Gate is an operation that can be applied to a collection of
qubits (objects with a
Gates can be applied
to qubits by calling their
on method, or, alternatively
calling the gate on the qubits. The object created by such calls
from cirq.ops import CNOT from cirq.devices import GridQubit q0, q1 = (GridQubit(0, 0), GridQubit(0, 1)) print(CNOT.on(q0, q1)) print(CNOT(q0, q1)) # prints # CNOT((0, 0), (0, 1)) # CNOT((0, 0), (0, 1))
A class that implements
Gate can be applied to qubits to produce an
In order to support functionality beyond that basic task, it is necessary to implement several magic methods.
Standard magic methods in python are
Cirq defines several additional magic methods, for functionality such as parameterization, diagramming, and simulation.
For example, if a gate specifies a
_unitary_ method that returns a matrix for the gate, then simulators will be able to simulate applying the gate.
Or, if a gate specifies a
__pow__ method that works for an exponent of -1, then
cirq.inverse will start to work on lists including the gate.
We describe some magic methods below.
When an object can be described by a unitary matrix, it can expose that unitary
matrix by implementing a
_unitary_(self) -> np.ndarray method.
Callers can query whether or not an object has a unitary matrix by calling
cirq.unitary on it.
_unitary_ method may also return
NotImplemented, in which case
cirq.unitary behaves as if the method is not implemented.
Operations and gates can be defined in terms of other operations by implementing a
_decompose_ method that returns those other operations.
_decompose_(self) whereas gates implement
_decompose_(self, qubits) (since gates don’t know their qubits ahead of time).
The main requirements on the output of
_decompose_ methods are:
- DO NOT CREATE CYCLES. The
cirq.decomposemethod will iterative decompose until it finds values satisfying a
keeppredicate. Cycles cause it to enter an infinite loop.
- Head towards operations defined by Cirq, because these operations have good decomposition methods that terminate in single-qubit and two qubit gates. These gates can be understood by the simulator, optimizers, and other code.
- All that matters is functional equivalence. Don’t worry about staying within or reaching a particular gate set; it’s too hard to predict what the caller will want. Gate-set-aware decomposition is useful, but this is not the protocol that does that. Gate-set-aware decomposition may be added in the future, but doesn’t exist within Cirq at the moment.
cirq.CCZ decomposes into a series of
This allows code that doesn’t understand three-qubit operation to work with
cirq.CCZ; by decomposing it into operations they do understand.
As another example,
cirq.TOFFOLI decomposes into a
cirq.H followed by a
cirq.CCZ followed by a
Although the output contains a three qubit operation (the CCZ), that operation can be decomposed into two qubit and one qubit operations.
So code that doesn’t understand three qubit operations can deal with Toffolis by decomposing them, and then decomposing the CCZs that result from the initial decomposition.
In general, decomposition-aware code consuming operations is expected to recursively decompose unknown operations until the code either hits operations it understands or hits a dead end where no more decomposition is possible.
cirq.decompose method implements logic for performing exactly this kind of recursive decomposition.
Callers specify a
keep predicate, and optionally specify intercepting and fallback decomposers, and then
cirq.decompose will repeatedly decompose whatever operations it was given until the operations satisfy the given
cirq.decompose hits a dead end, it raises an error.
Cirq doesn’t make any guarantees about the “target gate set” decomposition is heading towards.
cirq.decompose is not a method
Decompositions within Cirq happen to converge towards X, Y, Z, CZ, PhasedX, specified-matrix gates, and others.
But this set will vary from release to release, and so it is important for consumers of decompositions to look for generic properties of gates,
such as “two qubit gate with a unitary matrix”, instead of specific gate types such as CZ gates.
Gates and operations are considered to be invertable when they implement a
__pow__ method that returns a result besides
NotImplemented for an exponent of -1.
This inverse can be accessed either directly as
value**-1, or via the utility method
If you are sure that
value has an inverse, saying
value**-1 is more convenient than saying
cirq.inverse is for cases where you aren’t sure if
value is invertable, or where
value might be a sequence of invertible operations.
cirq.inverse has a
default parameter used as a fallback when
value isn’t invertable.
cirq.inverse(value, default=None) returns the inverse of
value, or else returns
value isn’t invertable.
default is specified and
value isn’t invertible, a
TypeError is raised.)
When you give
cirq.inverse a list, or any other kind of iterable thing, it will return a sequence of operations that (if run in order) undoes the operations of the original sequence (if run in order).
Basically, the items of the list are individually inverted and returned in reverse order.
For example, the expression
cirq.inverse([cirq.S(b), cirq.CNOT(a, b)]) will return the tuple
(cirq.CNOT(a, b), cirq.S(b)**-1).
Gates and operations can also return values beside
NotImplemented from their
__pow__ method for exponents besides
This pattern is used often by Cirq.
For example, the square root of X gate can be created by raising
cirq.X to 0.5:
import cirq print(cirq.unitary(cirq.X)) # prints # [[0.+0.j 1.+0.j] # [1.+0.j 0.+0.j]] sqrt_x = cirq.X**0.5 print(cirq.unitary(sqrt_x)) # prints # [[0.5+0.5j 0.5-0.5j] # [0.5-0.5j 0.5+0.5j]]
The Pauli gates included in Cirq use the convention
Z**0.5 ≡ S ≡ np.diag(1, i),
Z**-0.5 ≡ S**-1,
X**0.5 ≡ H·S·H, and the square root of
Y is inferred via the right hand rule.
_circuit_diagram_info_(self, args) and
cirq.circuit_diagram_info(val, [args], [default])¶
Circuit diagrams are useful for visualizing the structure of a
Gates can specify compact representations to use in diagrams by implementing a
For example, this is why SWAP gates are shown as linked ‘×’ characters in diagrams.
_circuit_diagram_info_ method takes an
args parameter of type
cirq.CircuitDiagramInfoArgs and returns either
a string (typically the gate’s name), a sequence of strings (a label to use on each qubit targeted by the gate), or an
cirq.CircuitDiagramInfo (which can specify more advanced properties such as exponents and will expand
in the future).
You can query the circuit diagram info of a value by passing it into
Google’s Xmon devices support a specific gate set. Gates
in this gate set operate on
GridQubits, which are qubits
arranged on a square grid and which have an
The native Xmon gates are
This gate is a rotation about an axis in the XY plane of the Bloch sphere.
PhasedXPowGate takes two parameters,
The gate is equivalent to the circuit
p is the
t is the
cirq.Z / cirq.Rz Rotations about the Pauli
The matrix of
exp(i pi |1><1| t) whereas the matrix of
exp(-i Z θ/2).
Note that in quantum computing hardware, this gate is often implemented in the
classical control hardware as a phase change on later operations, instead of as
a physical modification applied to the qubits.
(TODO: explain this in more detail)
cirq.CZ The controlled-Z gate.
A two qubit gate that phases the
The matrix of
exp(i pi |11><11| t).
cirq.MeasurementGate This is a single qubit measurement in the computational basis.
Other Common Gates¶
Cirq comes with a number of common named gates:
CNOT the controlled-X gate
SWAP the swap gate
H the Hadamard gate
S the square root of Z gate
and our error correcting friend the T gate
TODO: describe these in more detail.