Exact chiral symmetry with quantum signal processing

• URL: http://arxiv.org/abs/2607.28524v1
• Date: Thu, 30 Jul 2026 17:00:58 GMT
• Title: Exact chiral symmetry with quantum signal processing
• Abstract summary: We give a quantum signal processing algorithm for the overlap fermion Hamiltonian.<n>Applying the overlap Hamiltonian costs only a factor logarithmic in $_e$ more than the Wilson-Dirac Hamiltonian.
• Score: 39.146761527401424
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We give a quantum signal processing (QSP) algorithm for the overlap fermion Hamiltonian which preserves the Ginsparg-Wilson relation up to a controllable error $ε_e$. Quantum simulations of Dirac fermions with exact chiral symmetry are thus nearly free: applying the overlap Hamiltonian costs only a factor logarithmic in $ε_e$ more than the Wilson-Dirac Hamiltonian. Comparing to domain-wall fermions, a mild overhead is found in circuit complexity while reducing qubit costs. We show how QSP effectively constructs an extra dimension when simulating the overlap operator, illustrating that the scaling of quantum algorithms reflects the deeper physics of overlap fermions arising at the boundary of domain-wall fermions.

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