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pith:2URL3G3G

pith:2026:2URL3G3GLB4JSOMKQUMFNZ6T3Z

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Exact nonequilibrium steady states of boundary driven circuit with XYZ gates

Tomaz Prosen, Vladislav Popkov, Xin Zhang

Boundary-driven XXZ quantum circuits have exact many-body density operators via a spatially inhomogeneous matrix product ansatz with infinite bond dimension.

arxiv:2605.17018 v1 · 2026-05-16 · quant-ph · cond-mat.stat-mech · math-ph · math.MP

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Claims

C1strongest claim

We obtain the exact many-body density operator of a boundary-driven XXZ quantum circuit via a spatially inhomogeneous matrix product Ansatz. The Ansatz has formally infinite bond-dimension and generalizes authors' previous construction for the XXZ interactions. We find and describe a family of relatively robust separable chiral nonequilibrium steady states (NESS), which are elliptic analogs of spin helices for the circuit.

C2weakest assumption

The spatially inhomogeneous matrix product ansatz with formally infinite bond dimension is assumed to exactly represent the nonequilibrium steady state for arbitrary pure target states at the boundaries and for the XYZ-gate interactions.

C3one line summary

Exact many-body density operator for boundary-driven XXZ circuit with XYZ gates obtained via inhomogeneous matrix product ansatz, revealing family of separable chiral NESS as elliptic spin helices.

References

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[1] easy-plane-like

[2] V. Popkov and T. Prosen, Exact Nonequilibrium Steady State ofXXZCircuits Boundary Driven with Arbitrary Resets or Fields, Phys. Rev. Lett.135, 070401 (2025) 2025

[3] H.-P. Breuer and F. Petruccione,The theory of open quantum systems(Oxford University Press, 2002) 2002

[4] M. A. Nielsen and I. L. Chuang,Quantum computation and quantum information(Cambridge University press, 2010) 2010

[5] C. Gardiner and P. Zoller,Quantum noise: a handbook of Markovian and non-Markovian quantum stochastic meth- ods with applications to quantum optics(Springer Science & Business Media, 2004) 2004

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Receipt and verification

First computed	2026-05-20T00:03:36.241834Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d522bd9b66587899398a851856e7d3de73a84dc8282aad12c7d2a71fc3786275

Aliases

arxiv: 2605.17018 · arxiv_version: 2605.17018v1 · doi: 10.48550/arxiv.2605.17018 · pith_short_12: 2URL3G3GLB4J · pith_short_16: 2URL3G3GLB4JSOMK · pith_short_8: 2URL3G3G

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/2URL3G3GLB4JSOMKQUMFNZ6T3Z \
  | 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: d522bd9b66587899398a851856e7d3de73a84dc8282aad12c7d2a71fc3786275

Canonical record JSON

{
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    "abstract_canon_sha256": "7751ed35871ed0955f49ada96741031a587d85ab4c66a45e65836a5049062bb7",
    "cross_cats_sorted": [
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      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-16T14:37:11Z",
    "title_canon_sha256": "983c522efb0cc8b1ab7a3b349e83bc14f646df3fc0319e6c2e39f93248905494"
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  "source": {
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    "kind": "arxiv",
    "version": 1
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}