Visualizing Quantum Circuit Probability: Estimating Quantum State Complexity for Quantum Program Synthesis

Bao Gia Bach, Akash Kundu, Tamal Acharya, Aritra Sarkar*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

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.

Original languageEnglish
Article number763
Number of pages20
JournalEntropy
Volume25
Issue number5
DOIs
Publication statusPublished - 2023

Keywords

  • algorithmic probability
  • circuit complexity
  • expressibility
  • gate-based quantum computing
  • reachability

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