Shared glossary

physical lattice

The d-dimensional spatial cell complex carrying the quantum qudits. The package uses periodic cubical tori.

spacetime lattice

The physical lattice times the discrete imaginary-time circle of M slices. It has dimension d+1 and includes auxiliary temporal p-cells.

p-cell

A canonically oriented p-dimensional cubical cell. Physical qudits live on spatial p-cells. In the vertex model p=0.

chain

A sparse linear combination of oriented cells. Its boundary is computed using signed incidence, then reduced modulo N when requested.

cochain

Values on cells, paired with chains. A configuration phi is a binary spacetime p-cochain in the implemented sign-free representations.

cycle

A chain with zero boundary modulo its coefficient group. Every vertex collection is a 0-cycle in the unaugmented convention.

cocycle

A cochain with zero coboundary. Adding a logical coordinate cocycle leaves all plaquette characters invariant.

J and K

Positive projector coefficients of A and B stabilizers. For N=2, their nonconstant character coefficients are J/2 and K/2.

g and h

Uniform binary coherent source coefficients of X and Z, respectively. They are not noise probabilities or Monte Carlo proposal rates.

temperature

T>0 in energy units with kB=1. The inverse temperature is beta=1/T.

Trotter step

The imaginary-time spacing delta=beta/M. Increasing M at fixed Hamiltonian and temperature refines the ordered trace representation.

finite-M target

The measure representing Tr[(exp(-delta H_z) exp(-delta H_x))^M]. It is generally distinct from the exact quantum Gibbs trace at finite M.

action

In implementation descriptions, the dimensionless log weight S whose exponential is sampled. Conventional Euclidean action has opposite sign.

measurement family

A Z group on the source model or an X group measured diagonally on the dual model. Separate groups do not define a joint mixed-family sample.

collapsed ensemble

The higher-degree target with exact spatial logical-shift integration, sampled on redundant representatives with conditional physical estimators.

logical character

A binary vector describing an operator’s sign change under each coordinate logical shift. Products combine characters by XOR.

worldline proposal

A simultaneous flip of one spatial p-cell’s bits on all time slices, accepted against the full collapsed target.

sweep

In the higher-degree engine, exactly one spacetime spin count of attempted fixed-mixture updates. Stays and rejections count.

cluster attempt

In the vertex engine, one lazy or single-cluster transition. Its clock is independent of the number of spins flipped.

retained record

One saved joint observable evaluation after warmup and retention cadence. Correlated records are not automatically independent observations.

snapshot

A saved full configuration used to recompute its measurements. Only selected retained records have full snapshots.

checkpoint

State, caches, RNG and counters sufficient for a controlled continuation. General bounded continuation needs the run-level checkpoint index.

MCSE

An estimate of Monte Carlo standard error for a specified estimator under stationarity/dependence assumptions, distinct from physical variance.

Rhat and ESS

Multichain convergence/efficiency diagnostics. An available numerical value is not a proof of equilibration or nominal confidence coverage.

implementation freeze

A version and hash binding of the runtime module tree recorded by a run. Older results require their original identity for verified loading.