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oscillator

Oscillator gates.

CD(N, beta, ts=None)

Conditional displacement gate.

Parameters:

Name Type Description Default
N

Hilbert space dimension.

 required
beta

Conditional displacement amplitude.

 required
ts

Optional time sequence for hamiltonian simulation.

 None

Returns:

Type Description

Conditional displacement gate.
Source code in jaxquantum/circuits/library/oscillator.py 
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def CD(N, beta, ts=None):
    """Conditional displacement gate.

    Args:
        N: Hilbert space dimension.
        beta: Conditional displacement amplitude.
        ts: Optional time sequence for hamiltonian simulation.

    Returns:
        Conditional displacement gate.
    """
    gen_Ht = None
    if ts is not None:
        g = basis(2, 0)
        e = basis(2, 1)
        gg = g @ g.dag()
        ee = e @ e.dag()
        delta_t = ts[-1] - ts[0]
        amp = 1j * beta / delta_t / 2
        a = destroy(N)
        gen_Ht = lambda params: lambda t: (
            gg
            ^ (jnp.conj(amp) * a + amp * a.dag()) + ee
            ^ (jnp.conj(-amp) * a + (-amp) * a.dag())
        )

    return Gate.create(
        [2, N],
        name="CD",
        params={"beta": beta},
        gen_U=lambda params: _conditional_displacement(N, params["beta"]),
        gen_Ht=gen_Ht,
        ts=ts,
        num_modes=2,
    )

CR(N, theta)

Conditional rotation gate.

Parameters:

Name Type Description Default
N

Hilbert space dimension.

 required
theta

Conditional rotation angle.

 required

Returns:

Type Description

Conditional rotation gate.
Source code in jaxquantum/circuits/library/oscillator.py 
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def CR(N, theta):
    """Conditional rotation gate.

    Args:
        N: Hilbert space dimension.
        theta: Conditional rotation angle.

    Returns:
        Conditional rotation gate.
    """
    g = basis(2, 0)
    e = basis(2, 1)

    gg = g @ g.dag()
    ee = e @ e.dag()


    return Gate.create(
        [2, N],
        name="CR",
        params={"theta": theta},
        gen_U=lambda params: (gg ^ (-1.j*theta/2*create(N)@destroy(N)).expm())
        + (ee ^ (1.j*theta/2*create(N)@destroy(N)).expm()),
        num_modes=2,
    )

D(N, alpha, ts=None, c_ops=None)

Displacement gate.

Parameters:

Name Type Description Default
N

Hilbert space dimension.

 required
alpha

Displacement amplitude.

 required
ts

Optional time array for hamiltonian simulation.

 None
c_ops

Optional collapse operators.

 None

Returns:

Type Description

Displacement gate.
Source code in jaxquantum/circuits/library/oscillator.py 
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def D(N, alpha, ts=None, c_ops=None):
    """Displacement gate.

    Args:
        N: Hilbert space dimension.
        alpha: Displacement amplitude.
        ts: Optional time array for hamiltonian simulation.
        c_ops: Optional collapse operators.

    Returns:
        Displacement gate.
    """
    gen_Ht = None
    if ts is not None:
        delta_t = ts[-1] - ts[0]
        amp = 1j * alpha / delta_t
        a = destroy(N)
        gen_Ht = lambda params: (lambda t: jnp.conj(amp) * a + amp * a.dag())

    return Gate.create(
        N,
        name="D",
        params={"alpha": alpha},
        gen_U=lambda params: displace(N, params["alpha"]),
        gen_Ht=gen_Ht,
        ts=ts,
        gen_c_ops=lambda params: Qarray.from_list([]) if c_ops is None else c_ops,
        num_modes=1,
    )

ECD(N, beta, ts=None)

Echoed conditional displacement gate.

Parameters:

Name Type Description Default
N

Hilbert space dimension.

 required
beta

Conditional displacement amplitude.

 required
ts

Optional time sequence for hamiltonian simulation.

 None

Returns:

Type Description

Echoed conditional displacement gate.
Source code in jaxquantum/circuits/library/oscillator.py 
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def ECD(N, beta, ts=None):
    """Echoed conditional displacement gate.

    Args:
        N: Hilbert space dimension.
        beta: Conditional displacement amplitude.
        ts: Optional time sequence for hamiltonian simulation.

    Returns:
        Echoed conditional displacement gate.
    """
    return Gate.create(
        [2, N],
        name="ECD",
        params={"beta": beta},
        gen_U=lambda params: _conditional_displacement(
            N,
            params["beta"],
            echoed=True,
        ),
        gen_Ht=None,
        ts=ts,
        num_modes=2,
    )

diag_expm(diag_matrix)

Computes expm of a diagonal matrix efficiently (O(N) instead of O(N^3)).

Source code in jaxquantum/circuits/library/oscillator.py 
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def diag_expm(diag_matrix):
    """Computes expm of a diagonal matrix efficiently (O(N) instead of O(N^3))."""
    # Extract diagonal, exponentiate elements, put back on diagonal
    return jnp.diag(jnp.exp(jnp.diagonal(diag_matrix)))