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IEEE International Symposium on Information Theory (ISIT)

Computational Complexity of Optimally Encoding a Qubit

Idris Delsol, Omar Fawzi, Akshay Ramachandran

Published Jun 1, 2026• 0 citations
Publisher
DOI
10.1109/isit62367.2026.11654117

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Current universal quantum computers have a limited number of noisy qubits. Because of this, it is difficult to use them to solve large-scale complex optimization problems. In this paper we tackle this issue by proposing a quantum optimization scheme where discrete classical variables are encoded in non-orthogonal states of the quantum system. We develop the case of non-orthogonal qubit states, with individual qubits on the quantum computer handling more than one bit classical variable. Combining this idea with Variational Quantum Eigensolvers (VQE) and quantum state tomography, we show that it is possible to significantly reduce the number of qubits required by quantum hardware to solve complex optimization problems. We benchmark our algorithm by successfully optimizing a polynomial of degree 8 and 15 variables using only 15 qubits. Our proposal opens the path towards solving real-life useful optimization problems in today's limited quantum hardware.
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Quantum computers, leveraging superposition and entanglement, offer significant qubit efficiency for data processing compared to classical systems. However, encoding classical data into quantum states, given the current limitations of quantum hardware, often results in higher runtime complexity than classical methods, thus limiting the perceived quantum advantage. Previous quantum data compression methods, primarily based on Amplitude Encoding and mixed-state systems, result in lossy data recovery and necessitate extensive preprocessing. In this work, we propose Quantum Run-Length Encoding (QRLE), a novel lossless quantum data compression method that integrates Basic Encoding with Run-Length Encoding principles. By encoding repeated data sequences with their run lengths, QRLE achieves efficient and accurate data recovery on quantum computers, while exponentially reducing both qubit costs and runtime complexity compared to existing quantum data storage models. We further explore QRLE’s application in image processing, where it significantly optimizes quantum resource utilization over recent quantum image representation techniques. Experiments conducted on both quantum simulators and IBM’s superconducting quantum computer validate the efficiency of QRLE and confirm its compatibility with current quantum hardware.