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A Quantum-Circuit Analogue for Probabilistic Decision Commitment

Ondřej Šrámek

Published Jul 8, 2026• 0 citations
Publisher

Abstract

We present a minimal, fully reproducible quantum-circuit analogue for probabilistic decisioncommitment. A two-qubit variational quantum circuit, run on a classical statevector simulator,angle-encodes binary inputs and is trained (COBYLA) against a Pauli-Z expectation objective.Two experiments are reported: (1) an untrained circuit yields a probabilistic measurementspread that training reshapes toward a near-deterministic outcome — the collapse itself beingperformed by measurement — modelling an unresolved decision distribution resolving into acommitment; and (2) the same architecture learns XOR (4/4, zero training loss), the canonicalnon-linearly-separable function, with the entangling operation supplying the cross-featureinteraction required in this ansatz. We read the Pauli-Z expectation as a graded confidencesignal and propose a magnitude threshold as a measurable commit condition for probabilisticdecision systems, including external-scaffolding continuity frameworks for stateless languagemodels. We claim no quantum advantage and no quantum execution of language models; thecontribution is pedagogical clarity and a decision-commitment design lens — established resultsin quantum machine learning, reframed for decision discipline. All code is provided.

DOI
10.5281/zenodo.21257381

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We present a minimal, fully reproducible quantum-circuit analogue for probabilistic decisioncommitment. A two-qubit variational quantum circuit, run on a classical statevector simulator,angle-encodes binary inputs and is trained (COBYLA) against a Pauli-Z expectation objective.Two experiments are reported: (1) an untrained circuit yields a probabilistic measurementspread that training reshapes toward a near-deterministic outcome — the collapse itself beingperformed by measurement — modelling an unresolved decision distribution resolving into acommitment; and (2) the same architecture learns XOR (4/4, zero training loss), the canonicalnon-linearly-separable function, with the entangling operation supplying the cross-featureinteraction required in this ansatz. We read the Pauli-Z expectation as a graded confidencesignal and propose a magnitude threshold as a measurable commit condition for probabilisticdecision systems, including external-scaffolding continuity frameworks for stateless languagemodels. We claim no quantum advantage and no quantum execution of language models; thecontribution is pedagogical clarity and a decision-commitment design lens — established resultsin quantum machine learning, reframed for decision discipline. All code is provided.
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The state-of-the-art machine learning approaches are based on classical von Neumann computing architectures and have been widely used in many industrial and academic domains. With the recent development of quantum computing, researchers and tech-giants have attempted new quantum circuits for machine learning tasks. However, the existing quantum computing platforms are hard to simulate classical deep learning models or problems because of the intractability of deep quantum circuits. Thus, it is necessary to design feasible quantum algorithms for quantum machine learning for noisy intermediate scale quantum (NISQ) devices. This work explores variational quantum circuits for deep reinforcement learning. Specifically, we reshape classical deep reinforcement learning algorithms like experience replay and target network into a representation of variational quantum circuits. Moreover, we use a quantum information encoding scheme to reduce the number of model parameters compared to classical neural networks. To the best of our knowledge, this work is the first proof-of-principle demonstration of variational quantum circuits to approximate the deep Q-value function for decision-making and policy-selection reinforcement learning with experience replay and target network. Besides, our variational quantum circuits can be deployed in many near-term NISQ machines.
Quantum operations on pure states can be fully represented by unitary matrices. Variational quantum circuits, also known as quantum neural networks, embed data and trainable parameters into gate-based operations and optimize the parameters via gradient descent. The high cost of training and low fidelity of current quantum devices, however, restricts much of quantum machine learning to classical simulation. For few-qubit problems with large datasets, training the matrix elements directly, as is done with weight matrices in classical neural networks, can be faster than decomposing data and parameters into gates. We propose a method that trains matrices directly while maintaining unitarity through a single regularization term added to the loss function. A second training step, circuit alignment, then recovers a gate-based architecture from the resulting soft-unitary. On a five-qubit supervised classification task with 1000 datapoints, this two-step process produces a trained variational circuit in under four minutes, compared to over two hours for direct circuit training, while achieving lower binary cross-entropy loss. In a second experiment, soft-unitaries are embedded in a hybrid quantum-classical network for a reinforcement learning cartpole task, where the hybrid agent outperforms a purely classical baseline of comparable size.
Procedures to create, train, save, and reload a VQC with the Qiskit quantum machine learning framework: generating a synthetic dataset and building a parameterised quantum circuit using the RealAmplitudes ansatz as an encoding circuit to encode classical data into quantum states. A hybrid quantum/classical approach is utilised to train the variational quantum circuit on the dataset. The COBYLA optimizer and the sampling primitives from Qiskit are employed. The notebook outlines the steps for saving the trained quantum model to disc and then loading it for the incremental training. This experiment illustrates the model’s adaptability and consistency in the results. Visualisation tools are used to monitor the progress of the training and evaluate the model’s performance.. This example illustrates that the modern quantum software tools are ready for assessment in the NISQ era and can support the creation of sustainable workflows for quantum machine learning.