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qec/recovery.py ​

class Recovery ​

Construct common approximate/analytic recovery maps for a code subspace using PyTorch and localized qudit Gates.

leung ​

No Definition provided

py
def leung(channel: Channel, codes: List[pt.Tensor]) -> Channel [static]
Implementation
python
def leung(channel: Channel, codes: List[pt.Tensor]) -> Channel:
    device = codes[0].device
    dtype = codes[0].dtype
    first_gate = channel.ops[0][0]
    n = first_gate.wires
    d = first_gate.dims[0] if hasattr(first_gate, 'dims') else 2
    total_dim = codes[0].numel()
    P = pt.zeros((total_dim, total_dim), dtype=dtype, device=device)
    for c in codes:
        c_col = c.view(total_dim, 1)
        P += c_col @ c_col.conj().T
    R_gates = []
    for i, word in enumerate(channel.ops):
        Ek_mat = Recovery._apply(word, total_dim, device, dtype)
        A = Ek_mat @ P
        U, S, Vh = pt.linalg.svd(A, full_matrices=False)
        Uk = U @ Vh
        Rk_mat = P @ Uk.conj().T
        rg = Gate(Rk_mat, index=list(range(n)), wires=n, dim=d, name=f'R_leung_{i}')
        R_gates.append([rg])
    return Channel(R_gates)

cafaro ​

No Definition provided

py
def cafaro(channel: Channel, codes: List[pt.Tensor]) -> Channel [static]
Implementation
python
def cafaro(channel: Channel, codes: List[pt.Tensor]) -> Channel:
    device = codes[0].device
    dtype = codes[0].dtype
    first_gate = channel.ops[0][0]
    n = first_gate.wires
    d = first_gate.dims[0] if hasattr(first_gate, 'dims') else 2
    total_dim = codes[0].numel()
    R_gates = []
    for i, word in enumerate(channel.ops):
        Ek_mat = Recovery._apply(word, total_dim, device, dtype)
        Rk_mat = pt.zeros((total_dim, total_dim), dtype=dtype, device=device)
        for c in codes:
            c_col = c.view(total_dim, 1)
            overlap = (c_col.conj().T @ Ek_mat.conj().T @ Ek_mat @ c_col).squeeze().real
            if overlap > 1e-12:
                proj = c_col @ c_col.conj().T
                Rk_mat += proj @ Ek_mat.conj().T / math.sqrt(overlap)
        rg = Gate(Rk_mat, index=list(range(n)), wires=n, dim=d, name=f'R_cafaro_{i}')
        R_gates.append([rg])
    return Channel(R_gates)

petz ​

No Definition provided

py
def petz(channel: Channel, codes: List[pt.Tensor]) -> Channel [static]
Implementation
python
def petz(channel: Channel, codes: List[pt.Tensor]) -> Channel:
    device = codes[0].device
    first_gate = channel.ops[0][0]
    n = first_gate.wires
    d = first_gate.dims[0] if hasattr(first_gate, 'dims') else 2
    total_dim = codes[0].numel()
    P = pt.zeros((total_dim, total_dim), dtype=C64, device=device)
    for c in codes:
        c_col = c.view(total_dim, 1)
        P += c_col @ c_col.conj().T
    E_P = channel.run(P)
    L, V = pt.linalg.eigh(E_P)
    L_rinv = pt.zeros_like(L)
    mask = L > 1e-10
    L_rinv[mask] = 1.0 / pt.sqrt(L[mask])
    L, V = (L.to(C64), V.to(C64))
    L_rinv = L_rinv.to(C64)
    norm = V @ pt.diag(L_rinv) @ V.conj().T
    R_gates = []
    for i, word in enumerate(channel.ops):
        Ek_mat = Recovery._apply(word, total_dim, device, C64)
        Rk_mat = P @ Ek_mat.conj().T @ norm
        rg = Gate(Rk_mat, index=list(range(n)), wires=n, dim=d, name=f'R_petz_{i}')
        R_gates.append([rg])
    return Channel(R_gates)