The QVM device¶
The rigetti.qvm
device provides an interface between PennyLane and the Forest
SDK quantum virtual machine or the pyQuil builtin
pyQVM. The QVM is used to simulate various quantum abstract machines, ranging from simulations of
physical QPUs to completely connected lattices.
Usage¶
When initializing the rigetti.qvm
device, the following required keyword argument must also be passed:
device
(str or networkx.Graph)The name or topology of the quantum computer to initialize.
Nqqvm
: for a fully connected/unrestricted Nqubit QVM.9qsquareqvm
: a \(9\times 9\) lattice.Nqpyqvm
or9qsquarepyqvm
, for the same as the above but run via the builtin pyQuil pyQVM device.Any other supported Rigetti device architecture, for example a QPU lattice such as
'Aspen8'
.Graph topology (as a
networkx.Graph
object) representing the device architecture.
Note that, unlike rigetti.wavefunction
, you do not pass the number of wires  this is inferred
automatically from the requested quantum computer topology.
>>> import pennylane as qml
>>> dev = qml.device('rigetti.qvm', device='Aspen8')
>>> dev.num_wires
16
In addition, you may also request a QVM with noise models to better simulate a physical
QPU; this is done by passing the keyword argument noisy=True
:
>>> dev = qml.device('rigetti.qvm', device='Aspen8', noisy=True)
Note that only the default noise models provided by pyQuil are currently supported.
To specify the pyQVM, simply append pyqvm
to the end of the device name instead of qvm
:
>>> dev = qml.device('rigetti.qvm', device='4qpyqvm')
The device can then be used just like other devices for the definition and evaluation of QNodes within PennyLane.
A simple quantum function that returns the expectation value and variance of a measurement and depends on three classical input parameters would look like:
@qml.qnode(dev)
def circuit(x, y, z):
qml.RZ(z, wires=[0])
qml.RY(y, wires=[0])
qml.RX(x, wires=[0])
qml.CNOT(wires=[0, 1])
return qml.expval(qml.PauliZ(0)), var(qml.PauliZ(1))
You can then execute the circuit like any other function to get the quantum mechanical expectation value and variance:
>>> circuit(0.2, 0.1, 0.3)
array([0.97517033, 0.04904283])
Measurements and expectations¶
Since the QVM returns a number of trial measurements of the quantum circuit, the larger the number of
‘trials’ or ‘shots’, the closer PennyLane is able to approximate the expectation value,
and as a result the gradient. By default, shots=1024
, but this can be increased or decreased as required.
For example, see how increasing the shot count increases the expectation value and corresponding gradient accuracy:
def circuit(x):
qml.RX(x, wires=[0])
return qml.expval(qml.PauliZ(0))
dev_exact = qml.device('rigetti.wavefunction', wires=1)
dev_s1024 = qml.device('rigetti.qvm', device='1qqvm')
dev_s100000 = qml.device('rigetti.qvm', device='1qqvm', shots=100000)
circuit_exact = qml.QNode(circuit, dev_exact)
circuit_s1024 = qml.QNode(circuit, dev_s1024)
circuit_s100000 = qml.QNode(circuit, dev_s100000)
Printing out the results of the three device expectation values:
>>> circuit_exact(0.8)
0.6967067093471655
>>> circuit_s1024(0.8)
0.689453125
>>> circuit_s100000(0.8)
0.6977
Supported operations¶
All devices support all PennyLane operations and observables, with the exception of the PennyLane StatePrepBase
state preparation operations.
Supported observables¶
The QVM device supports qml.PauliZ
observables values ‘natively’, while also supporting qml.Identity
, qml.PauliY
, qml.Hadamard
, and qml.Hermitian
by performing implicit change of basis operations.
Native observables¶
The QVM currently supports only one measurement, returning 1
if the qubit is measured to be in the state \(1\rangle\), and 0
if the qubit is measured to be in the state \(0\rangle\). This is equivalent to measuring in the PauliZ basis, with state \(1\rangle\) corresponding to PauliZ eigenvalue \(\lambda=1\), and likewise state \(0\rangle\) corresponding to eigenvalue \(\lambda=1\). As a result, we can simply perform a rescaling of the measurement results to get the PauliZ expectation value of the \(i\) th wire:
where \(N\) is the total number of shots, and \(m_j\) is the \(j\) th measurement of wire \(i\).
Change of measurement basis¶
For the remaining observables, it is easy to perform a quantum change of basis operation before measurement such that the correct expectation value is performed. For example, say we have a unitary Hermitian observable \(\hat{A}\). Since, by definition, it must have eigenvalues \(\pm 1\), there will always exist a unitary matrix \(U\) such that it satisfies the following similarity transform:
Since \(U\) is unitary, it can be applied to the specified qubit before measurement in the PauliZ basis. Below is a table of the various change of basis operations performed implicitly by PennyLane.
Observable 
Change of basis gate \(U\) 


\(H\) 

\(H S^{1}=HSZ\) 

\(R_y(\pi/4)\) 
To see how this affects the resultant Quil program, you may use the program
property
to print out the Quil program after evaluation on the device.
dev = qml.device('rigetti.qvm', device='2qqvm')
@qml.qnode(dev)
def circuit(x):
qml.RX(x, wires=[0])
return expval(qml.PauliY(0))
>>> circuit(0.54)
0.525390625
>>> print(dev.program)
PRAGMA INITIAL_REWIRING "PARTIAL"
RX(0.54000000000000004) 0
Z 0
S 0
H 0
DECLARE ro BIT[1]
MEASURE 0 ro[0]
Note
program
will return the last evaluated quantum program performed on the device.
If viewing program
after evaluating a quantum gradient or performing an optimization,
this may not match the userdefined QNode, as PennyLane automatically modifies the QNode to take into account
the parameter shift rule, product rule, and chain rule.
Arbitrary Hermitian observables¶
Arbitrary Hermitian observables, qml.Hermitian
, are also supported by the QVM. However, since they are not necessarily unitary (and thus have eigenvalues \(\lambda_i\neq \pm 1\)), we cannot use the similarity transform approach above.
Instead, we can calculate the eigenvectors \(\mathbf{v}_i\) of \(\hat{A}\), and construct our unitary change of basis operation as follows:
After measuring the qubit state, we can determine the probability \(P_0\) of measuring state \(0\rangle\) and the probability \(P_1\) of measuring state \(1\rangle\), and, using the eigenvalues of \(\hat{A}\), recover the expectation value \(\langle\hat{A}\rangle\):
This process is done automatically behind the scenes in the QVM device when qml.expval(qml.Hermitian)
is returned.
QVM and quilc server configuration¶
Note
If using the downloadable Rigetti SDK with the default server configurations
for the QVM and the Quil compiler (i.e., you launch them with the commands
qvm S
and quilc R
), then no special configuration is needed.
If using a nondefault port or host for either of the servers, see the
pyQuil configuration documentation
for details on how to override the default values.