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name: algorithms-and-observables description: "Use Cirq to assemble textbook algorithm circuits, Pauli observables, expectation-value checks, and variational-loop validation." disable-model-invocation: true metadata: disco-role: operating license: Apache 2.0

Cirq algorithms and observables

Use this sub-skill when the task is about algorithm-level Cirq patterns or observable validation rather than basic circuit syntax. Typical triggers include QFT, phase estimation, Grover search, Bernstein-Vazirani, quantum teleportation, superdense coding, QAOA-style ansatz loops, PauliString, PauliSum, Pauli measurements, expectation values, or interpreting algorithm result histograms.

Start here

1. Pick the closest recipe in algorithm-recipes.md.
2. For observables, expectation values, qubit-order checks, or result validation, read observables-and-validation.md.
3. If a result looks wrong, use troubleshooting.md before changing the circuit.
4. For a tiny deterministic smoke check of Pauli expectations, run estimate_pauli_expectation.py:

python scripts/estimate_pauli_expectation.py --state bell --observable zz
python scripts/estimate_pauli_expectation.py --state zero --observable sum

Routing boundaries

• Route raw qubits, gates, moments, measurement keys, parameters, custom gates, JSON/QASM, and protocol mechanics to core-circuits-and-ops.
• Route simulator choice, noisy runs, sweeps, result objects, histograms at sampler depth, and plotting setup to simulation-study-and-noise.
• Route decomposition, optimizer passes, target gatesets, adjacency constraints, and hardware routing to transformers-and-compilation.
• Route provider packaging, cloud samplers, credentials, provider serializers, and widgets to hardware-providers-and-serialization.

API anchors covered here

• Built-in QFT: cirq.qft(*qubits, without_reverse=False, inverse=False) and cirq.QuantumFourierTransformGate(num_qubits, without_reverse=False).
• Observables: cirq.PauliString(*contents, qubit_pauli_map=None, coefficient=1) and cirq.PauliSum(linear_dict=None); prefer arithmetic or PauliSum.from_pauli_strings for user code.
• Exact expectations: PauliString.expectation_from_state_vector(...), PauliSum.expectation_from_state_vector(...), and density-matrix counterparts.
• Measurement of Pauli observables: cirq.measure_single_paulistring(...) and cirq.measure_paulistring_terms(...).
• Histogram/plot handoff: cirq.Result.histogram, custom fold_func bitstrings, and cirq.plot_state_histogram(...) for plotting after simulation.

Validation stance

Favor small, deterministic validation circuits before scaling an algorithm. For textbook examples, validate one known setting with a state-vector or expectation-value check, then validate sampled behavior with explicit measurement keys and qubit order. Treat Shor/HHL-scale examples and full optimizer loops as educational or integration tests, not fast smoke tests.