Quantum algorithms to simulate many-body physics of correlated fermions.

By Zhang Jiang, Kevin J Sung, Kostyantyn Kechedzhi, Vadim N. Smelyanskiy, Sergio Boixo. 2017

183 citations recorded by the source corpus.

Simulating strongly correlated fermionic systems is notoriously hard on classical computers. An alternative approach, as proposed by Feynman, is to use a quantum computer. Here, we discuss quantum simulation of strongly correlated fermionic systems. We focus specifically on 2D and linear geometry with nearest neighbor qubit-qubit couplings, typical for superconducting transmon qubit arrays. We improve an existing algorithm to prepare an arbitrary Slater determinant by exploiting a unitary symmetry. We also present a quantum algorithm to prepare an arbitrary fermionic Gaussian state with $O(N^2)$ gates and $O(N)$ circuit depth. Both algorithms are optimal in the sense that the numbers of parameters in the quantum circuits are equal to those to describe the quantum states. Furthermore, we propose an algorithm to implement the 2-dimensional (2D) fermionic Fourier transformation on a 2D qubit array with only $O(N^{1.5})$ gates and $O(\sqrt N)$ circuit depth, which is the minimum depth required for quantum information to travel across the qubit array. We also present methods to simulate each time step in the evolution of the 2D Fermi-Hubbard model---again on a 2D qubit array---with $O(N)$ gates and $O(\sqrt N)$ circuit depth. Finally, we discuss how these algorithms can be used to determine the ground state properties and phase diagrams of strongly correlated quantum systems using the Hubbard model as an example.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/7be861c82790a8d19100d5e714dc0d843db43c5b

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity (2018, background): “…accuracy (beyond the agreement of state-of-the-art numerical methods [97]) for this regime would be in the vicinity of Δ E ≈ t= 100 [100]; these choices would suggest a T complexity of approximately and an ancilla count of approximately We summarize these resources for various…”
Improved techniques for preparing eigenstates of fermionic Hamiltonians (2017, methodology): “Beyond applications in chemistry, one might want to prepare fermionic eigenstates in order to simulate quantum materials(5) including models of high-temperature superconductivity.(6) In the procedure introduced by Abrams and Lloyd,(7) one first initializes the system in some efficient-to-prepare ini”
Observation of separated dynamics of charge and spin in the Fermi-Hubbard model (2020, methodology): “Our platform enjoys the flexibility that analog devices do not, such as the ability to measure arbitrary observables, reverse the time evolution, and prepare for various initial states including BCS-type states [19].”
Hartree-Fock on a superconducting qubit quantum computer (2020, background): “Jiang et. al and Kivlichan et. al [26, 36] point out that in a ﬁxed particle manifold the circuit depth can be further minimized.”