def star_decoder(self, for_enc=None, as_dict=False):
r"""
Returns a tuple of a decoding Clifford and a :class:`qecc.PauliList`
specifying the recovery operation to perform as a function of the result
of a :math:`Z^{\otimes{n - k}}` measurement on the ancilla register.
For syndromes corresponding to errors of weight greater than the distance,
the relevant element of the recovery list will be set to
:obj:`qecc.Unspecified`.
:param for_enc: If not ``None``, specifies to use a given Clifford
operator as the encoder, instead of the first element yielded by
:meth:`encoding_cliffords`.
:param bool as_dict: If ``True``, returns a dictionary from recovery
operators to syndromes that indicate that recovery.
"""
def error_to_pauli(error):
if error == p.I.as_clifford():
return "I"
if error == p.X.as_clifford():
return "X"
if error == p.Y.as_clifford():
return "Y"
if error == p.Z.as_clifford():
return "Z"
if for_enc is None:
encoder = next(self.encoding_cliffords())
else:
encoder = for_enc
decoder = encoder.inv()
errors = pc.PauliList(p.eye_p(self.nq)) + pc.PauliList(
p.paulis_by_weight(self.nq, self.n_correctable))
syndrome_dict = defaultdict(lambda: Unspecified)
syndrome_meas = [
p.elem_gen(self.nq, idx, 'Z')
for idx in range(self.nq_logical, self.nq)
]
for error in errors:
effective_gate = decoder * error.as_clifford() * encoder
# FIXME: the following line emulates measurement until we have a real
# measurement simulation method.
syndrome = tuple(
[effective_gate(meas).ph / 2 for meas in syndrome_meas])
recovery = "".join([
# FIXME: the following is a broken hack to get the phases on the logical qubit register.
error_to_pauli(
c.Clifford([effective_gate.xout[idx][idx]],
[effective_gate.zout[idx][idx]]))
for idx in range(self.nq_logical)
])
# For degenerate codes, the syndromes can collide, so long as we
# correct the same way for each.
if syndrome in syndrome_dict and syndrome_dict[
syndrome] != recovery:
raise RuntimeError(
'Syndrome {} has collided.'.format(syndrome))
syndrome_dict[syndrome] = recovery
if as_dict:
outdict = dict()
keyfn = lambda syndrome_recovery: syndrome_recovery[1]
data = sorted(list(syndrome_dict.items()), key=keyfn)
for recovery, syndrome_group in it.groupby(data, keyfn):
outdict[recovery] = [syn[0] for syn in syndrome_group]
return decoder, outdict
else:
recovery_list = pc.PauliList(
syndrome_dict[syndrome]
for syndrome in it.product(list(range(2)),
repeat=self.n_constraints))
return decoder, recovery_list
def star_decoder(self, for_enc=None, as_dict=False):
r"""
Returns a tuple of a decoding Clifford and a :class:`qecc.PauliList`
specifying the recovery operation to perform as a function of the result
of a :math:`Z^{\otimes{n - k}}` measurement on the ancilla register.
For syndromes corresponding to errors of weight greater than the distance,
the relevant element of the recovery list will be set to
:obj:`qecc.Unspecified`.
:param for_enc: If not ``None``, specifies to use a given Clifford
operator as the encoder, instead of the first element yielded by
:meth:`encoding_cliffords`.
:param bool as_dict: If ``True``, returns a dictionary from recovery
operators to syndromes that indicate that recovery.
"""
def error_to_pauli(error):
if error == p.I.as_clifford():
return "I"
if error == p.X.as_clifford():
return "X"
if error == p.Y.as_clifford():
return "Y"
if error == p.Z.as_clifford():
return "Z"
if for_enc is None:
encoder = self.encoding_cliffords().next()
else:
encoder = for_enc
decoder = encoder.inv()
errors = pc.PauliList(p.eye_p(self.nq)) + pc.PauliList(p.paulis_by_weight(self.nq, self.n_correctable))
syndrome_dict = defaultdict(lambda: Unspecified)
syndrome_meas = [p.elem_gen(self.nq, idx, 'Z') for idx in range(self.nq_logical, self.nq)]
for error in errors:
effective_gate = decoder * error.as_clifford() * encoder
# FIXME: the following line emulates measurement until we have a real
# measurement simulation method.
syndrome = tuple([effective_gate(meas).ph / 2 for meas in syndrome_meas])
recovery = "".join([
# FIXME: the following is a broken hack to get the phases on the logical qubit register.
error_to_pauli(c.Clifford([effective_gate.xout[idx][idx]], [effective_gate.zout[idx][idx]]))
for idx in range(self.nq_logical)
])
# For degenerate codes, the syndromes can collide, so long as we
# correct the same way for each.
if syndrome in syndrome_dict and syndrome_dict[syndrome] != recovery:
raise RuntimeError('Syndrome {} has collided.'.format(syndrome))
syndrome_dict[syndrome] = recovery
if as_dict:
outdict = dict()
keyfn = lambda (syndrome, recovery): recovery
data = sorted(syndrome_dict.items(), key=keyfn)
for recovery, syndrome_group in it.groupby(data, keyfn):
outdict[recovery] = [syn[0] for syn in syndrome_group]
return decoder, outdict
else:
recovery_list = pc.PauliList(syndrome_dict[syndrome] for syndrome in it.product(range(2), repeat=self.n_constraints))
return decoder, recovery_list
class Location(object):
"""
Represents a gate, wait, measurement or preparation location in a
circuit.
Note that currently, only gate locations are implemented.
:param kind: The kind of location to be created. Each kind is an
abbreviation drawn from ``Location.KIND_NAMES``, or is the index in
``Location.KIND_NAMES`` corresponding to the desired location kind.
:type kind: int or str
:param qubits: Indicies of the qubits on which this location acts.
:type qubits: tuple of ints.
"""
## PRIVATE CLASS CONSTANTS ##
_CLIFFORD_GATE_KINDS = [
'I', 'X', 'Y', 'Z', 'H', 'R_pi4', 'CNOT', 'CZ', 'SWAP'
]
_CLIFFORD_GATE_FUNCS = {
'I': lambda nq, idx: cc.eye_c(nq),
'X': lambda nq, idx: pc.elem_gen(nq, idx, 'X').as_clifford(),
'Y': lambda nq, idx: pc.elem_gen(nq, idx, 'Y').as_clifford(),
'Z': lambda nq, idx: pc.elem_gen(nq, idx, 'Z').as_clifford(),
'H': cc.hadamard,
'R_pi4': cc.phase,
'CNOT': cc.cnot,
'CZ': cc.cz,
'SWAP': cc.swap
}
_QCVIEWER_NAMES = {
'I': 'I', # This one is implemented by a gate definition
# included by Circuit.as_qcviewer().
'X': 'X',
'Y': 'Y',
'Z': 'Z',
'H': 'H',
'R_pi4': 'P',
'CNOT': 'tof',
'CZ': 'Z',
'SWAP': 'swap'
}
## PUBLIC CLASS CONSTANTS ##
#: Names of the kinds of locations used by QuaEC.
KIND_NAMES = sum([_CLIFFORD_GATE_KINDS], [])
## INITIALIZER ##
def __init__(self, kind, *qubits):
if isinstance(kind, int):
self._kind = kind
elif isinstance(kind, str):
self._kind = self.KIND_NAMES.index(kind)
else:
raise TypeError("Location kind must be an int or str.")
#if not all(isinstance(q, int) for q in qubits):
# raise TypeError('Qubit indices must be integers. Got {} instead, which is of type {}.'.format(
# *(iter((q, type(q)) for q in qubits if not isinstance(q, int)).next())
# ))
try:
self._qubits = tuple(map(int, qubits))
except TypeError as e:
raise TypeError('Qubit integers must be int-like.')
self._is_clifford = bool(self.kind in self._CLIFFORD_GATE_KINDS)
## REPRESENTATION METHODS ##
def __str__(self):
return " {:<4} {}".format(self.kind,
' '.join(map(str, self.qubits)))
def __repr__(self):
return "<{} Location on qubits {}>".format(self.kind, self.qubits)
def __hash__(self):
return hash((self._kind, ) + self.qubits)
## IMPORT METHODS ##
@staticmethod
def from_quasm(source):
"""
Returns a :class:`qecc.Location` initialized from a QuASM-formatted line.
:type str source: A line of QuASM code specifying a location.
:rtype: :class:`qecc.Location`
:returns: The location represented by the given QuASM source.
"""
parts = source.split()
return Location(parts[0], *map(int, parts[1:]))
## PROPERTIES ##
@property
def kind(self):
"""
Returns a string defining which kind of location this instance
represents. Guaranteed to be a string that is an element of
``Location.KIND_NAMES``.
"""
return self.KIND_NAMES[self._kind]
@property
def qubits(self):
"""
Returns a tuple of ints describing which qubits this location acts upon.
"""
return self._qubits
@property
def nq(self):
"""
Returns the number of qubits in the smallest circuit that can contain
this location without relabeling qubits. For a :class:`qecc.Location`
``loc``, this property is defined as ``1 + max(loc.nq)``.
"""
return 1 + max(self.qubits)
@property
def is_clifford(self):
"""
Returns ``True`` if and only if this location represents a gate drawn
from the Clifford group.
"""
return self._is_clifford
@property
def wt(self):
"""
Returns the number of qubits on which this location acts.
"""
return len(self.qubits)
## SIMULATION METHODS ##
def as_clifford(self, nq=None):
"""
If this location represents a Clifford gate, returns the action of that
gate. Otherwise, a :obj:`RuntimeError` is raised.
:param int nq: Specifies how many qubits to represent this location as
acting upon. If not specified, defaults to the value of the ``nq``
property.
:rtype: :class:`qecc.Clifford`
"""
if not self.is_clifford:
raise RuntimeError("Location must be a Clifford gate.")
else:
if nq is None:
nq = self.nq
elif nq < self.nq:
raise ValueError(
'nq must be greater than or equal to the nq property.')
return self._CLIFFORD_GATE_FUNCS[self.kind](nq, *self.qubits)
## EXPORT METHODS ##
def as_qcviewer(self, qubit_names=None):
"""
Returns a representation of this location in a format suitable for
inclusion in a QCViewer file.
:param qubit_names: If specified, the given aliases will be used for the
qubits involved in this location when exporting to QCViewer.
Defaults to "q1", "q2", etc.
:rtype: str
Note that the identity (or "wait") location requires the following to be
added to QCViewer's ``gateLib``::
NAME wait
DRAWNAME "1"
SYMBOL I
1 , 0
0 , 1
"""
# FIXME: link to QCViewer in the docstring here.
return ' {gatename} {gatespec}\n'.format(
gatename=self._QCVIEWER_NAMES[self.kind],
gatespec=qubits_str(self.qubits, qubit_names),
)
## OTHER METHODS ##
def relabel_qubits(self, relabel_dict):
"""
Returns a new location related to this one by a relabeling of the
qubits. The relabelings are to be indicated by a dictionary that
specifies what each qubit index is to be mapped to.
>>> import qecc as q
>>> loc = q.Location('CNOT', 0, 1)
>>> print loc
CNOT 0 1
>>> print loc.relabel_qubits({1: 2})
CNOT 0 2
:param dict relabel_dict: If `i` is a key of `relabel_dict`, then qubit
`i` will be replaced by `relabel_dict[i]` in the returned location.
:rtype: :class:`qecc.Location`
:returns: A new location with the qubits relabeled as
specified by `relabel_dict`.
"""
return Location(
self.kind,
*tuple(relabel_dict[i] if i in relabel_dict else i
for i in self.qubits))
