Tensor Networks and Quantum Algorithms
summary
Claims that quantum computation ≡ approximating tensor networks, with a constructive reduction: pick a bubbling (an ordering), normalize each tensor by its operator norm, embed normalized maps into unitaries using one extra qubit, then the circuit’s success probability equals the tensor network value times the product of norms. Shows log‑depth, local quantum circuits are exactly classically simulatable by contracting across cuts that cross O(log n) edges. Leaves an open problem: can classical sampling match quantum additive approximations for all nonnegative tensor networks (L1 versus L2 norms)?
AI-written summary · about
chapters (8)
- 0:00Introduction
- 3:30Tensors
- 8:50Operations
- 15:00Linear algebra
- 18:27Tensor networks
- 31:44Approximating
- 47:04Quantum Algorithms
- 54:04Open Question
related talks
17mQuantum and Quantum-Inspired AI Solutions: Bridging Innovation and Industry Readiness
44mQuantum machine learning: Prospects and challenges
31mQuantum neural networks
15mEnsuring Robustness in Hybrid Quantum Neural Networks
34mThe physics of deep learning using tensor networks
39mNetworking for Quantum: how simulations help us to design the future
46mQuantum Machine Learning 101: An Introduction for Beginners with...
27mQuantum Machine Learning With TensorFlow Quantum