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name: simulation description: "Choose and operate PyQuil's in-process and service-backed simulators, inspect quantum states and observables, and diagnose ordering, noise, random-state, and scaling failures." disable-model-invocation: true metadata: disco-role: operating license: Apache 2.0

PyQuil simulation

Use this route when the task is to simulate a small Quil Program, inspect a wavefunction or density matrix, calculate Pauli expectations, sample outcomes, construct simulation matrices, or decide whether a QVM service is required. This route assumes a usable PyQuil installation and a concrete qubit count. For general program construction, use program-authoring. For compilation, QuantumComputer, QVM/QPU jobs, or QCS orchestration, use compile-execute. For complete channel, readout, and Experiment workflows, use noise-experiments.

First decision: local or service-backed

• Service-free local simulation: choose PyQVM for a QAM-shaped execution path, or use ReferenceWavefunctionSimulator/NumpyWavefunctionSimulator directly for a gate-only numerical path. PyQVM(n_qubits=..., seed=...) supplies a shared random state and is the safest default when measurement, sampling, control flow, or repeatable noise is involved.
• Service-backed wavefunction: pyquil.api.WavefunctionSimulator is a client for the QVM HTTP wavefunction/expectation/measurement endpoints. It is not an in-process simulator. With no QVM service, its .wavefunction(...) call attempts HTTP and raises api.QVMError (typically beginning Could not communicate with QVM at ...). Do not use it to prove service-free execution.
• Density/noise: PyQVM with post_gate_noise_probabilities selects ReferenceDensitySimulator by default. This is an experimental post-gate single-qubit Kraus path, not the full noise/Experiment API; route the latter to noise-experiments.

Read simulator-selection.md before choosing an engine, especially when a request mentions QVM, noise, state injection, or many qubits.

Minimal local workflow

1. Build or receive a Program from program-authoring. Count the qubits explicitly; PyQVM allocates the full Hilbert space.
2. For a gate-only state, use ReferenceWavefunctionSimulator(n_qubits) or NumpyWavefunctionSimulator(n_qubits), then .do_program(program).
3. For Quil/QAM semantics, use PyQVM(n_qubits, seed=integer).execute(program). Execution requires a Program, resets the simulator at each execute call, and returns the stateful PyQVM; inspect qam.wf_simulator.
4. Validate the state before interpreting it: a wavefunction has 2**n amplitudes; the NumPy tensor has shape (2,) * n; a density matrix has shape (2**n, 2**n), is Hermitian, and has trace one.
5. Convert results into the requested representation. Read state-and-observables.md for exact bit ordering, Wavefunction helpers, expectations, density observables, sampling, and matrix lifting.
6. Run the bundled deterministic Bell check when a service-free smoke test is needed: python scripts/bell_state_inprocess.py. Use python scripts/bell_state_inprocess.py --help to inspect its interface; it performs no network call or file write.

Engine-specific operating rules

• ReferenceWavefunctionSimulator stores a flat canonical vector and favors readable reference behavior. NumpyWavefunctionSimulator stores an n-dimensional tensor and is the default PyQVM backend without noise. Compare the NumPy tensor after reversing axes and flattening when comparing it with the reference vector.
• Direct simulators can apply gates and compute expectations, but stochastic measurement/sampling needs rs. Instantiate them with a numpy.random.RandomState, or prefer PyQVM(seed=...) so all stochastic actions share one deterministic stream.
• ReferenceDensitySimulator stores a dense matrix and supports the experimental post-gate noise names relaxation, dephasing, depolarizing, phase_flip, bit_flip, and bitphase_flip. Its current expectation method raises NotImplementedError; compute Tr(rho O) with a lifted Pauli matrix for a local diagnostic, or route full observable and Experiment work to noise-experiments.
• A direct simulator's do_program is gate-only. PyQVM adds classical memory/control-flow plumbing, measurement, and ordinary Program execution, but still rejects several instructions and parameterized DEFGATEs. Treat a failure as a backend capability issue, not automatically as a malformed program. See api-reference.md and troubleshooting.md.

Numerical and resource guardrails

• PyQuil's canonical basis vector order is 00, 01, 10, 11, ..., with qubit 0 as the least-significant/rightmost bit. Thus index 1 is bitstring 01 and means q0=1. Measurement arrays and user-selected qubit lists can use a different column presentation; never infer labels from array positions alone.
• A complex128 statevector needs 16 * 2**n bytes; a dense complex128 density matrix needs 16 * 4**n bytes, before temporary lifted matrices. Estimate memory before allocating and stop early for an exponential-size request.
• Use api-reference.md for verified signatures and state-and-observables.md for concrete shapes and matrix-ordering recipes. Use troubleshooting.md for recovery when a state is invalid, random state is absent, noise is incompatible, or a QVM boundary was mistaken for local execution.

Handoff checks

Before claiming a simulation result, record the engine and version, qubit count, seed policy, whether noise was applied, state shape, basis convention, and whether any service was contacted. Assert normalization and the expected ordering for at least one basis state. For Bell-like checks, compare vector, probabilities, XX/YY/ZZ expectations, and sampled bitstring columns across reference and PyQVM paths rather than comparing only a pretty-printed string.