The Quantum Linear Systems Problem - IPAM at UCLA

Explore the quantum linear systems problem (QLSP) in this 34-minute conference talk presented by Rolando Somma from Los Alamos National Laboratory at IPAM's Quantum Numerical Linear Algebra Workshop. Delve into improved quantum algorithms for QLSP, including one that enhances the precision of the HHL algorithm exponentially and another inspired by quantum adiabatic evolutions. Examine the complexity of quantum state verification and its implications for solving QLSP. Gain insights into the potential exponential quantum speedup for this fundamental linear algebra task, and understand the assumptions, queries, and frameworks involved in various approaches to QLSP. Discover the applications of techniques such as Linear Combination of Unitaries (LCU) and Variable Time Amplitude Amplification in quantum computing.

Main references
Linear systems problem (LSP)
Quantum linear systems problem (QLSP)
Why is this problem interesting?
Assumptions and queries in the USP
HHL algorithm
LCU Algorithm: Linear combination of unitaries
LCU Framework
Variable time amplitude amplification
Why are these improvements useful?
We claim an exponential speedup, but...
QLSP: Variational approach
Basic idea for proof
Conclusions