Well-conditioned multi-product formulas for hardware-friendly Hamiltonian simulation

Almudena Carrera Vazquez1,2, Daniel J. Egger1, David Ochsner1,2, and Stefan Woerner1

1IBM Quantum, IBM Research Europe – Zurich
2ETH Zurich

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Abstract

Simulating the time-evolution of a Hamiltonian is one of the most promising applications of quantum computers. Multi-Product Formulas (MPFs) are well suited to replace standard product formulas since they scale better with respect to time and approximation errors. Hamiltonian simulation with MPFs was first proposed in a fully quantum setting using a linear combination of unitaries. Here, we analyze and demonstrate a hybrid quantum-classical approach to MPFs that classically combines expectation values evaluated with a quantum computer. This has the same approximation bounds as the fully quantum MPFs, but, in contrast, requires no additional qubits, no controlled operations, and is not probabilistic. We show how to design MPFs that do not amplify the hardware and sampling errors, and demonstrate their performance. In particular, we illustrate the potential of our work by theoretically analyzing the benefits when applied to a classically intractable spin-boson model, and by computing the dynamics of the transverse field Ising model using a classical simulator as well as quantum hardware. We observe an error reduction of up to an order of magnitude when compared to a product formula approach by suppressing hardware noise with Pauli Twirling, pulse efficient transpilation, and a novel zero-noise extrapolation based on scaled cross-resonance pulses. The MPF methodology reduces the circuit depth and may therefore represent an important step towards quantum advantage for Hamiltonian simulation on noisy hardware.

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Cited by

[1] Atsushi MATSUO, Shigeru YAMASHITA, and Daniel J. EGGER, "A SAT Approach to the Initial Mapping Problem in SWAP Gate Insertion for Commuting Gates", IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E106.A 11, 1424 (2023).

[2] Stefan H. Sack and Daniel J. Egger, "Large-scale quantum approximate optimization on nonplanar graphs with machine learning noise mitigation", Physical Review Research 6 1, 013223 (2024).

[3] Daniel J. Egger, Chiara Capecci, Bibek Pokharel, Panagiotis Kl. Barkoutsos, Laurin E. Fischer, Leonardo Guidoni, and Ivano Tavernelli, "Pulse variational quantum eigensolver on cross-resonance-based hardware", Physical Review Research 5 3, 033159 (2023).

[4] Hugo Perrin, Thibault Scoquart, Alexander Shnirman, Jörg Schmalian, and Kyrylo Snizhko, "Mitigating crosstalk errors by randomized compiling: Simulation of the BCS model on a superconducting quantum computer", Physical Review Research 6 1, 013142 (2024).

[5] Gumaro Rendon, Jacob Watkins, and Nathan Wiebe, "Improved Accuracy for Trotter Simulations Using Chebyshev Interpolation", Quantum 8, 1266 (2024).

[6] Alberto Di Meglio, Karl Jansen, Ivano Tavernelli, Constantia Alexandrou, Srinivasan Arunachalam, Christian W. Bauer, Kerstin Borras, Stefano Carrazza, Arianna Crippa, Vincent Croft, Roland de Putter, Andrea Delgado, Vedran Dunjko, Daniel J. Egger, Elias Fernandez-Combarro, Elina Fuchs, Lena Funcke, Daniel Gonzalez-Cuadra, Michele Grossi, Jad C. Halimeh, Zoe Holmes, Stefan Kuhn, Denis Lacroix, Randy Lewis, Donatella Lucchesi, Miriam Lucio Martinez, Federico Meloni, Antonio Mezzacapo, Simone Montangero, Lento Nagano, Voica Radescu, Enrique Rico Ortega, Alessandro Roggero, Julian Schuhmacher, Joao Seixas, Pietro Silvi, Panagiotis Spentzouris, Francesco Tacchino, Kristan Temme, Koji Terashi, Jordi Tura, Cenk Tuysuz, Sofia Vallecorsa, Uwe-Jens Wiese, Shinjae Yoo, and Jinglei Zhang, "Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group", arXiv:2307.03236, (2023).

[7] Johannes Weidenfeller, Lucia C. Valor, Julien Gacon, Caroline Tornow, Luciano Bello, Stefan Woerner, and Daniel J. Egger, "Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware", Quantum 6, 870 (2022).

[8] Sergiy Zhuk, Niall Robertson, and Sergey Bravyi, "Trotter error bounds and dynamic multi-product formulas for Hamiltonian simulation", arXiv:2306.12569, (2023).

[9] Naoki Kanazawa, Daniel Egger, Yael Ben-Haim, Helena Zhang, William Shanks, Gadi Aleksandrowicz, and Christopher Wood, "Qiskit Experiments: A Python package to characterize and calibrate quantum computers", The Journal of Open Source Software 8 84, 5329 (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2024-03-02 11:11:53) and SAO/NASA ADS (last updated successfully 2024-03-02 11:11:54). The list may be incomplete as not all publishers provide suitable and complete citation data.