TY - JOUR

T1 - Visualizing Quantum Circuit Probability

T2 - Estimating Quantum State Complexity for Quantum Program Synthesis

AU - Bach, Bao Gia

AU - Kundu, Akash

AU - Acharya, Tamal

AU - Sarkar, Aritra

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - algorithmic probability

KW - circuit complexity

KW - expressibility

KW - gate-based quantum computing

KW - reachability

UR - http://www.scopus.com/inward/record.url?scp=85160548690&partnerID=8YFLogxK

U2 - 10.3390/e25050763

DO - 10.3390/e25050763

M3 - Article

AN - SCOPUS:85160548690

SN - 1099-4300

VL - 25

JO - Entropy

JF - Entropy

IS - 5

M1 - 763

ER -