arXiv subjects

Christian W Bauer

Publications and source records attributed to Christian W Bauer.

6 recordsLinked to original sources

arXiv2025

Block encoding bosons by signal processing

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 $φ^4$ theory using the Generalized QSP algorithm and compare the gate counts to those required for Trotter simulation.

quant-ph↗

arXiv2024

Strategies for simulating time evolution of Hamiltonian lattice field theories

Simulating the time evolution of quantum field theories given some Hamiltonian $H$ requires developing algorithms for implementing the unitary operator e^{-iHt}. A variety of techniques exist that accomplish this task, with the most common technique used so far being Trotterization, which is a special case of the application of a product formula. However, other techniques exist that promise better asymptotic scaling in certain parameters of the theory being simulated, the most efficient of which are based on the concept of block encoding. In this work we study the performance of such algorithms in simulating lattice field theories. We derive and compare the asymptotic gate complexities of several commonly used simulation techniques in application to Hamiltonian Lattice Field Theories. Using the scalar ϕ^4 theory as a test, we also perform numerical studies and compare the gate costs required by Product Formulas and Signal Processing based techniques to simulate time evolution. For the latter, we use the the Linear Combination of Unitaries construction augmented with the Quantum Fourier Transform circuit to switch between the field and momentum eigenbases, which leads to immediate order-of-magnitude improvement in the cost of preparing the block encoding. The paper also includes a pedagogical review of utilized techniques, in particular Product Formulas, LCU, Qubitization, QSP, as well as a technique we call HHKL based on its inventors' names.

quant-ph↗

arXiv2019

A Quantum Algorithm to Efficiently Sample from Interfering Binary Trees

Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by a binary tree, we construct an explicit quantum algorithm that runs in polynomial time to sample from the process once. The corresponding naive Markov Chain algorithm does not produce the correct probability distribution and an explicit classical calculation of the full distribution requires exponentially many operations. However, the problem can be reduced to a system of two qubits with repeated measurements, shedding light on a quantum-inspired efficient classical algorithm.

quant-ph↗

arXiv2018

Standard Model Fragmentation Functions at Very High Energies

We compute the leading-order evolution of parton fragmentation functions for all the Standard Model fermions and bosons up to energies far above the electroweak scale, where electroweak symmetry is restored. We discuss the difference between double-logarithmic and leading-logarithmic resummation, and show how the latter can be implemented through a scale choice in the SU(2) coupling. We present results for a wide range of partonic center-of-mass energies, including the polarization of fermion and vector boson fragmentation functions induced by electroweak evolution.

hep-ph↗

arXiv2017

Resummation of electroweak Sudakov logarithms for real radiation

Using the known resummation of virtual corrections together with knowledge of the leading-log structure of real radiation in a parton shower, we derive analytic expressions for the resummed real radiation after they have been integrated over all of phase space. Performing a numerical analysis for both the 13 TeV LHC and a 100 TeV $pp$ collider, we show that resummation of the real corrections is at least as important as resummation of the virtual corrections, and that this resummation has a sizable effect for partonic center of mass energies exceeding $\sqrt{s} = {\cal O}$(few TeV). For partonic center of mass energies $\sqrt{s} \gtrsim$ 10 TeV, which can be reached at a 100 TeV collider, resummation becomes an O(1) effect and needs to be included even for rough estimates of the cross-sections.

hep-ph↗

arXiv2004

Inclusive determinations of Vub and Vcb

In this talk I review the status of our ability to extract the CKM matrix elements Vub and Vcb from inclusive semileptonic decays. I focus on model independent determinations of these parameters and discuss the expected theoretical uncertainties.

hep-ph↗