Examples

Decoding

• Decoding classical LDPC codes
• Decoding 3-qubit repetition code
• Decoding 5-qubit perfect code
• Decoding Shor’s 9-qubit code
• Decoding surface code

• Decoding classical LDPC codes — Builds an MPS that encodes the superposition of all codewords of a random-regular Gallager (3,4) classical LDPC code and translates parity checks into MPO (XOR) constraints. Demonstrates “dephasing DMRG” to solve the main-component (max-likelihood) decoding problem and validates the end-to-end pipeline.

• Decoding 3-qubit repetition code — Minimal quantum decoding demo using the 3-qubit repetition code under bit-flip noise. Illustrates the tensor network site layout and shows agreement between the analytical logical failure rate and the numerical results.

• Decoding 5-qubit perfect code — Decode the [[5,1,3]] five-qubit “perfect code” using our MPS decoder under bit-flip noise. Dives into the details of the error passing through the decoder.

• Decoding Shor’s 9-qubit code — Demonstrates the 9-qubit Shor code with separated X/Z error handling in the TN framework. Serves as a bridge between toy codes and LDPC-like examples.

• Decoding surface code — Small planar surface-code instances (e.g., perfect syndrome). Visualise the underlying tensor network structure. Compare contraction strategies and explore accuracy/cost trade-offs as a function of maximum bond dimension.

Miscellaneous

• Ground state search for 1D quantum Ising model
• Random quantum circuit simulation
• Main component problem
• MPS-MPO contraction schedule optimisation

• Ground state search for 1D quantum Ising model — Solve a simple 1D quantum Ising chain using an MPS ground-state search. Compares observables and magnetisation curves from exact diagonalisation and DMRG to confirm correctness. A gentle introduction to MPS/MPO mechanics outside of decoding.

• Random quantum circuit simulation — Simulates random (checkerboard-style) circuits on MPS to study entanglement growth and contraction behaviour. Tracks fidelity decay at fixed bond dimension, providing a benchmarking harness for contraction strategies.

• Main component problem — Defines and solves the Main Component Problem (finding the basis state that contributes most to a given state) as a sanity check for the dephasing DMRG optimiser. Compares solutions from exact diagonalisation, standard DMRG, and dephasing DMRG, demonstrating agreement.

• MPS-MPO contraction schedule optimisation — Tests an MPO order-optimisation strategy (based on matrix bandwidth minimisation) to reduce intermediate bond growth during operator application. Shows how reordering lowers contraction cost and improves practical performance within experiments.

• <no title> — Illustrates how to leverage GPU acceleration (via CuPy) for MPS/MPO operations. Compares performance between CPU and GPU backends for key tensor network routines, demonstrating speedups on compatible hardware.