Non-Clifford Quantum Circuit Complexity as a Proposed Dynamical Driver of Emergent Gravitational Geodesics: Toward a Complexity-Resolved Reading of ER=EPR

We propose a dictionary relating the resource-theoretic magic (non-stabilizerness) of a quantum state’s preparing circuit to the local curvature of an emergent dual geometry, extending the complexity=volume (CV) and complexity=action (CA) conjectures. We show that within this dictionary, stabilizer states — states preparable by Clifford circuits alone — map to conformally flat, zero-magic-curvature slices, while non-Clifford gate count density sources an effective stressenergy-like term that bends geodesics in the bulk dual. We use this to re-derive, under stated assumptions, a complexity-volume duality for Einstein–Rosen bridges consistent with Susskind’s second law of complexity, and discuss the sense in which computational complexity growth can be read as stabilizing — not creating — wormhole volume growth against collapse, without violating unitarity or the no-cloning theorem. We conclude with an order-of-magnitude discussion of why table-top interferometric detection of magic-sourced curvature is currently far outside experimental reach, and what a realistic near-term analogue experiment could look like instead.