Probability distribution reconstruction using circuit cutting applied to a variational classifier

TL;DR

The paper tackles resource constraints on near-term quantum devices by evaluating circuit cutting to run larger circuits on smaller hardware and by reconstructing the full probability distribution rather than only expectation values. It introduces a probability-distribution reconstruction method and compares two training strategies, train-then-cut and cut-then-train, within a quantum variational classifier featuring three label-encodings: expected_value_model, modulo_model, and parity_model. A DivideQuantum Variational Classifier is developed to integrate circuit cutting with Qiskit additive tooling, enabling practical training and evaluation, including hardware tests on IBM Strasbourg. The results show that distribution reconstruction is robust and often comparable to expectation-value approaches, with parity encoding delivering the strongest performance; hardware and noisy simulations indicate a noise-mitigating effect of circuit cutting and highlight its potential for scalable quantum machine learning on limited qubit resources.

Abstract

Significant efforts are being spent on building a quantum computer. At the same time, developments in quantum software are rapidly progressing. Insufficient quantum resources often are the problem when running quantum algorithms. New techniques can aid in using smaller quantum computers to run larger quantum algorithms. One of these techniques is circuit cutting. With this method, a circuit is broken into multiple pieces, each of which is run on quantum hardware independently and then recombined to obtain the overall answer. These circuit cutting techniques require additional circuit evaluations, which can form a bottleneck for algorithms requiring many interactions. This work explores the potential of circuit cutting techniques precisely in this regime of many interactions. We consider two different models, a standard method based on expectation values, and a novel method based on probability distribution reconstruction. Next, we compare two different training methods we call train-then-cut and cut-then-train and show that in practice, cut-then-train still produces good results. This observation brings closer the practical applicability of circuit cutting techniques, as a train-then-cut strategy is often infeasible. We conclude by implementing a cut and uncut circuit and find that circuit cutting helps achieve higher fidelity results.

Figures (14)

• Figure 1: A graphical explanation of circuit cutting. In this example, the second qubit is cut and the resulting circuit consists of two smaller quantum circuits. Figure used from Meulen:2025.
• Figure 2: Overview of the QML models implemented in the VC package. The models use angle encoding and either expectation values (expected_value_model) or probability amplitudes (modulo_model and parity_model).
• Figure 3: Structure of the used variational quantum circuits used in this work. Shown is the detailed implementation of one unitary circuit layer of \ref{['fig:vc_circuits']} for $L=1$. Trainable layers are implemented using PennyLane's StronglyEntanglingLayersBergholm:2022 with a total of 24 trainable parameters ($\mathbf{w}$), while classical input features ($\mathbf{X}$) are encoded via PennyLane's AngleEmbeddingBergholm:2022. The illustrated circuit encodes the preprocessed feature vector $\mathbf{X}\!=\![5.9, 3.0, 4.2, 1.5]$ from the Iris dataset (class label $y\!=\!\rm{versicolor}$). The corresponding circuit cut strategy employed throughout is also depicted, showing 4 cut CNOT gates.
• Figure 4: Main structure and design of the DivideQuantumVariationalClassifier implemented in this work. It extends the core functionality of the original VC package TNOVCSOFTWARE:2025 to support circuit gate cuts and integrates seamlessly with the qiskit-addon-cutting package QISKITADDONCUTTING:2024. It features a dedicated Pennylane-to-Qiskit symbolic circuit converter developed in-house and is fully compatible with PyTorch tensors, optimizers, and loss functions via a specialized torch.autograd.Function connector.
• Figure 5: The circuits used for validating the circuit cutting implementations. For the random circuit, each gate $U_i$ represents a Haar-random unitary of appropriate size.

Theorems & Definitions (2)

• Theorem 1
• proof