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Variable Quantum Circuit

The multi-chip ensemble Variational Quantum Circuit (VQC) framework was established to handle major Quantum Machine Learning (QML) difficulties, especially those caused by Noisy Intermediate-Scale Quantum (NISQ) devices. These include noise, scaling issues, and desolate plateaus.

The multi-chip ensemble VQC system partitions high-dimensional calculations among numerous smaller quantum chips and classically aggregates their measurements. In contrast to this modular method, typical single-chip VQCs compute on a single, bigger quantum circuit.

VQC framework:

Architecture:

A tiny l-qubit quantum subcircuit is in each of the framework's k disjoint quantum chips. These constitute a larger n-qubit quantum system (n = k × l). There are no gates linking chips, therefore the quantum action is a tensor product of subcircuit actions.

Processing data:

From input data, a high-dimensional vector x, subvectors are produced. Each subvector xi is processed by a separate quantum circuit Ui on a quantum device. Each chip encodes data into a quantum state using a unitary Vi.

Classical Aggregation:

Each chip's quantum computation is measured. Classically aggregating the classical outputs from each chip using a combination function g yields the model's final output. This function may be a weighted sum for regression or a shallow neural network for classification.

Training:

The framework remains hybrid quantum-classical. The parameters θ for each subcircuit are tuned collectively to decrease the total loss function. The ability to calculate gradients individually and in parallel for each subcircuit makes training efficient even with several subcircuits. The framework uses parameter-shift rule for backpropagation-based end-to-end training.

Multi-Chip Ensemble VQC Advantages:

Multi-chip ensemble Variational Quantum Circuit (VQC) frameworks have many advantages over single-chip VQCs, notably for NISQ restrictions.

Increased Scalability: It allows high-dimensional data analysis without classical dimension reduction or exponentially deep circuits, which can lose information. Instead than using larger chips, horizontal scalability is achieved by adding more chips that process data. Current NISQ devices with few qubits per chip can employ this method. Better Trainability: The architecture instantly addresses the bleak plateau. It limits entanglement to within-chip boundaries to avoid barren plateaus from global entanglement patterns. According to theoretical analysis and experimental results, partitioning into many chips greatly enhances gradient variation compared to a fully-entangled single-chip solution. The framework reduces barren plateaus without being classically simulable. If l grows with the system size (n) to avoid polynomial subspaces, simulating each subcircuit may become exponentially expensive. Since inter-chip entanglement is absent, the system cannot approximate a global 2-design, reducing exponential gradient degradation. Controlled entanglement provides implicit regularisation for better generalisability. Restricting global entanglement reduces overfitting by limiting the model's ability to describe complex functions. Navigating the quantum bias-variance trade-off improves the model's generalisation performance. The architectural layout reduces quantum error variation and bias, improving noise resilience. When chips have limited operations, qubits are exposed to noise for less time. Classically averaging uncorrelated noise across chip outputs reduces total variance. For this dual reduction, the bias-variance trade-off of typical error mitigation schemes is avoided. Compatibility with hardware New modular quantum architectures and NISQ devices are compatible with the multi-chip ensemble Variational Quantum Circuit (VQC) framework. It solves hardware issues including sparse connectivity, coherence time, and qubit count by spreading computations and using classical aggregate instead of noisy inter-chip quantum transmission. The architecture supports IBM, IonQ, and Rigetti's modular systems and quantum interconnects.

Experimental validation:

Amplitude-damping and depolarising noise models were used to simulate NISQ settings, proving the framework's benefits. These tests used benchmark datasets (MNIST, FashionMNIST, and CIFAR-10) and PhysioNet EEG. Multi-chip ensemble VQCs surpassed single-chip VQCs in performance, speed, convergence, generalisation loss, and quantum errors, especially when processing high-dimensional data without conventional dimension reduction. Using 272 chips with 12 qubits each to apply the multi-chip ensemble approach to a quantum convolutional neural network (QCNN) on 3264-dimensional PhysioNet EEG data yielded better accuracy and less overfitting than single-chip QCNNs and CNNs.

Conclusion