{
  "slug": "backpropagation-for-pauli-propagation-715184",
  "title": "Backpropagation for Pauli Propagation",
  "dek": "A backpropagation algorithm for Pauli-propagation simulation that targets quantum-circuit parameter gradients with lower memory than conventional reverse-mode AD and fewer function evaluations than finite differences.",
  "summary": "Backpropagation for Pauli propagation: quantum-circuit gradients with O(n_param) lower memory than reverse-mode AD and fewer finite-difference evaluations.",
  "tags": [
    "pauli-propagation",
    "quantum-gradients",
    "quantum-circuits",
    "sparse-pauli-simulation",
    "reverse-mode-automatic-differentiation",
    "finite-differences",
    "state-preparation",
    "time-evolution-compression",
    "operator-complexity"
  ],
  "published_at": "2026-07-18T21:07:32.61+00:00",
  "grade": 8.5,
  "agent_utility": 8.2,
  "price_usdc": 0.261,
  "stats": {
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    "faq": 9,
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  "preview": {
    "faq_questions": [
      "What is the main contribution?",
      "What does the abstract claim about complexity and accuracy?",
      "How does it compare with conventional reverse-mode automatic differentiation?",
      "How does it compare with finite differences?",
      "Why does reversibility matter?",
      "What applications are explicitly named?",
      "What demonstrations are listed?",
      "Does the method support operator-complexity regularization?",
      "Is this presented as a quantum-hardware gradient method?"
    ],
    "entity_names": [
      {
        "name": "Backpropagation algorithm",
        "type": "technique"
      },
      {
        "name": "Parameter gradients",
        "type": "optimization quantity"
      },
      {
        "name": "Quantum circuits",
        "type": "system"
      },
      {
        "name": "Pauli propagation simulation",
        "type": "technique"
      },
      {
        "name": "Standard sparse Pauli simulation techniques",
        "type": "baseline"
      },
      {
        "name": "Observable expectation values",
        "type": "metric"
      },
      {
        "name": "Reversibility of quantum circuits",
        "type": "property"
      },
      {
        "name": "n_param",
        "type": "symbol"
      },
      {
        "name": "Conventional reverse-mode automatic differentiation",
        "type": "baseline"
      },
      {
        "name": "Finite difference methods",
        "type": "baseline"
      },
      {
        "name": "Classical optimization of quantum circuits",
        "type": "application setting"
      },
      {
        "name": "State preparation",
        "type": "application"
      },
      {
        "name": "Time-evolution compression",
        "type": "application"
      },
      {
        "name": "Operator-complexity measures",
        "type": "diagnostic"
      },
      {
        "name": "Operator stabilizer Rényi entropy",
        "type": "metric"
      },
      {
        "name": "Transverse-field Ising models",
        "type": "benchmark model"
      },
      {
        "name": "Three-dimensional Heisenberg model",
        "type": "benchmark model"
      },
      {
        "name": "Two-dimensional time-evolution circuits",
        "type": "benchmark target"
      }
    ],
    "related_work_titles": [
      "Standard sparse Pauli simulation techniques",
      "Conventional reverse-mode automatic differentiation",
      "Finite difference methods",
      "State-preparation circuit optimization",
      "Time-evolution circuit compression",
      "Operator-complexity regularization"
    ],
    "application_industries": [
      "quantum software",
      "classical quantum-circuit optimization",
      "many-body quantum simulation benchmarks",
      "quantum circuit compression",
      "operator-complexity-aware optimization"
    ],
    "glossary_terms": [
      "backpropagation",
      "parameter gradient",
      "quantum circuit",
      "Pauli propagation simulation",
      "standard sparse Pauli simulation techniques",
      "observable expectation value",
      "n_param",
      "conventional reverse-mode automatic differentiation",
      "finite difference method",
      "function evaluation",
      "state preparation",
      "time-evolution compression",
      "operator-complexity measure",
      "operator stabilizer Rényi entropy",
      "reversibility of quantum circuits",
      "classical optimization of quantum circuits",
      "transverse-field Ising model",
      "three-dimensional Heisenberg model"
    ]
  },
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    "version": 2,
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    "price": 0.261,
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