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Tensor-Network-Initialized Noise-Mitigated Molecular Ground State Estimation

A variational quantum eigensolver run on real noisy hardware does not fail in one place, so it cannot be fixed in one place. This concept works through a four-part defence of the computed ground state energy of a small molecule and asks the learner to attribute each part to the error it removes. Ansatz: build the parameterised trial circuit from the structure of a matrix product state, mapping each local tensor of the chain to a two-qubit block of a CNOT between single-qubit rotations, so that the entanglement the chain can carry matches the locality of the target state while circuit depth stays shallow - roughly ninety gates where a unitary coupled-cluster ansatz needs thousands on the same eight qubits. Initialisation: optimise the matrix product state classically first and transplant its parameters into the circuit, because identical circuits started from different random parameters converge to different answers, and pre-training removes that variance rather than averaging over it. Mitigation: deliberately amplify the hardware noise by folding gates, measure the expectation value at several noise scale factors, and fit a model across those points to extrapolate back to the zero-noise limit - with the fitting function itself learned rather than assumed linear or exponential. Measurement: partition the Hamiltonian Pauli terms into mutually commuting groups so that each group is estimated from one set of shots, cutting both shot count and accumulated readout error. The evaluation to reason about is the comparison against an exact benchmark under a stated noise model: the noiseless energies of every ansatz agree to a few thousandths of a Hartree, and it is only under noise that they separate, with the tensor-network-initialised circuit losing about a hundredth of a Hartree while the deeper conventional ansatze lose one to one and a half. That separation is the argument that on near-term devices gate count, not expressivity, is the binding constraint.