Speakers
Description
The ground state of the kagome Heisenberg antiferromagnet is a candidate quantum spin liquid. The lattices natural frustration renders it challenging M.L. task for classical and quantum models. The SU(2)-equivariant ansatz of ~[1] is built from invariant gates, so it stays in one total-spin sector, and on the small
plaquettes where every triangle can host a singlet dimer it prepares the ground state
exactly in noiseless simulation. We ask what symmetry buys on a real device, beyond the
trainability arguments of geometric QML~[4,8]. We find three things. First,
the trained circuit can be compressed. An SU(2)-aware compression~[3] only has to reproduce each gate on
the singlet sector, cutting the 8-spin circuit from 172 two-qubit gates to 46. In noise sweeps the
compressed circuit wins above a two-qubit error an order of magnitude below today's rates, and a single
mitigated run on \texttt{ibm_torino} gives an energy error of 0.47 (exact ground energy $-12$), in line
with a device-faithful simulation of the chip (0.53). Second, the symmetry filters noise,
because the target state has zero magnetisation. Third, excited states come at no extra
cost. A different initial singlet covering places the ansatz in a different magnetisation sector, and the
same circuit then reaches the lowest state of each $S_z$ sector of the 12-spin star. Three noiseless layers
reach the frustrated 18-spin plaquette within 2.5\% of the exact energy. At today's error rates the compression is worth its
noiseless cost, and at 18 spins the limit is the device rather than the ansatz.
| Topic | Quantum variational circuits and their applications |
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