Measurement-Induced Quantum Neural Network

Abstract

We introduce a measurement-induced quantum neural network (MINN), an adaptive monitored-circuit architecture in which mid-circuit measurement outcomes determine the entangling gates in subsequent layers. In contrast to standard monitored circuits where sites and gates are sampled randomly, the gates are parametrized and variational, producing correlated history-dependent dynamics and injecting nonlinearity through measurement back-action. A generic MINN is not expected to be efficiently classically simulable. To demonstrate feasibility, we study a matchgate MINN that admits exact fermionic simulation and can be trained with gradient estimators. We apply the architecture to continuous optimization, image classification, and ground-state search in the Sherrington-Kirkpatrick spin glass, finding effective training and performance over a broad range of monitoring rates.

Figures (5)

• Figure 1: Brick-wall circuit architecture commonly studied in MIPT. Sites are labeled by spacetime coordinates $(l,j)$; here the circuit contains four layers and eight qubits. The alternating even–odd pattern of two-qubit gates spreads entanglement throughout the system. Gate subscripts indicate both the qubits acted upon and the layer index of the first qubit in each pair, illustrated explicitly in the first two layers. Rotation angles $\boldsymbol{\theta}$ subscripts indicate the time index and the first qubit index. Projective measurements punctuate the spacetime circuit, producing alternating unitary and measurement layers. The MINN extends this architecture to a dynamic and adaptive circuit in which measurement outcomes feed forward to subsequent unitary layers, while circuit parameters , the rotation angles, are optimized to minimize the expectation value of a loss function.
• Figure 2: Optimization landscapes for the Lévy (top left) and Ackley (top right) benchmark functions. Bottom panels display the optimization trajectories projected onto contour maps, illustrating convergence toward the global minima; trajectories are highlighted in gold. The measurement probability is $p=0.5$ with measurement sites reset between evaluations.
• Figure 3: For a 10-d case of each loss function: loss as a function of optimization step, showing both the best value obtained within each sampling batch and the sample-averaged (coarse-grained) loss. Left is Lévy and right Ackley. The measurement probability is $p=0.5$ with measurement sites reset each time the circuit is evaluated during training or inference.
• Figure 4: Inference results on MNIST show that validation performance is unaffected by measurement sites being fixed or reset. Near-unitary evolution or moderate nonlinearities lead to improved classification accuracy. Measurement plays a role analogous to dropout, indicating redundancy in the learned representation.
• Figure 5: Energy as a function of optimization step. The MINN is effectively optimized, with the ground-state energy estimate converging smoothly during training. The measurement probability is $p=0.5$ with measurement sites reset between evaluations.