# Transpiler (qiskit.transpiler)¶

## Overview¶

Transpilation is the process of rewriting a given input circuit to match the topoplogy of a specific quantum device, and/or to optimize the circuit for execution on present day noisy quantum systems.

Most circuits must undergo a series of transformations that make them compatible with a given target device, and optimize them to reduce the effects of noise on the resulting outcomes. Rewriting quantum circuits to match hardware constraints and optimizing for performance can be far from trivial. The flow of logic in the rewriting tool chain need not be linear, and can often have iterative sub-loops, conditional branches, and other complex behaviors. That being said, the basic building blocks follow the structure given below:

Qiskit has four pre-built transpilation pipelines available here: qiskit.transpiler.preset_passmanagers. Unless the reader is familiar with quantum circuit optimization methods and their usage, it is best to use one of these ready-made routines.

## Supplementary Information¶

Basis Gates

When writing a quantum circuit you are free to use any quantum gate (unitary operator) that you like, along with a collection of non-gate operations such as qubit measurements and reset operations. However, when running a circuit on a real quantum device one no longer has this flexibility. Due to limitations in, for example, the physical interactions between qubits, difficulty in implementing multi-qubit gates, control electronics etc, a quantum computing device can only natively support a handful of quantum gates and non-gate operations. In the present case of IBM Q devices, the native gate set can be found by querying the devices themselves, and looking for the corresponding attribute in their configuration:

backend.configuration().basis_gates
['id', 'u1', 'u2', 'u3', 'cx']

Every quantum circuit run on an IBM Q device must be expressed using only these basis gates. For example, suppose one wants to run a simple phase estimation circuit:

import numpy as np
from qiskit import QuantumCircuit
qc = QuantumCircuit(2, 1)

qc.h(0)
qc.x(1)
qc.cp(np.pi/4, 0, 1)
qc.h(0)
qc.measure([0], [0])
qc.draw(output='mpl')

We have $$H$$, $$X$$, and controlled-$$P$$ gates, all of which are not in our devices basis gate set, and must be expanded. This expansion is taken care of for us in the qiskit.execute() function. However, we can decompose the circuit to show what it would look like in the native gate set of the IBM Quantum devices:

qc_basis = qc.decompose()
qc_basis.draw(output='mpl')

A few things to highlight. First, the circuit has gotten longer with respect to the initial one. This can be verified by checking the depth of the circuits:

print('Original depth:', qc.depth(), 'Decomposed Depth:', qc_basis.depth())
Original depth: 4 Decomposed Depth: 7

Second, although we had a single controlled gate, the fact that it was not in the basis set means that, when expanded, it requires more than a single cx gate to implement. All said, unrolling to the basis set of gates leads to an increase in the depth of a quantum circuit and the number of gates.

It is important to highlight two special cases:

1. A SWAP gate is not a native gate on the IBM Q devices, and must be decomposed into three CNOT gates:

swap_circ = QuantumCircuit(2)
swap_circ.swap(0, 1)
swap_circ.decompose().draw(output='mpl')

As a product of three CNOT gates, SWAP gates are expensive operations to perform on a noisy quantum devices. However, such operations are usually necessary for embedding a circuit into the limited entangling gate connectivities of actual devices. Thus, minimizing the number of SWAP gates in a circuit is a primary goal in the transpilation process.

2. A Toffoli, or controlled-controlled-not gate (ccx), is a three-qubit gate. Given that our basis gate set includes only single- and two-qubit gates, it is obvious that this gate must be decomposed. This decomposition is quite costly:

ccx_circ = QuantumCircuit(3)
ccx_circ.ccx(0, 1, 2)
ccx_circ.decompose().draw(output='mpl')

For every Toffoli gate in a quantum circuit, the IBM Quantum hardware may execute up to six CNOT gates, and a handful of single-qubit gates. From this example, it should be clear that any algorithm that makes use of multiple Toffoli gates will end up as a circuit with large depth and will therefore be appreciably affected by noise and gate errors.

Initial Layout

Quantum circuits are abstract entities whose qubits are 《virtual》 representations of actual qubits used in computations. We need to be able to map these virtual qubits in a one-to-one manner to the 《physical》 qubits in an actual quantum device.

By default, qiskit will do this mapping for you. The choice of mapping depends on the properties of the circuit, the particular device you are targeting, and the optimization level that is chosen. The basic mapping strategies are the following:

• Trivial layout: Map virtual qubits to the same numbered physical qubit on the device, i.e. [0,1,2,3,4] -> [0,1,2,3,4] (default in optimization_level=0 and optimization_level=1).

• Dense layout: Find the sub-graph of the device with same number of qubits as the circuit with the greatest connectivity (default in optimization_level=2 and optimization_level=3).

The choice of initial layout is extremely important when:

1. Computing the number of SWAP operations needed to map the input circuit onto the device topology.

2. Taking into account the noise properties of the device.

The choice of initial_layout can mean the difference between getting a result, and getting nothing but noise.

Lets see what layouts are automatically picked at various optimization levels. The modified circuits returned by qiskit.compiler.transpile() have this initial layout information in them, and we can view this layout selection graphically using qiskit.visualization.plot_circuit_layout():

from qiskit import QuantumCircuit, transpile
from qiskit.visualization import plot_circuit_layout
from qiskit.test.mock import FakeVigo
backend = FakeVigo()

ghz = QuantumCircuit(3, 3)
ghz.h(0)
ghz.cx(0,range(1,3))
ghz.barrier()
ghz.measure(range(3), range(3))
ghz.draw(output='mpl')
• Layout Using Optimization Level 0

new_circ_lv0 = transpile(ghz, backend=backend, optimization_level=0)
plot_circuit_layout(new_circ_lv0, backend)

• Layout Using Optimization Level 3

new_circ_lv3 = transpile(ghz, backend=backend, optimization_level=3)
plot_circuit_layout(new_circ_lv3, backend)

It is completely possible to specify your own initial layout. To do so we can pass a list of integers to qiskit.compiler.transpile() via the initial_layout keyword argument, where the index labels the virtual qubit in the circuit and the corresponding value is the label for the physical qubit to map onto:

# Virtual -> physical
#    0    ->    3
#    1    ->    4
#    2    ->    2

my_ghz = transpile(ghz, backend, initial_layout=[3, 4, 2])
plot_circuit_layout(my_ghz, backend)

Mapping Circuits to Hardware Topology

In order to implement a CNOT gate between qubits in a quantum circuit that are not directly connected on a quantum device one or more SWAP gates must be inserted into the circuit to move the qubit states around until they are adjacent on the device gate map. Each SWAP gate is decomposed into three CNOT gates on the IBM Quantum devices, and represents an expensive and noisy operation to perform. Thus, finding the minimum number of SWAP gates needed to map a circuit onto a given device, is an important step (if not the most important) in the whole execution process.

However, as with many important things in life, finding the optimal SWAP mapping is hard. In fact it is in a class of problems called NP-Hard, and is thus prohibitively expensive to compute for all but the smallest quantum devices and input circuits. To get around this, by default Qiskit uses a stochastic heuristic algorithm called Qiskit.transpiler.passes.StochasticSwap to compute a good, but not necessarily minimal SWAP count. The use of a stochastic method means the circuits generated by Qiskit.compiler.transpile() (or Qiskit.execute() that calls transpile internally) are not guaranteed to be the same over repeated runs. Indeed, running the same circuit repeatedly will in general result in a distribution of circuit depths and gate counts at the output.

In order to highlight this, we run a GHZ circuit 100 times, using a 《bad》 (disconnected) initial_layout:

import matplotlib.pyplot as plt
from qiskit import QuantumCircuit, transpile
from qiskit.test.mock import FakeBoeblingen
backend = FakeBoeblingen()

ghz = QuantumCircuit(5)
ghz.h(0)
ghz.cx(0,range(1,5))
ghz.draw(output='mpl')
depths = []
for _ in range(100):
depths.append(transpile(ghz,
backend,
initial_layout=[7, 0, 4, 15, 19],
).depth())

plt.figure(figsize=(8, 6))
plt.hist(depths, bins=list(range(14,36)), align='left', color='#AC557C')
plt.xlabel('Depth', fontsize=14)
plt.ylabel('Counts', fontsize=14);

This distribution is quite wide, signaling the difficultly the SWAP mapper is having in computing the best mapping. Most circuits will have a distribution of depths, perhaps not as wide as this one, due to the stochastic nature of the default SWAP mapper. Of course, we want the best circuit we can get, especially in cases where the depth is critical to success or failure. In cases like this, it is best to transpile() a circuit several times, e.g. 10, and take the one with the lowest depth. The transpile() function will automatically run in parallel mode, making this procedure relatively speedy in most cases.

Gate Optimization

Decomposing quantum circuits into the basis gate set of the IBM Quantum devices, and the addition of SWAP gates needed to match hardware topology, conspire to increase the depth and gate count of quantum circuits. Fortunately many routines for optimizing circuits by combining or eliminating gates exist. In some cases these methods are so effective the output circuits have lower depth than the inputs. In other cases, not much can be done, and the computation may be difficult to perform on noisy devices. Different gate optimizations are turned on with different optimization_level values. Below we show the benefits gained from setting the optimization level higher:

중요

The output from transpile() varies due to the stochastic swap mapper. So the numbers below will likely change each time you run the code.

import matplotlib.pyplot as plt
from qiskit import QuantumCircuit, transpile
from qiskit.test.mock import FakeBoeblingen
backend = FakeBoeblingen()

ghz = QuantumCircuit(5)
ghz.h(0)
ghz.cx(0,range(1,5))
ghz.draw(output='mpl')
for kk in range(4):
circ = transpile(ghz, backend, optimization_level=kk)
print('Optimization Level {}'.format(kk))
print('Depth:', circ.depth())
print('Gate counts:', circ.count_ops())
print()
Optimization Level 0
Depth: 14
Gate counts: OrderedDict([('cx', 13), ('u2', 1)])

Optimization Level 1
Depth: 11
Gate counts: OrderedDict([('cx', 13), ('u2', 1)])

Optimization Level 2
Depth: 11
Gate counts: OrderedDict([('cx', 13), ('u2', 1)])

Optimization Level 3
Depth: 11
Gate counts: OrderedDict([('u2', 11), ('cx', 9)])

## Transpiler API¶

### Pass Manager Construction¶

 PassManager([passes, max_iteration, callback]) Manager for a set of Passes and their scheduling during transpilation. PassManagerConfig([initial_layout, …]) Pass Manager Configuration. PropertySet A default dictionary-like object FlowController(passes, options, …) Base class for multiple types of working list.

### Layout and Topology¶

 Layout([input_dict]) Two-ways dict to represent a Layout. CouplingMap([couplinglist, description]) Directed graph specifying fixed coupling.

### Scheduling¶

 InstructionDurations([instruction_durations, dt]) Helper class to provide durations of instructions for scheduling.

### Fenced Objects¶

 FencedDAGCircuit(dag_circuit_instance) A dag circuit that cannot be modified (via remove_op_node) FencedPropertySet(property_set_instance) A property set that cannot be written (via __setitem__)

### Exceptions¶

 TranspilerError(*message) Exceptions raised during transpilation. TranspilerAccessError(*message) DEPRECATED: Exception of access error in the transpiler passes.