tools/states.py

GHZ

Construct an $n$-partite qudit GHZ state.

Returns $\sum _{i=0}^{d-1}|i{⟩}^{\otimes n}$ (unnormalized).

def GHZ(n: int, d: int) -> State

Implementation

def GHZ(n: int, d: int) -> State:
    Ket = Basis(d)
    vals = sum([Ket(f'{i}' * n) for i in range(d)])
    return State(vals)

W

Construct the $n$-qubit $W$ state (single-excitation symmetric state).

Returns $\sum _{i=0}^{n-1}|0\cdots 1_i\cdots 0⟩$ (unnormalized).

def W(n: int) -> State

Implementation

def W(n: int) -> State:
    Ket = Basis(2)
    vals = ['0' * i + '1' + '0' * (n - i - 1) for i in range(n)]
    vals = sum([Ket(v) for v in vals])
    return State(vals)

NOON

Construct a two-mode NOON-like state.

Returns $|n,0⟩+e^{in\theta }|0,n⟩$ (unnormalized) in a local dimension $n+1$.

def NOON(n: int, theta: float) -> State

Implementation

def NOON(n: int, theta: float=0.0) -> State:
    Ket = Basis(n + 1)
    kets = [Ket(0, n), Ket(n, 0)]
    kets = kets[0] + np.exp(1j * n * theta) * kets[1]
    return State(kets)

Dicke

Construct an $n$-qubit Dicke state with $k$ zeros (and $n-k$ ones).

Returns the uniform (unnormalized) superposition over all distinct permutations of $k$ symbols $0$ and $n-k$ symbols $1$.

def Dicke(n: int, k: int) -> State

Implementation

def Dicke(n: int, k: int) -> State:
    Ket = Basis(2)
    vals = ['0'] * k + ['1'] * (n - k)
    vals = set([''.join(p) for p in permutations(vals)])
    vals = sum([Ket(v) for v in vals])
    return State(vals)

Coherent

Truncated coherent state in a finite $(N+1)$-dimensional Fock space.

Builds $\sum _{n=0}^N{\alpha }^n/\sqrt{n!}|n⟩$ with a normalization correction from the incomplete gamma function.

Reference at arxiv:1402.1487

def Coherent(N: int, alpha: complex) -> State

Implementation

def Coherent(N: int, alpha: complex=1.0) -> State:
    Ket = Basis(N + 1)
    a2 = abs(alpha) ** 2
    norm = np.exp(a2) * (1 - g(N + 1, a2) / F(N))
    norm = 1 / np.sqrt(norm)
    vec = sum((alpha ** n / np.sqrt(F(n)) * Ket(n) for n in range(N + 1)))
    return State(norm * vec)