Direct Estimation of the Density of States for Fermionic Systems

• URL: http://arxiv.org/abs/2407.03414v1
• Date: Wed, 3 Jul 2024 18:00:05 GMT
• Title: Direct Estimation of the Density of States for Fermionic Systems
• Authors: Matthew L. Goh, Bálint Koczor,
• Abstract summary: We develop quantum algorithms to extract thermodynamic properties by estimating the density of states (DOS) Our approach allows one to estimate the DOS for a specific subspace of the full Hilbert space. We show that our approach is highly robust to algorithmic errors in the time evolution and to gate noise.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Simulating time evolution is one of the most natural applications of quantum computers and is thus one of the most promising prospects for achieving practical quantum advantage. Here we develop quantum algorithms to extract thermodynamic properties by estimating the density of states (DOS), a central object in quantum statistical mechanics. We introduce key innovations that significantly improve the practicality and extend the generality of previous techniques. First, our approach allows one to estimate the DOS for a specific subspace of the full Hilbert space. This is crucial for fermionic systems, since fermion-to-qubit mappings partition the full Hilbert space into subspaces of fixed number, on which both canonical and grand canonical ensemble properties depend. Second, in our approach, by time evolving very simple, random initial states (e.g. random computational basis states), we can exactly recover the DOS on average. Third, due to circuit-depth limitations, we only reconstruct the DOS up to a convolution with a Gaussian window - thus all imperfections that shift the energy levels by less than the width of the convolution window will not significantly affect the estimated DOS. For these reasons we find the approach is a promising candidate for early quantum advantage as even short-time, noisy dynamics yield a semi-quantitative reconstruction of the DOS (convolution with a broad Gaussian window), while early fault tolerant devices will likely enable higher resolution DOS reconstruction through longer time evolution. We demonstrate the practicality of our approach in representative Fermi-Hubbard and spin models and find that our approach is highly robust to algorithmic errors in the time evolution and to gate noise. We show that our approach is compatible with NISQ-friendly variational methods, introducing a new technique for variational time evolution in noisy DOS computations.

Related papers

• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• Scalable Imaginary Time Evolution with Neural Network Quantum States [0.0]
  The representation of a quantum wave function as a neural network quantum state (NQS) provides a powerful variational ansatz for finding the ground states of many-body quantum systems. We introduce an approach that bypasses the computation of the metric tensor and instead relies exclusively on first-order descent with Euclidean metric. We make this method adaptive and stable by determining the optimal time step and keeping the target fixed until the energy of the NQS decreases.
  arXiv  Detail & Related papers  (2023-07-28T12:26:43Z)
• Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search [77.34726150561087]
  We consider an environment formed by incoherent photons as a resource for controlling open quantum systems via an incoherent control. We exploit a coherent control in the Hamiltonian and an incoherent control in the dissipator which induces the time-dependent decoherence rates.
  arXiv  Detail & Related papers  (2023-02-28T07:36:02Z)
• On optimization of coherent and incoherent controls for two-level quantum systems [77.34726150561087]
  This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr"odinger equation with coherent control. The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation.
  arXiv  Detail & Related papers  (2022-05-05T09:08:03Z)
• Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer [0.029316801942271296]
  We show an efficient, low-depth variational quantum algorithm with few parameters can reproduce important qualitative features of medium-size instances of the Fermi-Hubbard model. We address 1x8 and 2x4 instances on 16 qubits on a superconducting quantum processor. We observe the onset of the metal-insulator transition and Friedel oscillations in 1D, and antiferromagnetic order in both 1D and 2D.
  arXiv  Detail & Related papers  (2021-12-03T17:14:20Z)
• Probabilistic imaginary-time evolution by using forward and backward real-time evolution with a single ancilla: first-quantized eigensolver of quantum chemistry for ground states [0.0]
  Imaginary-time evolution (ITE) on a quantum computer is a promising formalism for obtaining the ground state of a quantum system. We propose a new approach of PITE which requires only a single ancillary qubit. We discuss the application of our approach to quantum chemistry by focusing on the scaling of computational cost.
  arXiv  Detail & Related papers  (2021-11-24T12:54:27Z)
• Unraveling correlated material properties with noisy quantum computers: Natural orbitalized variational quantum eigensolving of extended impurity models within a slave-boson approach [0.0]
  We propose a method for computing space-resolved correlation properties of the two-dimensional Hubbard model within a quantum-classical embedding strategy. We solve a two-impurity embedded model requiring eight qubits with an advanced hybrid scheme on top of the Variational Quantum Eigensolver algorithm. This paves the way to a controlled solution of the Hubbard model with larger and larger embedded problems solved by quantum computers.
  arXiv  Detail & Related papers  (2021-08-24T14:58:14Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Experimental Realization of Nonadiabatic Holonomic Single-Qubit Quantum Gates with Two Dark Paths in a Trapped Ion [41.36300605844117]
  We show nonadiabatic holonomic single-qubit quantum gates on two dark paths in a trapped $171mathrmYb+$ ion based on four-level systems with resonant drives. We find that nontrivial holonomic two-qubit quantum gates can also be realized within current experimental technologies.
  arXiv  Detail & Related papers  (2021-01-19T06:57:50Z)
• Quantum-optimal-control-inspired ansatz for variational quantum algorithms [105.54048699217668]
  A central component of variational quantum algorithms (VQA) is the state-preparation circuit, also known as ansatz or variational form. Here, we show that this approach is not always advantageous by introducing ans"atze that incorporate symmetry-breaking unitaries. This work constitutes a first step towards the development of a more general class of symmetry-breaking ans"atze with applications to physics and chemistry problems.
  arXiv  Detail & Related papers  (2020-08-03T18:00:05Z)
• Accelerated variational algorithms for digital quantum simulation of many-body ground states [0.0]
  One of the key applications for the quantum simulators is to emulate the ground state of many-body systems. variational methods have also been proposed and realized in quantum simulators for emulating the ground state of many-body systems.
  arXiv  Detail & Related papers  (2020-06-16T18:01:35Z)

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.