Block encoding bosons by signal processing

Journal Article · Tue Dec 31 23:00:00 EST 2024 · Quantum

DOI:https://doi.org/10.22331/q-2025-05-15-1747· OSTI ID:2569051

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

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 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 theory using the Generalized QSP algorithm and compare the gate counts to those required for Trotter simulation.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: US Department of Energy; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22), Scientific User Facilities Division (SC-22.3 )
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 2569051
• Journal Information: Quantum, Journal Name: Quantum Vol. 9
• Country of Publication: United States
• Language: English