Symmetric Quantum Circuits as a Symmetry-Preserving Model of Quantum Computation
A restricted model of quantum computation in which every gate layer commutes with the action of the symmetry group that leaves the computational problem invariant, so the circuit is equivariant by construction. The model isolates how symmetry constrains and enables quantum speedups, extending symmetric computation from the classical setting; symmetric quantum circuits admit efficient amplitude amplification, phase estimation, and linear combination of unitaries, and separate exponentially from symmetric classical circuits on XOR-SAT.
Symmetric quantum computation Davi Castro-Silva∗ Tom Gur∗ Sergii Strelchuk† October 7, 2025
Symmetric quantum circuits are a restricted model of quantum computation in which the circuit is required to respect (be equivariant under) the group of symmetries under which the target problem is i…