Calculating the Single-Particle Many-body Green's Functions via the Quantum Singular Value Transform Algorithm

• URL: http://arxiv.org/abs/2307.13583v1
• Date: Tue, 25 Jul 2023 15:38:03 GMT
• Title: Calculating the Single-Particle Many-body Green's Functions via the Quantum Singular Value Transform Algorithm
• Authors: Alexis Ralli, Gabriel Greene-Diniz, David Mu\~noz Ramo, Nathan Fitzpatrick
• Abstract summary: We implement a noise-free simulation of the technique to investigate how it can be used to perform matrix inversion. We also propose a new circuit construction for the linear combination of unitaries block encoding technique, that reduces the number of single and two-qubit gates required.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Quantum Singular Value Transformation (QSVT) is a technique that provides a unified framework for describing many of the quantum algorithms discovered to date. We implement a noise-free simulation of the technique to investigate how it can be used to perform matrix inversion, which is an important step in calculating the single-particle Green's function in the Lehmann representation. Due to the inverse function not being defined at zero, we explore the effect of approximating f(x)=1/x with a polynomial. This is carried out by calculating the single-particle Green's function of the two-site single-impurity Anderson model. We also propose a new circuit construction for the linear combination of unitaries block encoding technique, that reduces the number of single and two-qubit gates required.

Related papers

• Inference of response functions with the help of machine learning algorithms [42.12937192948916]
  We employ a neural network prediction algorithm to reconstruct a response function $S(omega)$ defined over a range in $omega$. We compare the quality of response functions obtained using coefficients calculated using a neural network (NN) algorithm with those computed using the Gaussian Integral Transform (GIT) method. In the regime where only a small number of terms in the Chebyshev series are retained, we find that the NN scheme outperforms the GIT method.
  arXiv  Detail & Related papers  (2025-01-17T22:21:41Z)
• Quantum Algorithm for Green's Functions Measurements in the Fermi-Hubbard Model [0.0]
  We propose a new quantum algorithm, which uses an analog of the Kubo formula within linear response theory adapted to a quantum circuit the Hubbard model. We find a drastic reduction in gate count of two-qubits gates and limitations on hardware design as compared to previous approaches.
  arXiv  Detail & Related papers  (2023-10-16T13:55:10Z)
• Variational-quantum-eigensolver-inspired optimization for spin-chain work extraction [39.58317527488534]
  Energy extraction from quantum sources is a key task to develop new quantum devices such as quantum batteries. One of the main issues to fully extract energy from the quantum source is the assumption that any unitary operation can be done on the system. We propose an approach to optimize the extractable energy inspired by the variational quantum eigensolver (VQE) algorithm.
  arXiv  Detail & Related papers  (2023-10-11T15:59:54Z)
• Quantum algorithm for imaginary-time Green's functions [0.0]
  We present a hybrid quantum-classical algorithm to calculate the imaginary-time one-particle Green's function. The proposed algorithm combines variational quantum eigensolver and quantum subspace expansion to calculate Green's function.
  arXiv  Detail & Related papers  (2023-09-18T16:28:11Z)
• Efficient quantum amplitude encoding of polynomial functions [0.0]
  We present and compare two efficient methods for encoding on real functions on $n$ qubits. First, we encode the linear function into the quantum registers with a swallow sequence multi-controlled gates. Second, we use this construction as a building block to achieve a block encoding of the amplitudes corresponding to the linear function.
  arXiv  Detail & Related papers  (2023-07-20T14:40:55Z)
• Quantum state preparation without coherent arithmetic [5.478764356647437]
  We introduce a versatile method for preparing a quantum state whose amplitudes are given by some known function.magnitude existing approaches. We use a template quantum eigenvalue transformation circuit to convert a low cost block encoding of the sine function into the desired function.
  arXiv  Detail & Related papers  (2022-10-26T17:48:31Z)
• Quantum Goemans-Williamson Algorithm with the Hadamard Test and Approximate Amplitude Constraints [62.72309460291971]
  We introduce a variational quantum algorithm for Goemans-Williamson algorithm that uses only $n+1$ qubits. Efficient optimization is achieved by encoding the objective matrix as a properly parameterized unitary conditioned on an auxilary qubit. We demonstrate the effectiveness of our protocol by devising an efficient quantum implementation of the Goemans-Williamson algorithm for various NP-hard problems.
  arXiv  Detail & Related papers  (2022-06-30T03:15:23Z)
• Near-term quantum algorithm for computing molecular and materials properties based on recursive variational series methods [44.99833362998488]
  We propose a quantum algorithm to estimate the properties of molecules using near-term quantum devices. We test our method by computing the one-particle Green's function in the energy domain and the autocorrelation function in the time domain.
  arXiv  Detail & Related papers  (2022-06-20T16:33:23Z)
• Fourier-based quantum signal processing [0.0]
  Implementing general functions of operators is a powerful tool in quantum computation. Quantum signal processing is the state of the art for this aim. We present an algorithm for Hermitian-operator function design from an oracle given by the unitary evolution.
  arXiv  Detail & Related papers  (2022-06-06T18:02:30Z)
• Synthesis of Quantum Circuits with an Island Genetic Algorithm [44.99833362998488]
  Given a unitary matrix that performs certain operation, obtaining the equivalent quantum circuit is a non-trivial task. Three problems are explored: the coin for the quantum walker, the Toffoli gate and the Fredkin gate. The algorithm proposed proved to be efficient in decomposition of quantum circuits, and as a generic approach, it is limited only by the available computational power.
  arXiv  Detail & Related papers  (2021-06-06T13:15:25Z)
• Variational Monte Carlo calculations of $\mathbf{A\leq 4}$ nuclei with an artificial neural-network correlator ansatz [62.997667081978825]
  We introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei. We compute the binding energies and point-nucleon densities of $Aleq 4$ nuclei as emerging from a leading-order pionless effective field theory Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-28T14:52:28Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.