Papers › Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ansätze
Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ansätze
Han Zheng, Zimu Li, Junyu Liu, Sergii Strelchuk, Risi Kondor
We develop a theoretical framework for Sₙ-equivariant convolutional quantum circuits with SU$(d)-symmetry, building on and significantly generalizing Jordan′s Permutational Quantum Computing (PQC) formalism based on Schur-Weyl duality connecting both SU(d)$ and Sₙ actions on qudits. In particular, we utilize the Okounkov-Vershik approach to prove Harrow's statement (Ph.D. Thesis 2005 p.160) on the equivalence between SU(d) and Sₙ irrep bases and to establish the Sₙ-equivariant Convolutional Quantum Alternating Ans\"atze (Sₙ-CQA) using Young-Jucys-Murphy (YJM) elements. We prove that Sₙ-CQA is able to generate any unitary in any given Sₙ irrep sector, which may serve as a universal model for a wide array of quantum machine learning problems with the presence of SU(d) symmetry. Our method provides another way to prove the universality of Quantum Approximate Optimization Algorithm (QAOA) and verifies that 4-local SU(d) symmetric unitaries are sufficient to build generic SU(d) symmetric quantum circuits up to relative phase factors. We present numerical simulations to showcase the effectiveness of the ans\"atze to find the ground state energy of the J₁--J₂ antiferromagnetic Heisenberg model on the rectangular and Kagome lattices. Our work provides the first application of the celebrated Okounkov-Vershik's Sₙ representation theory to quantum physics and machine learning, from which to propose quantum variational ans\"atze that strongly suggests to be classically intractable tailored towards a specific optimization problem.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Tasks
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections