HHL algorithm mechanics, resource requirements, and practical applicability to logistics linear system problems.
Where Kalman filters, state-space models, and network flow depend on solving Ax=b.
Harrow, Hassidim, and Lloyd (2009): exponential speedup with caveats. Key areas include: HHL algorithm structure: quantum phase estimation, controlled rotation, and amplitude amplification for solving Ax=b; The exponential speedup claim: O(log N) versus O(N) for sparse systems, and why the fine print matters; Input/output bottleneck: quantum state preparation and readout constraints that limit practical advantage (Aaronson 2015).
Kalman filtering, state-space inference, and network flow computation. Key areas include: Kalman filtering for logistics: demand state estimation, fleet position tracking, and inventory level inference as linear system problems; State-space models: hidden Markov structure in supply chain dynamics where the transition matrix solve is the computational bottleneck; Network flow computation: multi-commodity flow problems on logistics networks where linear system solves dominate runtime.
Implementing a quantum linear solver on a logistics state-space problem. Key areas include: Building an HHL circuit for a 4x4 state-space model using Qiskit with quantum phase estimation; Comparing solution accuracy against NumPy dense solver and scipy.sparse iterative solver on the same system; Measuring circuit depth and qubit requirements as system dimension increases from 4 to 16.
Why HHL requires error correction and what that means for timelines. Key areas include: Circuit depth requirements: HHL for an N-dimensional system needs O(log^2 N) depth with controlled rotations that exceed NISQ coherence times; Error correction overhead: logical qubit counts for practical HHL instances require thousands of physical qubits per logical qubit; Variational quantum linear solvers (VQLS): Bravo-Prieto et al. (2020) as a NISQ-compatible alternative with shallower circuits but weaker guarantees.
What to use today and when quantum linear solvers become practical.
Q&A and Action Planning: this session covers the core principles and technical underpinnings relevant to the subject area.
Discuss this topic with senior peers.
