From curved spacetime to quantum circuits
A research-level track covering numerical general relativity, gravitational-wave astronomy, and quantum computing applied to the simulation of compact astrophysical objects. Built around the Cactus/Carpet/CarpetX software ecosystem used by the global NR community.
CORE EQUATIONS
\( R_{\mu\nu} - \tfrac{1}{2}g_{\mu\nu}R + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4}\,T_{\mu\nu} \) Einstein field equations
\( \partial_t \tilde{\gamma}_{ij} = -2\alpha \tilde{A}_{ij} + \beta^k \partial_k \tilde{\gamma}_{ij} + \tilde{\gamma}_{ik}\partial_j\beta^k + \tilde{\gamma}_{jk}\partial_i\beta^k - \tfrac{2}{3}\tilde{\gamma}_{ij}\partial_k\beta^k \) BSSN evolution
\( |x\rangle = A^{-1}|b\rangle \) HHL quantum linear solver
Modules 02–04 are independent after completing Module 01. Total track: ~150 hours.
BSSN · Z4c · AMR · Quantum circuit mappings
Complete 8-chapter module: ADM decomposition, BSSN/Z4c formalisms, Cactus framework anatomy (flesh, thorns, parameter files), Berger-Oliger AMR with Carpet and CarpetX, HHL/VQE/QPE quantum algorithms, quantum circuit mappings for GR operators, and hybrid classical-quantum workflows.
Matched filtering · Bayesian inference · LIGO/LISA
Matched filtering for compact binary coalescence, power spectral density estimation, Bayesian parameter estimation with nested sampling, the PyCBC / Bilby / LALSuite ecosystem, and the physics of O1–O4 events.
SpECTRE · Chebyshev · hp-AMR · Task-based parallelism
Mathematical foundations of spectral and pseudo-spectral methods for NR, the SpECTRE code architecture, hp-adaptive refinement, domain decomposition for binary black holes, and LISA-era waveform production requirements.
LQG · Spin foams · AdS/CFT · Tensor networks
Loop quantum gravity, spin foam models, the AdS/CFT correspondence and holographic entanglement entropy, tensor-network descriptions of quantum geometry, and the black hole information paradox.
Quantum tunneling in curved spacetime — hydrogen-transfer suppression in bicyclic scaffolds
Shared AMR / PDE simulation methodology — CarpetX and SUMO both use task-based adaptive solvers