Simulates large quantum systems using tensor network compression, scaling to hundreds of qubits where exact state-vector simulation is impossible — breaking the exponential memory barrier without sacrificing accuracy for circuits with bounded entanglement.
Exact state-vector simulation requires memory that doubles with every added qubit — a 50-qubit system requires over a petabyte to represent exactly, and a 100-qubit system is completely beyond any conceivable hardware. Matrix Product State simulation addresses this by representing the quantum state as a network of smaller tensors whose combined size scales with the entanglement in the state, not the qubit count. For circuits where entanglement remains bounded — including most practically relevant circuits — MPS simulation gives exact or near-exact results at a fraction of the memory cost.
The φCoherent MPS engine uses a Fibonacci bond dimension schedule — the maximum entanglement complexity tracked per tensor boundary follows Fibonacci steps rather than uniform increments. This gives finer-grained control over the accuracy-cost trade-off and naturally aligns with the Fibonacci-structured entanglement patterns generated by other stack components, particularly the error-correction codes and entanglement fabric.
Represents quantum states as tensor networks, reducing memory requirements from exponential in qubit count to polynomial in the entanglement complexity of the circuit.
The entanglement complexity tracked per boundary follows Fibonacci increments, giving smooth control over the accuracy-cost trade-off.
Circuits with bounded entanglement that are completely beyond exact simulation are tractable with MPS simulation, enabling development and testing at realistic application scales.
Registers as a HAL backend, so any circuit targeting the MPS engine runs identically through the standard stack interface without modification to the circuit description.
GHZ states exact at bond dim = 2 for any qubit count: 10q in 0.040 ms, 50q in 0.169 ms, 200q in 0.829 ms — all 100/100 samples correct. A 200-qubit statevector would require 2200 ≈ 1060 amplitudes; MPS needs O(800) complex numbers. Crossover point: statevector faster below 8 qubits (SV 0.017 ms vs MPS 0.046 ms at 4q); MPS faster from 8 qubits (MPS 0.126 ms vs SV 0.290 ms at 8q). 30-qubit VQE ansatz (164 gates): circuit 0.22 ms, 1000-shot sampling 7.07 ms. Entanglement entropy S = ln(2) at every bond for 10-qubit GHZ — exact match to analytical result, validating the Fibonacci bond schedule.
Analyzes multi-scale entanglement in states that MPS simulation represents, revealing structure that guides further approximation.
The exact state-vector alternative for smaller circuits where full fidelity is required and qubit counts are manageable.
Published under the GNU AGPLv3 with whitepaper and reference implementation. Commercial licensing is available for closed-source deployments.