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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.18767 |
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| _version_ | 1866911399661273088 |
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| author | Nibbi, Martina Della Chiara, Filippo Shen, Yizhi Szasz, Aaron Van Beeumen, Roel |
| author_facet | Nibbi, Martina Della Chiara, Filippo Shen, Yizhi Szasz, Aaron Van Beeumen, Roel |
| contents | Quantum circuits naturally implement unitary operations on input quantum states. However, non-unitary operations can also be implemented through block encodings, where additional ancilla qubits are introduced and later measured. While block encoding has a number of well-established theoretical applications, its practical implementation has been prohibitively expensive for current quantum hardware. In this paper, we present practical and explicit block encoding circuits implementing matrix polynomial transformations of a target matrix. With standard approaches, block-encoding a degree-$d$ matrix polynomial requires a circuit depth scaling as $d$ times the depth for block-encoding the original matrix alone. By leveraging the recently introduced Fast One-Qubit Controlled Select LCU (FOQCS-LCU) framework, we show that the additional circuit-depth overhead required for encoding matrix polynomials can be reduced to scale linearly in $d$ with no dependence on system size or the cost of block encoding the original matrix. Moreover, we demonstrate that the FOQCS-LCU circuits and their associated matrix polynomial transformations can be controlled with negligible overhead, enabling efficient applications such as Hadamard tests. Finally, we provide explicit circuits for representative spin models, together with detailed non-asymptotic gate counts and circuit depths. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18767 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Practical block encodings of matrix polynomials that can also be trivially controlled Nibbi, Martina Della Chiara, Filippo Shen, Yizhi Szasz, Aaron Van Beeumen, Roel Quantum Physics Quantum circuits naturally implement unitary operations on input quantum states. However, non-unitary operations can also be implemented through block encodings, where additional ancilla qubits are introduced and later measured. While block encoding has a number of well-established theoretical applications, its practical implementation has been prohibitively expensive for current quantum hardware. In this paper, we present practical and explicit block encoding circuits implementing matrix polynomial transformations of a target matrix. With standard approaches, block-encoding a degree-$d$ matrix polynomial requires a circuit depth scaling as $d$ times the depth for block-encoding the original matrix alone. By leveraging the recently introduced Fast One-Qubit Controlled Select LCU (FOQCS-LCU) framework, we show that the additional circuit-depth overhead required for encoding matrix polynomials can be reduced to scale linearly in $d$ with no dependence on system size or the cost of block encoding the original matrix. Moreover, we demonstrate that the FOQCS-LCU circuits and their associated matrix polynomial transformations can be controlled with negligible overhead, enabling efficient applications such as Hadamard tests. Finally, we provide explicit circuits for representative spin models, together with detailed non-asymptotic gate counts and circuit depths. |
| title | Practical block encodings of matrix polynomials that can also be trivially controlled |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.18767 |