Pith Number

pith:AKZVM2KT

pith:2026:AKZVM2KT63CKFSYK4LJOJFDG7R

not attested not anchored not stored refs resolved

Solving Classical and Quantum Spin Glasses with Deep Boltzmann Quantum States

Arka Dutta, Enrico Prati, Luca Leone, Markus Heyl, Pietro Torta

Deep Boltzmann Quantum States solve large classical and quantum spin glasses by matching exact or best-known ground states.

arxiv:2605.15899 v1 · 2026-05-15 · cond-mat.dis-nn · quant-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AKZVM2KT63CKFSYK4LJOJFDG7R}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We match the exact solution or the best available estimate for several instances of classical and quantum Ising spin-glass models with infinite-range interactions and hundreds of spins. We also solve instances of the NP-hard Job Shop Scheduling Problem exceeding the current limitations of quantum annealing hardware.

C2weakest assumption

The neural network ansatz combined with block Gibbs sampling and the hardness-interpolation schedule is expressive enough to reach the global ground state without becoming trapped in the exponentially many local minima characteristic of spin glasses, even when the instantaneous adiabatic state is not closely tracked at intermediate hardness values.

C3one line summary

Deep Boltzmann Quantum States with natural-gradient optimization and annealing-like training match exact or best-known solutions for large infinite-range Ising spin glasses and solve job shop scheduling instances.

References

145 extracted · 145 resolved · 7 Pith anchors

[1] A noteworthy observation is that imaginary-time TDVP is formally equivalent to the optimization of the cost func- tion in Eq

[2] The resulting high-level im- plementation of VQA for optimizing a variational ansatz (typically an NQS) is illustrated in Algorithm 2

[3] [123] and known as pmRBM uses two independent RBMs to model the phase and the modulus of the wave- function

[4] DBM wavefunctions A possible quantum extension of DBMs based on the same principle of the cRBM was introduced in Ref. [32] and reads ψ(x;θ)= X x(l) l>0 e PNL −1 l=0 x(l)T W (l)x(l+1)+PNL l=0 b(l)T x(l

[5] Quantum Boltzmann Machines Another possible extension, dubbed Quantum Boltz- mann Machine (QBM), was proposed in Ref. [122]. The units of the BM are promoted to quantum spins, and the state of the sys

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:24.465306Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

02b3566953f6c4a2cb0ae2d2e49466fc44532c6d17d7d7d357e5d2b049e46337

Aliases

arxiv: 2605.15899 · arxiv_version: 2605.15899v1 · doi: 10.48550/arxiv.2605.15899 · pith_short_12: AKZVM2KT63CK · pith_short_16: AKZVM2KT63CKFSYK · pith_short_8: AKZVM2KT

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/AKZVM2KT63CKFSYK4LJOJFDG7R \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 02b3566953f6c4a2cb0ae2d2e49466fc44532c6d17d7d7d357e5d2b049e46337

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fdf96e956d077e5f48d5c9d1489c99105fe88fe5dbcb460d134781815b670569",
    "cross_cats_sorted": [
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.dis-nn",
    "submitted_at": "2026-05-15T12:30:07Z",
    "title_canon_sha256": "d34f5ee3b916bab9495c115bc2cc197a7d5dc2493f9207f8ca720cd9835a8bd4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15899",
    "kind": "arxiv",
    "version": 1
  }
}