Low-depth Simulations Of Fermionic Systems On Square-grid Quantum Hardware

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Manuel G. Algaba, P. V. Sriluckshmy, Martin Leib, and Fedor Šimkovic IV

IQM, Nymphenburgerstr. 86, 80636 Munich, Germany

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Abstract

We present a general strategy for mapping fermionic systems to quantum hardware with square qubit connectivity which yields low-depth quantum circuits, counted in the number of native two-qubit fSIM gates. We achieve this by leveraging novel operator decomposition and circuit compression techniques paired with specifically chosen low-depth fermion-to-qubit mappings and allow for a high degree of gate cancellations and parallelism. Our mappings retain the flexibility to simultaneously optimize for qubit counts or qubit operator weights and can be used to investigate arbitrary fermionic lattice geometries. We showcase our approach by investigating the tight-binding model, the Fermi-Hubbard model as well as the multi-orbital Hubbard-Kanamori model. We report unprecedentedly low circuit depths per single Trotter layer with up to a $70 %$ improvement upon previous state-of-the-art. Our compression technique also results in significant reduction of two-qubit gates. We find the lowest gate-counts when applying the XYZ-formalism to the DK mapping. Additionally, we show that our decomposition and compression formalism produces favourable circuits even when no native parameterized two-qubit gates are available.

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Featured image: a) Fermionic connectivity graph for a 3-by-3 square NN lattice with 4 orbitals per lattice site with two spin-modes each. b) Vertex (black) and edge (blue, green, red, purple, pink) operators mapping this fermionic connectivity to a square qubit layout using the PAA mapping. Each lattice site is encoded into a linear chain consisting of four spin-up (full) and four spin-down (empty) physical qubits (squares) connected to the neighboring sites through ancilla qubits (circles). Dashed qubit connections are not required. c) Minimal-depth circuit for the simulation of one Trotter step of the Hubbard-Kanamori model in 55 parallel steps. Size of blocks is not to scale: $t_h$-$t_v$-$t_v$ blocks are depth-seven, $t_h$-terms are depth-three, J terms are depth-five, $U$, $U_1$, $U_2$ terms and fSWAPs can be performed with a single two-qubit gate. Further circuit compression can be applied within grey shaded areas of the circuit.

Popular summary

Simulating fermions like electrons or nucleons using qubits, which show different commutation relations require a transformation between these two kind of entities called fermion-to-qubit mappings. These mappings may transform local fermionic operators into non-local qubit gates. For avoiding this issue different local fermion-to-qubit mappings have been created. In this work, we describe a novel family of fermion-to-qubit mappings that intertwines very well with the XYZ decomposition and we show that the latter can optimally decompose fermionic hopping operators into qubit gates. These improvements upon previous literature allow us to find the shallowest quantum circuits ever described for simulating a Trotter step of the Fermi-Hubbard model, which is a key model in condensed matter physics and high temperature superconductivity. We extend this work to other non-trivial models that allow richer physics, i.e. the Hubbard-Kanamori Hamiltonian.

► BibTeX data

@article{Algaba2024lowdepthsimulations, doi = {10.22331/q-2024-04-30-1327}, url = {https://doi.org/10.22331/q-2024-04-30-1327}, title = {Low-depth simulations of fermionic systems on square-grid quantum hardware}, author = {Algaba, Manuel G. and Sriluckshmy, P. V. and Leib, Martin and {v{S}}imkovic IV, Fedor}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {8}, pages = {1327}, month = apr, year = {2024} }

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Cited by

[1] Roland C. Farrell, Marc Illa, Anthony N. Ciavarella, and Martin J. Savage, “Quantum Simulations of Hadron Dynamics in the Schwinger Model using 112 Qubits”, arXiv:2401.08044, (2024).

[2] Roland C. Farrell, Marc Illa, Anthony N. Ciavarella, and Martin J. Savage, “Scalable Circuits for Preparing Ground States on Digital Quantum Computers: The Schwinger Model Vacuum on 100 Qubits”, PRX Quantum 5 2, 020315 (2024).

[3] Yu-An Chen, Alexey V. Gorshkov, and Yijia Xu, “Error-correcting codes for fermionic quantum simulation”, SciPost Physics 16 1, 033 (2024).

[4] P. V. Sriluckshmy, Vicente Pina-Canelles, Mario Ponce, Manuel G. Algaba, IV Fedor Šimkovic, and Martin Leib, “Optimal, hardware native decomposition of parameterized multi-qubit Pauli gates”, Quantum Science and Technology 8 4, 045029 (2023).

[5] Georg Bergner, Masanori Hanada, Enrico Rinaldi, and Andreas Schafer, “Toward QCD on Quantum Computer: Orbifold Lattice Approach”, arXiv:2401.12045, (2024).

The above citations are from SAO/NASA ADS (last updated successfully 2024-04-30 15:48:35). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2024-04-30 15:48:34: Could not fetch cited-by data for 10.22331/q-2024-04-30-1327 from Crossref. This is normal if the DOI was registered recently.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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Source: https://quantum-journal.org/papers/q-2024-04-30-1327/

Time Stamp: April 30, 2024

Time Stamp: Feb 5, 2024

Quantum simulation of real-space dynamics

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Quantum Journal

Source Node: 1757535

Time Stamp: Nov 17, 2022

Low-depth simulations of fermionic systems on square-grid quantum hardware

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