Assessing the query complexity limits of quantum phase estimation using symmetry aware spectral bounds

• URL: http://arxiv.org/abs/2403.04737v2
• Date: Sun, 26 May 2024 18:02:41 GMT
• Title: Assessing the query complexity limits of quantum phase estimation using symmetry aware spectral bounds
• Authors: Cristian L. Cortes, Dario Rocca, Jerome Gonthier, Pauline J. Ollitrault, Robert M. Parrish, Gian-Luca R. Anselmetti, Matthias Degroote, Nikolaj Moll, Raffaele Santagati, Michael Streif,
• Abstract summary: computational cost of quantum algorithms for physics and chemistry is closely linked to the spectrum of the Hamiltonian. We introduce a hierarchy of symmetry-aware spectral bounds that provide a unified understanding of the performance of quantum phase estimation algorithms.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The computational cost of quantum algorithms for physics and chemistry is closely linked to the spectrum of the Hamiltonian, a property that manifests in the necessary rescaling of its eigenvalues. The typical approach of using the 1-norm as an upper bound to the spectral norm to rescale the Hamiltonian suits the most general case of bounded Hermitian operators but neglects the influence of symmetries commonly found in chemical systems. In this work, we introduce a hierarchy of symmetry-aware spectral bounds that provide a unified understanding of the performance of quantum phase estimation algorithms using block-encoded electronic structure Hamiltonians. We present a variational and numerically tractable method for computing these bounds, based on orbital optimization, to demonstrate that the computed bounds are smaller than conventional spectral bounds for a variety of molecular benchmark systems. We also highlight the unique analytical and numerical scaling behavior of these bounds in the thermodynamic and complete basis set limits. Our work shows that there is room for improvement in reducing the 1-norm, not yet achieved through methods like double factorization and tensor hypercontraction, but highlights potential challenges in improving the performance of current quantum algorithms beyond small constant factors through 1-norm reduction techniques alone.

Related papers

• A quantum eigenvalue solver based on tensor networks [0.0]
  Electronic ground states are of central importance in chemical simulations, but have remained beyond the reach of efficient classical algorithms. We introduce a hybrid quantum-classical eigenvalue solver that constructs a wavefunction ansatz from a linear combination of matrix product states in rotated orbital bases. This study suggests a promising new avenue for scaling up simulations of strongly correlated chemical systems on near-term quantum hardware.
  arXiv  Detail & Related papers  (2024-04-16T02:04:47Z)
• Reducing the runtime of fault-tolerant quantum simulations in chemistry through symmetry-compressed double factorization [0.0]
  We introduce the symmetry-compressed double factorization (SCDF) approach, which combines a compressed double factorization of the Hamiltonian with the symmetry shift technique, significantly reducing the 1-norm value. For the systems considered here, SCDF leads to a sizeable reduction of the Toffoli gate count in comparison to other variants of double factorization or even tensor hypercontraction.
  arXiv  Detail & Related papers  (2024-03-06T07:11:02Z)
• A hybrid quantum-classical algorithm for multichannel quantum scattering of atoms and molecules [62.997667081978825]
  We propose a hybrid quantum-classical algorithm for solving the Schr"odinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix. We show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules.
  arXiv  Detail & Related papers  (2023-04-12T18:10:47Z)
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory [44.99833362998488]
  We introduce quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple quantum numbers. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories.
  arXiv  Detail & Related papers  (2022-12-28T18:56:25Z)
• The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learning [52.77024349608834]
  Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. Key issue is how to address the inherent non-linearity of classical deep learning. We introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning.
  arXiv  Detail & Related papers  (2022-12-22T16:06:24Z)
• Efficient Quantum Analytic Nuclear Gradients with Double Factorization [0.0]
  We report a Lagrangian-based approach for evaluating relaxed one- and two-particle reduced density matrices from double factorized Hamiltonians. We demonstrate the accuracy and feasibility of our Lagrangian-based approach to recover all off-diagonal density matrix elements in classically-simulated examples.
  arXiv  Detail & Related papers  (2022-07-26T18:47:48Z)
• Numerical Simulations of Noisy Quantum Circuits for Computational Chemistry [51.827942608832025]
  Near-term quantum computers can calculate the ground-state properties of small molecules. We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
  arXiv  Detail & Related papers  (2021-12-31T16:33:10Z)
• Circuit Symmetry Verification Mitigates Quantum-Domain Impairments [69.33243249411113]
  We propose circuit-oriented symmetry verification that are capable of verifying the commutativity of quantum circuits without the knowledge of the quantum state. In particular, we propose the Fourier-temporal stabilizer (STS) technique, which generalizes the conventional quantum-domain formalism to circuit-oriented stabilizers.
  arXiv  Detail & Related papers  (2021-12-27T21:15:35Z)
• Analytical nonadiabatic couplings and gradients within the state-averaged orbital-optimized variational quantum eigensolver [0.0]
  We introduce several technical and analytical extensions to our recent state-averaged orbital-optimized variational quantum eigensolver (SA-OO-VQE) algorithm. Motivated by the limitations of current quantum computers, the first extension consists in an efficient state-resolution procedure to find the SA-OO-VQE eigenstates. The second extension allows for the estimation of analytical gradients and non-adiabatic couplings.
  arXiv  Detail & Related papers  (2021-09-09T22:38:56Z)
• Quantum-Classical Hybrid Algorithm for the Simulation of All-Electron Correlation [58.720142291102135]
  We present a novel hybrid-classical algorithm that computes a molecule's all-electron energy and properties on the classical computer. We demonstrate the ability of the quantum-classical hybrid algorithms to achieve chemically relevant results and accuracy on currently available quantum computers.
  arXiv  Detail & Related papers  (2021-06-22T18:00:00Z)
• Spectral Analysis of Product Formulas for Quantum Simulation [0.0]
  We show that the Trotter step size needed to estimate an energy eigenvalue within precision can be improved in scaling from $epsilon$ to $epsilon1/2$ for a large class of systems. Results partially generalize to diabatic processes, which remain in a narrow energy band separated from the rest of the spectrum by a gap.
  arXiv  Detail & Related papers  (2021-02-25T03:17:25Z)

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.