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States (common state-preparation circuits)

State-preparation circuits returned as gate-tuple lists, ready for run_circuit.

states

Common state-preparation circuits, returned as gate-tuple lists ready to feed straight into run_circuit (or to concatenate with more gates first). The GHZ-state snippet in particular -- [('h', 0), ('cx', 0, 1), ('cx', 1, 2), ...] -- shows up hand-written at the top of practically every experiment and test script built on this package; ghz_state is that snippet, written once.

ghz_state 

ghz_state(n_qubits)

Build the GHZ-state preparation circuit: (|00...0> + |11...1>) / sqrt(2).

Implementation: H on qubit 0, then a linear CX chain (qubit 0 -> 1, 1 -> 2, ..., n-2 -> n-1) propagating the superposition outward -- reuses entangling_layer(n_qubits, pattern='linear') for the chain.

Parameters

n_qubits : int Number of qubits, must be >= 2 (a single qubit has no partner to entangle with, so an n=1 "GHZ state" is undefined here).

Returns

list[tuple] e.g. ghz_state(3) == [('h', 0), ('cx', 0, 1), ('cx', 1, 2)]

Examples

import dense_evolution as de sim = de.DenseSVSimulator(3) sim.run_circuit(de.ghz_state(3)) sim.get_probabilities()[[0, 7]] # |000> and |111>, each 0.5

Source code in dense_evolution/states.py 
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def ghz_state(n_qubits):
    """
    Build the GHZ-state preparation circuit:
    (|00...0> + |11...1>) / sqrt(2).

    Implementation: H on qubit 0, then a linear CX chain (qubit 0 -> 1,
    1 -> 2, ..., n-2 -> n-1) propagating the superposition outward --
    reuses `entangling_layer(n_qubits, pattern='linear')` for the chain.

    Parameters
    ----------
    n_qubits : int
        Number of qubits, must be >= 2 (a single qubit has no partner to
        entangle with, so an n=1 "GHZ state" is undefined here).

    Returns
    -------
    list[tuple]
        e.g. ghz_state(3) == [('h', 0), ('cx', 0, 1), ('cx', 1, 2)]

    Examples
    --------
    >>> import dense_evolution as de
    >>> sim = de.DenseSVSimulator(3)
    >>> sim.run_circuit(de.ghz_state(3))
    >>> sim.get_probabilities()[[0, 7]]  # |000> and |111>, each 0.5
    """
    if n_qubits < 2:
        raise ValueError(f"ghz_state needs at least 2 qubits, got {n_qubits}")
    return [('h', 0)] + entangling_layer(n_qubits, pattern='linear', gate='cx')

See also: entangling_layer, which ghz_state builds its CX chain from.