Quantum Reports

Quantum error mitigation (QEM) can improve target observables without ensuring that reconstructed experimental data satisfy known physical consistency conditions. We introduce a constraint-preserving QEM framework that represents reconstruction error in residual coordinates and projects the estimated residual onto the locally admissible tangent space defined by a differentiable physical constraint. The method removes the complete first-order constraint-violating component and suppresses generic constraint leakage to second order. We develop the construction analytically for CHSH correlations using no-signalling as the benchmark constraint and extend it to general smooth constraints. Deterministic and finite-shot simulations confirm the predicted suppression, including improved sampling behavior after projection. The method composes with calibrated readout mitigation and zero-noise extrapolation, while covariance-informed metrics provide optional task-dependent refinements. Real-device experiments on IBM quantum hardware validate the approach across eight disjoint physical qubit pairs and 24 pair-block realizations. After readout mitigation, projection reduces the no-signalling residual in all 24 realizations, with a mean paired reduction of $96.61\%$ and negligible additional change in CHSH. A separate shot-count sweep improves all 15 hardware realizations, with a mean paired reduction of $97.38\%$, while revealing a hardware-limited residual floor at high shot count. Constraint-selectivity tests further show that different constraints remove different residual components. The method is entirely classical, requires no additional qubits, ancillas, or circuit depth, and provides a resource-efficient consistency layer for existing QEM pipelines.

We study a four-dimensional toric code on the $D_4$ lattice, the densest four-dimensional lattice packing. Qubits sit on the $16L^4$ triangles of its Delaunay decomposition into regular 16-cells. Each X-stabilizer acts on the four triangles of a tetrahedron, the smallest possible weight, and each Z-stabilizer on the eight triangles meeting along an edge. Up to exchanging X and Z, this is the face code of the dual 24-cell honeycomb, which has been proposed before without its parameters. We prove that the code is $\left[[16L^4,6,2L^2]\right]$ for every even $L\ge 4$, with $d_X=2L^2$ and $d_Z=4L^2$ exactly. A logical operator must cast a shadow covering a two-dimensional cross-section of the torus, and a single triangle shadows an area of at most $1/2$; explicit operators built from flat planes attain the resulting bounds in both sectors. The code reaches distance d with $4d^2$ qubits against $6d^2$ for the standard hypercubic code, although rotated hypercubic codes need fewer. Hook errors from the weight-8 checks cost no more than those from the weight-4 checks. Excitations in both sectors are loops, and the slices of the lattice are face-centered cubic. Published scripts verify all results.

We develop an information-geometric framework for analyzing quantum state-update processes generated by explicit collapse dynamics. Whereas a purely geometric description characterizes collapse as a finite displacement between an initial and a final statistical state, the present approach incorporates the dynamical law governing the intermediate evolution. A quantum state is represented by a density operator $\rho \left(t\right)$ satisfying a specified dynamical equation, or, more generally, by a unitary-plus-collapse evolution in which the collapse contribution is explicitly identified. The resulting trajectory is embedded in the statistical manifold of quantum states and analyzed using the quantum Fisher information metric. This allows one to define the instantaneous Fisher speed, the information-geometric length of the collapse trajectory, and an integrated geometric cost associated with the dynamical state change. The framework also permits comparison between the actual trajectory generated by a collapse model and the corresponding Fisher-geodesic trajectory connecting the same initial and final states. Relative entropy provides a complementary global measure of the distinguishability generated by the evolution, while the quantum Fisher metric characterizes its local statistical structure. The formalism is constructed so that different dynamical collapse proposals can be analyzed within a common geometric language without assuming that the geometric quantities themselves constitute a collapse mechanism: this is a diagnostic framework rather than a mechanism. In particular, once a specific collapse generator is supplied, the framework can determine how its parameters, localization properties, stochasticity, and time scale are reflected in the geometry of the associated state trajectory. The resulting formulation therefore provides a bridge between dynamical models of wave-function collapse and the information geometry of a quantum state space, while preserving the distinction between a physical collapse law and its geometric characterization.