The State Preparation of Multivariate Normal Distributions using Tree Tensor Network
The quantum state preparation of probability distributions is an important subroutine for many quantum algorithms. When embedding $D$-dimensional multivariate probability distributions by discretizing each dimension into $2^n$ points, we need a state preparation circuit comprising a total of $nD$ qu...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-05-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-05-28-1755/pdf/ |
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| author | Hidetaka Manabe Yuichi Sano |
| author_facet | Hidetaka Manabe Yuichi Sano |
| author_sort | Hidetaka Manabe |
| collection | DOAJ |
| description | The quantum state preparation of probability distributions is an important subroutine for many quantum algorithms. When embedding $D$-dimensional multivariate probability distributions by discretizing each dimension into $2^n$ points, we need a state preparation circuit comprising a total of $nD$ qubits, which is often difficult to compile. In this study, we propose a scalable method to generate state preparation circuits for $D$-dimensional multivariate normal distributions, utilizing tree tensor networks (TTN). We establish theoretical guarantees that multivariate normal distributions with 1D correlation structures can be efficiently represented using TTN. Based on these analyses, we propose a compilation method that uses automatic structural optimization to find the most efficient network structure and compact circuit. We apply our method to state preparation circuits for various high-dimensional random multivariate normal distributions. The numerical results suggest that our method can dramatically reduce the circuit depth and CNOT count while maintaining fidelity compared to existing approaches. |
| format | Article |
| id | doaj-art-be76a4d02aab4962b41419e552eb0759 |
| institution | DOAJ |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-05-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-be76a4d02aab4962b41419e552eb07592025-08-20T03:12:50ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-05-019175510.22331/q-2025-05-28-175510.22331/q-2025-05-28-1755The State Preparation of Multivariate Normal Distributions using Tree Tensor NetworkHidetaka ManabeYuichi SanoThe quantum state preparation of probability distributions is an important subroutine for many quantum algorithms. When embedding $D$-dimensional multivariate probability distributions by discretizing each dimension into $2^n$ points, we need a state preparation circuit comprising a total of $nD$ qubits, which is often difficult to compile. In this study, we propose a scalable method to generate state preparation circuits for $D$-dimensional multivariate normal distributions, utilizing tree tensor networks (TTN). We establish theoretical guarantees that multivariate normal distributions with 1D correlation structures can be efficiently represented using TTN. Based on these analyses, we propose a compilation method that uses automatic structural optimization to find the most efficient network structure and compact circuit. We apply our method to state preparation circuits for various high-dimensional random multivariate normal distributions. The numerical results suggest that our method can dramatically reduce the circuit depth and CNOT count while maintaining fidelity compared to existing approaches.https://quantum-journal.org/papers/q-2025-05-28-1755/pdf/ |
| spellingShingle | Hidetaka Manabe Yuichi Sano The State Preparation of Multivariate Normal Distributions using Tree Tensor Network Quantum |
| title | The State Preparation of Multivariate Normal Distributions using Tree Tensor Network |
| title_full | The State Preparation of Multivariate Normal Distributions using Tree Tensor Network |
| title_fullStr | The State Preparation of Multivariate Normal Distributions using Tree Tensor Network |
| title_full_unstemmed | The State Preparation of Multivariate Normal Distributions using Tree Tensor Network |
| title_short | The State Preparation of Multivariate Normal Distributions using Tree Tensor Network |
| title_sort | state preparation of multivariate normal distributions using tree tensor network |
| url | https://quantum-journal.org/papers/q-2025-05-28-1755/pdf/ |
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