Matrix Product States (MPS) | Tensor Network Simulation of 100+ Qubits
Quick Technical Answer:
Matrix Product States (MPS) is a tensor network ansatz that decomposes a 2^N quantum statevector into a 1D chain of N 3-index tensors, enabling exact and truncated classical simulation of 100+ qubits for quantum systems with 1D area-law entanglement.
Formula / Unitary:
|\psi\rangle = \sum_{s_1, \dots, s_N} A_1^{s_1} A_2^{s_2} \cdots A_N^{s_N} |s_1 s_2 \dots s_N\rangle, \quad \chi \le \chi_{\text{max}}
Simulate this in Itachi Quantum Studio
Inspect state amplitudes, 3D Bloch sphere vector, and OpenQASM code live.
SVD Truncation & Bond Dimension
By truncating singular values smaller than a threshold ε (or capping the maximum bond dimension χ), MPS reduces the memory complexity of representing N qubits from exponential O(2^N) down to polynomial O(N · d · χ²).
Frequently Asked Questions
When does the MPS simulation backend fail to scale?
When circuits contain high volumes of non-local 2-qubit gates across distant qubits, the entanglement entropy crosses bipartite volume laws, requiring exponential bond dimension χ ~ 2^{N/2}.