Visualizing Quantum Circuit Probability: Estimating Quantum State Complexity for Quantum Program Synthesis
This work applies concepts from algorithmic probability to Boolean and quantum combinatorial logic circuits. The relations among the statistical, algorithmic, computational, and circuit complexities of states are reviewed. Thereafter, the probability of states in the circuit model of computation is...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-05-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/25/5/763 |
| _version_ | 1797600214181216256 |
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| author | Bao Gia Bach Akash Kundu Tamal Acharya Aritra Sarkar |
| author_facet | Bao Gia Bach Akash Kundu Tamal Acharya Aritra Sarkar |
| author_sort | Bao Gia Bach |
| collection | DOAJ |
| description | This work applies concepts from algorithmic probability to Boolean and quantum combinatorial logic circuits. The relations among the statistical, algorithmic, computational, and circuit complexities of states are reviewed. Thereafter, the probability of states in the circuit model of computation is defined. Classical and quantum gate sets are compared to select some characteristic sets. The reachability and expressibility in a space-time-bounded setting for these gate sets are enumerated and visualized. These results are studied in terms of computational resources, universality, and quantum behavior. The article suggests how applications like geometric quantum machine learning, novel quantum algorithm synthesis, and quantum artificial general intelligence can benefit by studying circuit probabilities. |
| first_indexed | 2024-03-11T03:46:04Z |
| format | Article |
| id | doaj.art-c738a7db4f4542b3bdee02cca3947a41 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T03:46:04Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-c738a7db4f4542b3bdee02cca3947a412023-11-18T01:16:03ZengMDPI AGEntropy1099-43002023-05-0125576310.3390/e25050763Visualizing Quantum Circuit Probability: Estimating Quantum State Complexity for Quantum Program SynthesisBao Gia Bach0Akash Kundu1Tamal Acharya2Aritra Sarkar3Faculty of Computer Science and Engineering, Ho Chi Minh City University of Technology, Ho Chi Minh City 70000, VietnamQuantum Intelligence Research Team, Department of Quantum & Computer Engineering, Delft University of Technology, 2628 CD Delft, The NetherlandsQuantum Intelligence Research Team, Department of Quantum & Computer Engineering, Delft University of Technology, 2628 CD Delft, The NetherlandsQuantum Intelligence Research Team, Department of Quantum & Computer Engineering, Delft University of Technology, 2628 CD Delft, The NetherlandsThis work applies concepts from algorithmic probability to Boolean and quantum combinatorial logic circuits. The relations among the statistical, algorithmic, computational, and circuit complexities of states are reviewed. Thereafter, the probability of states in the circuit model of computation is defined. Classical and quantum gate sets are compared to select some characteristic sets. The reachability and expressibility in a space-time-bounded setting for these gate sets are enumerated and visualized. These results are studied in terms of computational resources, universality, and quantum behavior. The article suggests how applications like geometric quantum machine learning, novel quantum algorithm synthesis, and quantum artificial general intelligence can benefit by studying circuit probabilities.https://www.mdpi.com/1099-4300/25/5/763gate-based quantum computingalgorithmic probabilitycircuit complexityreachabilityexpressibility |
| spellingShingle | Bao Gia Bach Akash Kundu Tamal Acharya Aritra Sarkar Visualizing Quantum Circuit Probability: Estimating Quantum State Complexity for Quantum Program Synthesis Entropy gate-based quantum computing algorithmic probability circuit complexity reachability expressibility |
| title | Visualizing Quantum Circuit Probability: Estimating Quantum State Complexity for Quantum Program Synthesis |
| title_full | Visualizing Quantum Circuit Probability: Estimating Quantum State Complexity for Quantum Program Synthesis |
| title_fullStr | Visualizing Quantum Circuit Probability: Estimating Quantum State Complexity for Quantum Program Synthesis |
| title_full_unstemmed | Visualizing Quantum Circuit Probability: Estimating Quantum State Complexity for Quantum Program Synthesis |
| title_short | Visualizing Quantum Circuit Probability: Estimating Quantum State Complexity for Quantum Program Synthesis |
| title_sort | visualizing quantum circuit probability estimating quantum state complexity for quantum program synthesis |
| topic | gate-based quantum computing algorithmic probability circuit complexity reachability expressibility |
| url | https://www.mdpi.com/1099-4300/25/5/763 |
| work_keys_str_mv | AT baogiabach visualizingquantumcircuitprobabilityestimatingquantumstatecomplexityforquantumprogramsynthesis AT akashkundu visualizingquantumcircuitprobabilityestimatingquantumstatecomplexityforquantumprogramsynthesis AT tamalacharya visualizingquantumcircuitprobabilityestimatingquantumstatecomplexityforquantumprogramsynthesis AT aritrasarkar visualizingquantumcircuitprobabilityestimatingquantumstatecomplexityforquantumprogramsynthesis |