Kernel-Function Based Quantum Algorithms for Finite Temperature Quantum Simulation

Abstract

Computing finite temperature properties of a quantum many-body system is key to describing a broad range of correlated quantum many-body physics from quantum chemistry and condensed matter to thermal quantum field theories. Quantum computing with rapid developments in recent years has a huge potential to impact the computation of quantum thermodynamics. To fulfill the potential impacts, it is crucial to design quantum algorithms that utilize the computation power of the quantum computing devices. Here we present a quantum kernel function expansion (QKFE) algorithm for solving thermodynamic properties of quantum many-body systems. In this quantum algorithm, the many-body density of states is approximated by a kernel-Fourier expansion, whose expansion moments are obtained by random state sampling and quantum interferometric measurements. As compared to its classical counterpart, namely the kernel polynomial method (KPM), QKFE has an exponential advantage in the cost of both time and memory. In computing low temperature properties, QKFE becomes inefficient, as similar to classical KPM. To resolve this difficulty, we further construct a thermal ensemble and approaches the low temperature regime step-by-step. For quantum Hamiltonians, whose ground states are preparable with polynomial quantum circuits, THEI has an overall polynomial complexity. We demonstrate its efficiency with applications to one and two-dimensional quantum spin models, and a fermionic lattice. With our analysis on the realization with digital and analogue quantum devices, we expect the quantum algorithm is accessible to current quantum technology.

11 pages, 5 figures

References in corpus (17)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Probing many-body dynamics on a 51-atom quantum simulator
• Quantum computational advantage using photons
• Theory of ultracold Fermi gases
• Simulated Quantum Computation of Molecular Energies
• Strong quantum computational advantage using a superconducting quantum processor
• The Kernel Polynomial Method
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Photonic Boson Sampling in a Tunable Circuit
• Quantum magnetism and criticality
• Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms
• Quasiclassical calculations of BBR-induced depopulation rates and effective lifetimes of Rydberg nS, nP and nD alkali-metal atoms with n < 80
• Observation of Time-Crystalline Eigenstate Order on a Quantum Processor
• Feshbach resonances in ultracold K(39)
• Probing many-body quantum chaos with quantum simulators
• Quantum imaginary time evolution steered by reinforcement learning

Cited by in corpus (2)

• Calculating the many-body density of states on a digital quantum computer
• Near-term quantum algorithm for computing molecular and materials properties based on recursive variational series methods