Translation symmetry: TranslationGroup + orbit-representative Pauli-sum merging

[AlexSchuckert]

PR 1 of 4 splitting #178 into reviewable chunks (this → CTPP core → symmetry-merged evolution → ledgers). Full development history: branch continuous-time-pauli-propagation.

Adds ppvm_pauli_sum::symmetry (pure Rust, no new dependencies):

• TranslationGroup: finite abelian permutation groups — 1D chains, 2D/3D tori, multi-leg ladders, or arbitrary generator lists — with lex-min orbit canonicalization, shift counters, and momentum-sector characters χ_k(g).
• k = 0 merging: canonicalize_pauli_sum (Vec-pair form used by the upcoming adaptive evolution) and symmetry_merge_pauli_sum (PauliSum form). Preserves all G-invariant expectation values for G-commuting dynamics (Theorem 1 of Teng, Chang, Rudolph & Holmes, arXiv:2512.12094).
• k ≠ 0: canonicalize_pauli_sum_complex (character-weighted projection with 1/|G| normalization) and check_momentum_sector to validate inputs before projecting (silent projection discards physics).

Tests: canonicalization/orbit properties on chains, tori, ladders; merge correctness; momentum-eigenstate round trips; a Trotter end-to-end check that per-step merging matches merge-at-end in the dt → 0 limit.

🤖 Generated with Claude Code

[github-actions]

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[Copilot]

Pull request overview

Adds a new Rust-only symmetry layer to ppvm-pauli-sum for translation-invariant (and momentum-resolved) Pauli-sum canonicalization/merging, intended to support upcoming continuous-time Pauli propagation work (#178 split).

Changes:

• Introduces ppvm_pauli_sum::symmetry with TranslationGroup plus orbit-canonicalization utilities.
• Adds real (k=0) and complex/momentum-sector merging/canonicalization helpers, along with momentum-sector validation.
• Exposes the new module from ppvm-pauli-sum’s public API and adds a comprehensive test suite for canonicalization/merge behavior.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 4 comments.

File	Description
crates/ppvm-pauli-sum/src/symmetry.rs	New symmetry module: translation group model, orbit canonicalization, (momentum) merging, and tests.
crates/ppvm-pauli-sum/src/lib.rs	Exposes the new symmetry module publicly.

---

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[Copilot]

Pull request overview

Copilot reviewed 2 out of 2 changed files in this pull request and generated 9 comments.

[david-pl]

@AlexSchuckert I think this is a pretty good boiled down PR here. I just saw that the single file here was pretty large.

codex suggested some semantic split, see below.

Codex output:

symmetry.rs is approaching 1,000 lines, and I think there is a worthwhile semantic split here beyond simply moving code around. I would suggest preserving the existing ppvm_pauli_sum::symmetry::* API through re-exports, but organizing the implementation as:

symmetry/
├── mod.rs # module docs and public re-exports
├── group.rs # TranslationGroup, constructors, orbit/canonicalization
├── merge.rs # k=0 Vec/PauliSum orbit merging
├── momentum.rs # characters, complex projection, sector validation/error
└── tests.rs # current tests

The group versus reduction boundary is already quite clear in the current file. I think momentum also merits its own module because canonicalize_pauli_sum_complex is a normalized sector projection, not merely the complex-coefficient equivalent of the plain merge; colocating it with character, check_momentum_sector, and SectorCheckError would make that semantic distinction easier to maintain.

I would not split the individual lattice constructors into separate files—the 1D/2D/3D/ladder constructors are cohesive parts of TranslationGroup. Also, about a third of the current file is tests, so moving those out alone would make the production code substantially easier to scan.

[Copilot]

Pull request overview

Copilot reviewed 2 out of 2 changed files in this pull request and generated 4 comments.

Comments suppressed due to low confidence (6)

crates/ppvm-pauli-sum/src/symmetry.rs:101

• from_generators accepts orders that can be zero. That leads to division/modulo by zero later (e.g. character divides by orders[g], and mixed-radix decoding uses % o). Add an upfront order > 0 validation per generator.

 pub fn from_generators(n_qubits: usize, perms: Vec<Vec<u32>>, orders: Vec<u32>) -> Self {
assert_eq!(perms.len(), orders.len(), "perms and orders must match");
for (g, perm) in perms.iter().enumerate() {

crates/ppvm-pauli-sum/src/symmetry.rs:219

• TranslationGroup::order() multiplies generator orders with product(), which can silently overflow usize in release builds. That can make order() wrong and can even feed 1.0 / order in momentum merging. Use checked multiplication and fail fast on overflow.

 /// Total group order: `Π orders[g]`.
pub fn order(&self) -> usize {
self.orders.iter().map(|&o| o as usize).product()
}

crates/ppvm-pauli-sum/src/symmetry.rs:133

• The convenience constructors can panic on zero dimensions (e.g. chain_1d(0) does (q + 1) % n). Add explicit assert!(...) guards so invalid sizes fail with a clear message.

 /// 1D chain of `n` sites with periodic boundary conditions.
/// Single generator: cyclic shift by one site.
pub fn chain_1d(n: usize) -> Self {
let perm: Vec<u32> = (0..n).map(|q| ((q + 1) % n) as u32).collect();
Self::from_generators(n, vec![perm], vec![n as u32])
}

crates/ppvm-pauli-sum/src/symmetry.rs:152

• torus_2d(0, ly) / torus_2d(lx, 0) will panic due to modulo-by-zero in the permutation builders. Add explicit dimension assertions so the API fails fast with a clear message.

 /// 2D `lx × ly` torus, qubit at `(i, j)` indexed as `j*lx + i`.
/// Two generators: x-shift (i → i+1 mod lx) and y-shift (j → j+1 mod ly).
pub fn torus_2d(lx: usize, ly: usize) -> Self {
let n = lx * ly;
let perm_x: Vec<u32> = (0..n)
.map(|q| {
let (i, j) = (q % lx, q / lx);
(j * lx + (i + 1) % lx) as u32
})
.collect();
let perm_y: Vec<u32> = (0..n)
.map(|q| {
let (i, j) = (q % lx, q / lx);
(((j + 1) % ly) * lx + i) as u32
})
.collect();
Self::from_generators(n, vec![perm_x, perm_y], vec![lx as u32, ly as u32])
}

crates/ppvm-pauli-sum/src/symmetry.rs:187

• torus_3d has the same modulo-by-zero hazard as torus_2d when any dimension is zero. Add explicit assertions for lx, ly, and lz > 0.

 /// 3D `lx × ly × lz` torus, qubit at `(i, j, k)` indexed as
/// `k*lx*ly + j*lx + i`.
pub fn torus_3d(lx: usize, ly: usize, lz: usize) -> Self {
let n = lx * ly * lz;
let perm_x: Vec<u32> = (0..n)
.map(|q| {
let i = q % lx;
let j = (q / lx) % ly;
let k = q / (lx * ly);
(k * lx * ly + j * lx + (i + 1) % lx) as u32
})
.collect();
let perm_y: Vec<u32> = (0..n)
.map(|q| {
let i = q % lx;
let j = (q / lx) % ly;
let k = q / (lx * ly);
(k * lx * ly + ((j + 1) % ly) * lx + i) as u32
})
.collect();
let perm_z: Vec<u32> = (0..n)
.map(|q| {
let i = q % lx;
let j = (q / lx) % ly;
let k = q / (lx * ly);
(((k + 1) % lz) * lx * ly + j * lx + i) as u32
})
.collect();
Self::from_generators(
n,
vec![perm_x, perm_y, perm_z],
vec![lx as u32, ly as u32, lz as u32],
)
}

crates/ppvm-pauli-sum/src/symmetry.rs:204

• ladder(l, n_legs) can panic when l == 0 due to (j + 1) % l, and n_legs == 0 produces a degenerate 0-qubit group. Add input validation for clarity and to avoid modulo-by-zero.

 /// Multi-leg ladder: `l` sites along the chain × `n_legs` legs.
/// Single generator: cyclic shift along the chain direction (all
/// legs simultaneously). Qubit at `(leg, j)` indexed as
/// `leg * l + j`. No translation along the leg axis (legs are
/// distinguished).
pub fn ladder(l: usize, n_legs: usize) -> Self {
let n = l * n_legs;
let perm: Vec<u32> = (0..n)
.map(|q| {
let leg = q / l;
let j = q % l;
(leg * l + (j + 1) % l) as u32
})
.collect();
Self::from_generators(n, vec![perm], vec![l as u32])
}

[Copilot]

🔵 Needs a closer look

Review details

• Files reviewed: 14/14 changed files
• Comments generated: 1
• Review effort level: Lite

[Copilot]

🟡 Changes recommended

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Review details

Suppressed comments (1)

crates/ppvm-pauli-sum/src/symmetry/momentum.rs:325

• SectorCheckError::CoefficientMismatch's Display message is misleading: it says the orbit representative "expected c=…" but expected is the expected coefficient for the offending orbit member (after applying the sector relation). This makes debugging confusing.

 Self::CoefficientMismatch {
rep,
offending_pauli,
expected,
actual,
shift,
} => write!(
f,
"input not in target momentum sector: orbit rep {rep} expected c={expected:?}, \
but orbit member {offending_pauli} (shift {shift:?}) has c={actual:?}"
),

• Files reviewed: 7/7 changed files
• Comments generated: 1
• Review effort level: Lite