Fault-tolerant quantum computation of molecular observables

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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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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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 19 22, 8201 (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] Amara Katabarwa, Katerina Gratsea, Athena Caesura, and Peter D. Johnson, "Early Fault-Tolerant Quantum Computing", arXiv:2311.14814, (2023).

[5] 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).

[6] 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 2023-12-07 09:30:47) and SAO/NASA ADS (last updated successfully 2023-12-07 09:30:48). The list may be incomplete as not all publishers provide suitable and complete citation data.