they serve as a lucid proof of principle for quantum computation [3] and, at the same time, are directly related to
state-of-the-art quantum hardware. The electronic states and
the operators acting on them for a given Hamiltonian have
to be mapped to the qubits comprising a quantum computer
and the operators for them by an appropriate transformation
[4]. The Jordan-Wigner (JW) [5] and Bravyi-Kitaev (BK)
[6] transformations are often used for quantum chemistry
calculations. Various approaches for obtaining the energy
spectra of a many-electron system have been proposed. The
earliest one [7] employs the quantum phase estimation (QPE)
algorithm [8,9] and the Suzuki-Trotter decomposition [10] of
the qubit Hamiltonian into a sequence of one- and two-qubit
logic gates [11] for unitary operations. This approach was
realized [12] by using superconducting qubits. The variational
quantum eigensolver (VQE) is a newer approach, in which
a trial many-electron state is prepared via a quantum circuit
with parameters to be optimized aiming at the ground state. It
uses a classical computer for updating the parameters based
on the measurement results of the qubits, which is why it is
also called a quantum-classical hybrid algorithm [13]. This
approach was first realized [14] by using a quantum photonic
device. It has also been realized by superconducting [12,15]
and ion-trap [16] quantum computers. Another approach for
obtaining the energy spectra is the imaginary-time evolution.
It was recently proposed [17–19] as a quantum-classical hybrid algorithm based on McLachlan’s variational principle
[20].
An experiment of photoelectron spectroscopy (PES) irradiates light to a sample and measures the energy of photoelectrons coming out of the sample. An experiment of inverse
PES is for the reverse process of PES. ...

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