Expressiveness of Commutative Quantum Circuits: A Probabilistic Approach
This study investigates the frame potential and expressiveness of commutative quantum circuits. Based on the Fourier series representation of these circuits, we express quantum expectation and pairwise fidelity as characteristic functions of random variables, and we characterize expressiveness as th...
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| Format: | Article |
| Language: | English |
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IEEE
2024-01-01
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| Series: | IEEE Transactions on Quantum Engineering |
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| Online Access: | https://ieeexplore.ieee.org/document/10738429/ |
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| author | Jorge M. Ramirez Elaine Wong Caio Alves Sarah Chehade Ryan Bennink |
| author_facet | Jorge M. Ramirez Elaine Wong Caio Alves Sarah Chehade Ryan Bennink |
| author_sort | Jorge M. Ramirez |
| collection | DOAJ |
| description | This study investigates the frame potential and expressiveness of commutative quantum circuits. Based on the Fourier series representation of these circuits, we express quantum expectation and pairwise fidelity as characteristic functions of random variables, and we characterize expressiveness as the recurrence probability of a random walk on a lattice. A central outcome of our work includes formulas to approximate the frame potential and expressiveness for any commutative quantum circuit, underpinned by convergence theorems in the probability theory. We identify the lattice volume of the random walk as means to approximate expressiveness based on circuit architecture. In the specific case of commutative circuits involving Pauli-<inline-formula><tex-math notation="LaTeX">$Z$</tex-math></inline-formula> rotations, we provide theoretical results relating expressiveness and circuit structure. Our probabilistic representation also provides means for bounding and approximately calculating the frame potential of a circuit through sampling methods. |
| format | Article |
| id | doaj-art-3510679bf21d4febbdb613a078bc4d4a |
| institution | Kabale University |
| issn | 2689-1808 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Transactions on Quantum Engineering |
| spelling | doaj-art-3510679bf21d4febbdb613a078bc4d4a2025-01-25T00:03:43ZengIEEEIEEE Transactions on Quantum Engineering2689-18082024-01-01511510.1109/TQE.2024.348851810738429Expressiveness of Commutative Quantum Circuits: A Probabilistic ApproachJorge M. Ramirez0https://orcid.org/0000-0002-0402-7484Elaine Wong1https://orcid.org/0000-0003-1354-2020Caio Alves2Sarah Chehade3https://orcid.org/0000-0003-3130-1247Ryan Bennink4https://orcid.org/0000-0002-4810-9369Oak Ridge National Laboratory, Oak Ridge, TN, USAOak Ridge National Laboratory, Oak Ridge, TN, USAOak Ridge National Laboratory, Oak Ridge, TN, USAOak Ridge National Laboratory, Oak Ridge, TN, USAOak Ridge National Laboratory, Oak Ridge, TN, USAThis study investigates the frame potential and expressiveness of commutative quantum circuits. Based on the Fourier series representation of these circuits, we express quantum expectation and pairwise fidelity as characteristic functions of random variables, and we characterize expressiveness as the recurrence probability of a random walk on a lattice. A central outcome of our work includes formulas to approximate the frame potential and expressiveness for any commutative quantum circuit, underpinned by convergence theorems in the probability theory. We identify the lattice volume of the random walk as means to approximate expressiveness based on circuit architecture. In the specific case of commutative circuits involving Pauli-<inline-formula><tex-math notation="LaTeX">$Z$</tex-math></inline-formula> rotations, we provide theoretical results relating expressiveness and circuit structure. Our probabilistic representation also provides means for bounding and approximately calculating the frame potential of a circuit through sampling methods.https://ieeexplore.ieee.org/document/10738429/Commutative quantum circuitexpressivenessframe potential |
| spellingShingle | Jorge M. Ramirez Elaine Wong Caio Alves Sarah Chehade Ryan Bennink Expressiveness of Commutative Quantum Circuits: A Probabilistic Approach IEEE Transactions on Quantum Engineering Commutative quantum circuit expressiveness frame potential |
| title | Expressiveness of Commutative Quantum Circuits: A Probabilistic Approach |
| title_full | Expressiveness of Commutative Quantum Circuits: A Probabilistic Approach |
| title_fullStr | Expressiveness of Commutative Quantum Circuits: A Probabilistic Approach |
| title_full_unstemmed | Expressiveness of Commutative Quantum Circuits: A Probabilistic Approach |
| title_short | Expressiveness of Commutative Quantum Circuits: A Probabilistic Approach |
| title_sort | expressiveness of commutative quantum circuits a probabilistic approach |
| topic | Commutative quantum circuit expressiveness frame potential |
| url | https://ieeexplore.ieee.org/document/10738429/ |
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