parity_decoder

Classes for decoding states from parity code space.

class parityos.encodings.parity_decoder.StateDecoder

Bases: Generic[LogicalQubitT, PhysicalQubitT], ABC

A base class for decoding states in a code-space to the original computational space.

abstractmethod decode(state: PauliBasisState[PhysicalQubitT, Z[Never]]) → frozenset[PauliBasisState[LogicalQubitT, Z[Never]]]

Decode a physical state to a frozenset of equally likely logical states.

Parameters:

state – Physical state to decode.

Returns:

A set of equally likely logical states this physical state encodes.

class parityos.encodings.parity_decoder.ParityStateDecoder(parity_mapping: ParityMapping[LogicalQubitT, PhysicalQubitT])

Bases: StateDecoder[LogicalQubitT, PhysicalQubitT]

A decoder for parity mapping encoded states.

It offers the following methods for decoding physical states into logical states:

• decode

• closest_valid_physical_states

• select_reduced_readout_qubits

• make_full_state_from_partial.

It is possible to use a partial read-out to construct a full physical state, based on the redundant encoding that the Parity architecture offers. This is especially useful if only a limited number of qubits can be read out in the hardware setup, or if the read-out failed on some qubits.

parity_mapping: ParityMapping[LogicalQubitT, PhysicalQubitT]

Mapping between logical and physical qubits based on parities of logical qubit groups.

decode(state: PauliBasisState[PhysicalQubitT, Z[Never]]) → frozenset[PauliBasisState[LogicalQubitT, Z[Never]]]

Decode a physical state back to a logical one, it is important that the state contains enough qubits to reconstruct the logical state. If not enough qubits are included, a ParityOSException will be raised.

Parameters:

state – Physical state to decode.

Returns:

frozenset of all equally likely logical states that correspond to the physical state.

closest_valid_physical_states(state: PauliBasisState[PhysicalQubitT, Z[Never]]) → frozenset[PauliBasisState[PhysicalQubitT, Z[Never]]]

Construct the most likely physical states that correspond to a physical state which does not necessarily satisfies the constraints.

The resulting states are computed as all valid physical states that are at a Hamming distance d from the original state, with d the smallest possible distance that yields a non-zero amount of valid physical states.

Parameters:

state – Physical state to correct for errors.

Returns:

frozenset of possible physical states that satisfy all constraints (and hence are part of the physical code subspace)

select_reduced_readout_qubits(random_generator: Random | None = None) → frozenset[Qubit]

Construct a random minimal set of qubits that can be read-out and still be used to recover the full logical states.

Note

When these qubits are used for read-out, no error correction can be applied.

Parameters:

random_generator – Random number generator. If None, the default random number generator random.Random is used. Optional.

Returns:

Random set of qubits that are selected for read-out.

make_full_state_from_partial(state: PauliBasisState[PhysicalQubitT, Z[Never]], return_incomplete: bool = False) → PauliBasisState[QubitT, Z[Never]]

Reconstruct a full physical state from a partial one using the parity constraints in parity_mapping.

Parameters:

• state – Partial physical state to extend.

• return_incomplete – If True, return a physical state even if the full state could not be reconstructed. The state returned in that case contains all the qubits that could be deduced.

Returns:

Full physical state deduced from the parity constraints.

check_parity(state: PauliBasisState[PhysicalQubitT, Z[Never]]) → bool

Check whether a state satisfies all the constraints.

Parameters:

state – Physical state to check.

Returns:

True if it satisfies all constraints, False otherwise.