Block encoding bosons by signal processing

Christopher F. Kane; Siddharth Hariprakash; Neel S. Modi; Michael Kreshchuk; Christian W Bauer

doi:10.22331/q-2025-05-15-1747

Block encoding bosons by signal processing

Christopher F. Kane¹, Siddharth Hariprakash^2,3,4, Neel S. Modi^2,3, Michael Kreshchuk^3,5, and Christian W Bauer³

¹Department of Physics, University of Arizona, Tucson, Arizona 85719, USA
²Center for Theoretical Physics and Department of Physics, University of California, Berkeley, California 94720, USA
³Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
⁴National Energy Research Scientific Computing Center (NERSC), Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA,
⁵Phasecraft Inc., Washington, DC 20001, USA

Published:	2025-05-15, volume 9, page 1747
Editor:	Tongyang Li
Eprint:	arXiv:2408.16824v3
Doi:	https://doi.org/10.22331/q-2025-05-15-1747
Citation:	Quantum 9, 1747 (2025).

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Abstract

Block Encoding (BE) is a crucial subroutine in many modern quantum algorithms, including those with near-optimal scaling for simulating quantum many-body systems, which often rely on Quantum Signal Processing (QSP). Currently, the primary methods for constructing BEs are the Linear Combination of Unitaries (LCU) and the sparse oracle approach. In this work, we demonstrate that QSP-based techniques, such as Quantum Singular Value Transformation (QSVT) and Quantum Eigenvalue Transformation for Unitary Matrices (QETU), can themselves be efficiently utilized for BE implementation. Specifically, we present several examples of using QSVT and QETU algorithms, along with their combinations, to block encode Hamiltonians for lattice bosons, an essential ingredient in simulations of high-energy physics. We also introduce a straightforward approach to BE based on the exact implementation of Linear Operators Via Exponentiation and LCU (LOVE-LCU). We find that, while using QSVT for BE results in the best asymptotic gate count scaling with the number of qubits per site, LOVE-LCU outperforms all other methods for operators acting on up to $\lesssim11$ qubits, highlighting the importance of concrete circuit constructions over mere comparisons of asymptotic scalings. Using LOVE-LCU to implement the BE, we simulate the time evolution of single-site and two-site systems in the lattice $\varphi^4$ theory using the Generalized QSP algorithm and compare the gate counts to those required for Trotter simulation.

► BibTeX data

@article{Kane2025blockencodingbosons,
  doi = {10.22331/q-2025-05-15-1747},
  url = {https://doi.org/10.22331/q-2025-05-15-1747},
  title = {Block encoding bosons by signal processing},
  author = {Kane, Christopher F. and Hariprakash, Siddharth and Modi, Neel S. and Kreshchuk, Michael and Bauer, Christian W},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1747},
  month = may,
  year = {2025}
}

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[1] Christian W. Bauer, "Efficient use of quantum computers for collider physics", Journal of High Energy Physics 2025 11, 108 (2025).

[2] Nishitha Reddy Venkannagari, Varun Puram, and Johnson P Thomas, 2025 5th International Conference on AI-ML-Systems (AIMLSystems) 436 (2025) ISBN:979-8-3315-7318-8.

[3] Kevin J. Joven, Elin Ranjan Das, Joel Bierman, Aishwarya Majumdar, Masoud Hakimi Heris, and Yuan Liu, "Scalable quantum computational science: A perspective from block-encodings and polynomial transformations", APL Computational Physics 2 1, 010901 (2026).

[4] I. Novikau and I. Joseph, "An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations", Journal of Computational Physics 564, 115132 (2026).

[5] Yuan Liu, Shraddha Singh, Kevin C. Smith, Eleanor Crane, John M. Martyn, Alec Eickbusch, Alexander Schuckert, Richard D. Li, Jasmine Sinanan-Singh, Micheline B. Soley, Takahiro Tsunoda, Isaac L. Chuang, Nathan Wiebe, and Steven M. Girvin, "Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications", PRX Quantum 7 1, 010201 (2026).

[6] Siddharth Hariprakash, Neel S. Modi, Michael Kreshchuk, Christopher F. Kane, and Christian W. Bauer, "Strategies for simulating the time evolution of Hamiltonian lattice field theories", Physical Review A 111 2, 022419 (2025).

[7] Dorota M. Grabowska, Christopher F. Kane, and Christian W. Bauer, "Fully gauge-fixed SU(2) Hamiltonian for quantum simulations", Physical Review D 111 11, 114516 (2025).

[8] Mason L. Rhodes, Michael Kreshchuk, and Shivesh Pathak, "Exponential Improvements in the Simulation of Lattice Gauge Theories Using Near-Optimal Techniques", PRX Quantum 5 4, 040347 (2024).

[9] Wenyang Qian, Meijian Li, Carlos A. Salgado, and Michael Kreshchuk, "Efficient quantum simulation of QCD jets on the light front", Physical Review D 111 9, 096001 (2025).

[10] Christopher F. Kane, Siddharth Hariprakash, and Christian W. Bauer, "Obtaining continuum physics from dynamical simulations of Hamiltonian lattice gauge theories", arXiv:2506.16559, (2025).

[11] S. E. Skelton, "The Hitchhiker's Guide to QSP pre-processing", arXiv:2501.05977, (2025).

[12] Siddharth Hariprakash, Roel Van Beeumen, Katherine Klymko, and Daan Camps, "The Practicality of Randomized Quantum Linear Systems Solvers", arXiv:2510.13766, (2025).

[13] Erik J. Gustafson and Henry Lamm, "Preparing Fermions via Classical Sampling and Linear Combinations of Unitaries", arXiv:2603.22422, (2026).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-11 22:09:47) and SAO/NASA ADS (last updated successfully 2026-08-11 22:09:48). The list may be incomplete as not all publishers provide suitable and complete citation data.

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