Resource-Efficient Variational Quantum Classifier

TL;DR

The paper tackles the prediction-time overhead in variational quantum classifiers caused by quantum measurement randomness. It introduces an unambiguous quantum classifier that uses a threshold-based readout so that, if uncertain, the experiment is repeated until a definite label is obtained, yielding near-deterministic predictions with substantially fewer circuit executions. Analytically, it derives how the standard and threshold-based readouts behave under depolarizing noise and shows that lifted training can push the maximum achievable label probability close to the ideal $(1+\delta)/2$ while preserving efficient acceptance, often with an expected number of shots near 1–2. Empirical validation on three binary-classification datasets using a 3- and 5-qubit VQC with data re-uploading demonstrates that the unambiguous classifier can reduce circuit executions by about 2–3 orders of magnitude at a modest accuracy drop (roughly 6–7 percentage points in ideal/noisy settings), indicating a practical pathway toward resource-efficient QML on current hardware.

Abstract

Quantum computing promises a revolution in information processing, with significant potential for machine learning and classification tasks. However, achieving this potential requires overcoming several fundamental challenges. One key limitation arises at the prediction stage, where the intrinsic randomness of quantum model outputs necessitates repeated executions, resulting in substantial overhead. To overcome this, we propose a novel measurement strategy for a variational quantum classifier that allows us to define the unambiguous quantum classifier. This strategy achieves near-deterministic predictions while maintaining competitive classification accuracy in noisy environments, all with significantly fewer quantum circuit executions. Although this approach entails a slight reduction in performance, it represents a favorable trade-off for improved resource efficiency. We further validate our theoretical model with supporting experimental results.

Figures (9)

• Figure 1: Quantum circuit of ZZ-entangling feature map $U_{FM}(x_i)$ for data point $x_i$ of $k$ data features. At the input, we consider a tensor product state of $k$ qubits, each initialized in an default $\ket{0}$ quantum state. After single-qubits rotations $P(\varphi)$ of angle $\varphi$ and two-qubits entangled gates CNOT we obtain the output $U_{FM}(x_i)\ket{0}^{\otimes k}$ with encoded data point $x_i$.
• Figure 2: Parametrized circuit (ansatz) $U_A(x_i, \theta)$ with reverse-entangling and data re-uploading for trainable parameters $\theta_{l,i}$ for current layer $l$ on $i$-th qubit. This ansatz implements data re-uploading perez2020data, introducing the data point $x_i$ to each layer. At the input, we consider an entangled state $U_{FM}(x_i) \ket{0}^{\otimes k}$. At the output we already have $U_A(x_i, \theta)U_{FM}(x_i) \ket{0}^{\otimes k}$, with processed quantum state by ansatz.
• Figure 3: VQC binary classifier circuit $U_{VQC}(x_i, \theta)$ composed of layered feature map $U_{FM}(x_i)$ with $l_{FM}$ layers and ansatz $U_A(x_i, \theta)$ with $l_{A}$ layers. Input data point is depicted as $x_i$ and trainable weights as $\theta$. The output is obtained either by sampling each qubit in the Z-basis or by estimating the expectation value, which enables the use of gradient-based classical optimizers during training.
• Figure 4: Comparison of classification performance and the number of executions required to achieve a near-deterministic prediction for each model using a circuit with 3 qubits, 2 ansatz layers, and 1 feature map layer on Dataset C.
• Figure 5: Comparison of classification performance and the number of executions required to achieve a near-deterministic prediction for each model using a circuit with 5 qubits, 2 ansatz layers, and 1 feature map layer on Dataset C.