Fault-tolerant Quantum Computation Of Molecular Observables

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Mark Steudtner¹, Sam Morley-Short¹, William Pol¹, Sukin Sim¹, Cristian L. Cortes², Matthias Loipersberger², Robert M. Parrish², Matthias Degroote³, Nikolaj Moll³, Raffaele Santagati³, and Michael Streif³

¹PsiQuantum, 700 Hansen Way, Palo Alto, CA 94304, USA
²QC Ware Corp, Palo Alto, CA 94306, USA
³Quantum Lab, Boehringer Ingelheim, 55218 Ingelheim am Rhein, Germany

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Abstract

Over the past three decades significant reductions have been made to the cost of estimating ground-state energies of molecular Hamiltonians with quantum computers. However, comparatively little attention has been paid to estimating the expectation values of other observables with respect to said ground states, which is important for many industrial applications. In this work we present a novel expectation value estimation (EVE) quantum algorithm which can be applied to estimate the expectation values of arbitrary observables with respect to any of the system’s eigenstates. In particular, we consider two variants of EVE: std-EVE, based on standard quantum phase estimation, and QSP-EVE, which utilizes quantum signal processing (QSP) techniques. We provide rigorous error analysis for both both variants and minimize the number of individual phase factors for QSPEVE. These error analyses enable us to produce constant-factor quantum resource estimates for both std-EVE and QSP-EVE across a variety of molecular systems and observables. For the systems considered, we show that QSP-EVE reduces (Toffoli) gate counts by up to three orders of magnitude and reduces qubit width by up to 25% compared to std-EVE. While estimated resource counts remain far too high for the first generations of fault-tolerant quantum computers, our estimates mark a first of their kind for both the application of expectation value estimation and modern QSP-based techniques.

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► BibTeX data

@article{Steudtner2023faulttolerant, doi = {10.22331/q-2023-11-06-1164}, url = {https://doi.org/10.22331/q-2023-11-06-1164}, title = {Fault-tolerant quantum computation of molecular observables}, author = {Steudtner, Mark and Morley-Short, Sam and Pol, William and Sim, Sukin and Cortes, Cristian L. and Loipersberger, Matthias and Parrish, Robert M. and Degroote, Matthias and Moll, Nikolaj and Santagati, Raffaele and Streif, Michael}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1164}, month = nov, year = {2023}<br /> }

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Cited by

[1] Ignacio Loaiza and Artur F. Izmaylov, “Block-Invariant Symmetry Shift: Preprocessing Technique for Second-Quantized Hamiltonians to Improve Their Decompositions to Linear Combination of Unitaries”, Journal of Chemical Theory and Computation acs.jctc.3c00912 (2023).

[2] Alexander M. Dalzell, Sam McArdle, Mario Berta, Przemyslaw Bienias, Chi-Fang Chen, András Gilyén, Connor T. Hann, Michael J. Kastoryano, Emil T. Khabiboulline, Aleksander Kubica, Grant Salton, Samson Wang, and Fernando G. S. L. Brandão, “Quantum algorithms: A survey of applications and end-to-end complexities”, arXiv:2310.03011, (2023).

[3] Cristian L. Cortes, Matthias Loipersberger, Robert M. Parrish, Sam Morley-Short, William Pol, Sukin Sim, Mark Steudtner, Christofer S. Tautermann, Matthias Degroote, Nikolaj Moll, Raffaele Santagati, and Michael Streif, “Fault-tolerant quantum algorithm for symmetry-adapted perturbation theory”, arXiv:2305.07009, (2023).

[4] Sophia Simon, Raffaele Santagati, Matthias Degroote, Nikolaj Moll, Michael Streif, and Nathan Wiebe, “Improved precision scaling for simulating coupled quantum-classical dynamics”, arXiv:2307.13033, (2023).

[5] Ignacio Loaiza and Artur F. Izmaylov, “Block-Invariant Symmetry Shift: Preprocessing technique for second-quantized Hamiltonians to improve their decompositions to Linear Combination of Unitaries”, arXiv:2304.13772, (2023).

The above citations are from Crossref’s cited-by service (last updated successfully 2023-11-13 12:50:11) and SAO/NASA ADS (last updated successfully 2023-11-13 12:50:12). The list may be incomplete as not all publishers provide suitable and complete citation data.

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-2023-11-06-1164/

Time Stamp: November 6, 2023

Time Stamp: Nov 7, 2023

Fault-tolerant quantum computation of molecular observables

Republished By Plato

Abstract

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