Quantum error correction thresholds, entanglement and the limits of classical simulation, advanced with reproducible numerics and proofs.
Map the boundary of classical simulability for quantum-advantage random circuit sampling experiments by improving tensor-network and other classical algorithms, with reproducible cost estimates and fidelity benchmarks.
Improve reproducible, circuit-level-noise thresholds and logical error rates for surface codes and quantum LDPC codes through better codes, syndrome circuits and decoders, benchmarked with open simulators such as Stim.
Prove that a symmetric informationally complete POVM (d^2 equiangular lines in C^d) exists in every dimension d, and extend the list of dimensions with exact or numerical solutions.
Decide whether four (or seven) mutually unbiased bases exist in C^6; only three are known, and a complete set of seven is widely believed not to exist.
Quantum Max Cut is the quantum analog of Max Cut. Given a graph G = (E,V), it asks for the maximum eigenvalue of H_G = Σ_(ij) ∈ E (I - X_iX_j - Y_iY_j - Z_i Z_j), where X_i, Y_i, Z_i are the Pauli matrices acting on the i'th tensor factor and trivially on all other coordinates.
Special case in dimension 6: determine the maximal number of mutually unbiased orthonormal bases in ℂ^6.
Benchmark open subproblem: existence of a SIC-POVM in dimension 56.
Open benchmark statement: does an AME(8,4) state exist?
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