One of the main painpoints in executing circuits on IBM Quantum hardware is finding the best qubit mapping. For a given circuit, one typically tries to pick the best initial_layout for a given target system, and then SWAP maps using that set of qubits as the starting point. However there are a couple of issues with that execution model. First, an initial_layout selected, for example with respect to the noise characteristics of the system, need not be optimal for the SWAP mapping. In practice this leads to either low-noise layouts with extra SWAP gates inserted in the circuit, or optimally SWAP mapped circuits on (possibly) lousy qubits. Second, there is no way to know if the system you targeted in the compilation is actually the best one to execute the compiled circuit on. With 20+ quantum systems, it is hard to determine which device is actually ideal for a given problem.
mapomatic tries to tackle these issues in a different way. mapomatic is a post-compilation routine that finds the best low noise sub-graph on which to run a circuit given one or more quantum systems as target devices. Once compiled, a circuit has been rewritten so that its two-qubit gate structure matches that of a given sub-graph on the target system. mapomatic then searches for matching sub-graphs using the VF2 mapper in Qiskit (retworkx actually), and uses a heuristic to rank them based on error rates determined by the current calibration data. That is to say that given a single target system, mapomatic will return the best set of qubits on which to execute the compiled circuit. Or, given a list of systems, it will find the best system and set of qubits on which to run your circuit. Given the current size of quantum hardware, and the excellent performance of the VF2 mapper, this whole process is actually very fast.
The same algorithm used in mapomatic is integrated into the Qiskit transpiler
by default as the VF2PostLayout pass (https://qiskit.org/documentation/stubs/qiskit.transpiler.passes.VF2PostLayout.html)
which gets run by default in optimization levels 1, 2, and 3. Using mapomatic
as a standalone tool has two primary advantages, the first is to enable
running over multiple backends, and the second is to experiment with alternative
heuristic scoring (VF2PostLayout supports custom heuristic scoring, but it
is more difficult to integrate that into transpile()).
mapomatic can be installed via pip: pip install mapomatic or installed from source.
To begin we first import what we need and load our IBM Quantum account.
import numpy as np
from qiskit import *
import mapomatic as mm
IBMQ.load_account()Second we will select a provider that has one or more systems of interest in it:
provider = IBMQ.get_provider(group='deployed')We then go through the usual step of making a circuit and calling transpile on a given backend:
qc = QuantumCircuit(5)
qc.h(0)
qc.cx(0,1)
qc.cx(0,2)
qc.cx(0,3)
qc.cx(0,4)
qc.measure_all()Here we use optimization_level=3 as it is the best overall. It is also not noise-aware though, and thus can select lousy qubits on which to do a good SWAP mapping
backend = provider.get_backend('ibm_auckland')
trans_qc = transpile(qc, backend, optimization_level=3)Now, a call to transpile inflates the circuit to the number of qubits in the target system. For small problems like the example here, this prevents us from finding the smaller sub-graphs. Thus we need to deflate the circuit down to just the number of active qubits:
small_qc = mm.deflate_circuit(trans_qc)We can now find all the matching subgraphs of the target backend onto which the deflated circuit fits:
layouts = mm.matching_layouts(small_qc, backend)returning a list of possible layouts:
[[3, 2, 0, 1, 4, 7],
[7, 4, 0, 1, 2, 3],
[1, 4, 6, 7, 10, 12],
[12, 10, 6, 7, 4, 1],
[3, 5, 9, 8, 11, 14],
[14, 11, 9, 8, 5, 3],
[7, 10, 15, 12, 13, 14],
[7, 10, 13, 12, 15, 18],
[14, 13, 15, 12, 10, 7],
[14, 13, 10, 12, 15, 18],
[18, 15, 13, 12, 10, 7],
[18, 15, 10, 12, 13, 14],
[8, 11, 16, 14, 13, 12],
[8, 11, 13, 14, 16, 19],
[12, 13, 16, 14, 11, 8],
[12, 13, 11, 14, 16, 19],
[19, 16, 13, 14, 11, 8],
[19, 16, 11, 14, 13, 12],
[12, 15, 17, 18, 21, 23],
[23, 21, 17, 18, 15, 12],
[14, 16, 20, 19, 22, 25],
[25, 22, 20, 19, 16, 14],
[19, 22, 26, 25, 24, 23],
[23, 24, 26, 25, 22, 19]]We can then evaluate the "cost" of each layout, by default just the total error rate from gate and readout errors, to find a good candidate:
scores = mm.evaluate_layouts(small_qc, layouts, backend)[([3, 5, 9, 8, 11, 14], 0.1409544035570952),
([3, 2, 0, 1, 4, 7], 0.159886911767115),
([14, 11, 9, 8, 5, 3], 0.16797160130080224),
([19, 16, 13, 14, 11, 8], 0.1825119371865237),
([8, 11, 13, 14, 16, 19], 0.18331648549982482),
([7, 4, 0, 1, 2, 3], 0.19124485963881122),
([23, 24, 26, 25, 22, 19], 0.19226855309761348),
([25, 22, 20, 19, 16, 14], 0.19228399510047922),
([19, 22, 26, 25, 24, 23], 0.2000625493093675),
([14, 16, 20, 19, 22, 25], 0.20604403000055715),
([8, 11, 16, 14, 13, 12], 0.2580131332633393),
([12, 13, 16, 14, 11, 8], 0.27134706745983517),
([19, 16, 11, 14, 13, 12], 0.2755049869801992),
([12, 13, 11, 14, 16, 19], 0.2879346238104463),
([14, 13, 15, 12, 10, 7], 0.3474625243348848),
([1, 4, 6, 7, 10, 12], 0.34887580284018227),
([18, 15, 10, 12, 13, 14], 0.35020374737523874),
([7, 10, 15, 12, 13, 14], 0.35023196005467194),
([12, 10, 6, 7, 4, 1], 0.3628988750928549),
([18, 15, 13, 12, 10, 7], 0.39637978849009425),
([14, 13, 10, 12, 15, 18], 0.4063300698900274),
([23, 21, 17, 18, 15, 12], 0.41564717799937645),
([12, 15, 17, 18, 21, 23], 0.43370673744503807),
([7, 10, 13, 12, 15, 18], 0.4472384837396254)]The return layouts and costs are sorted from lowest to highest. You can then use the best layout in a new call to transpile
which will then do the desired mapping for you:
best_qc = transpile(small_qc, backend, initial_layout=scores[0][0])Alternatively, it is possible to do the same computation over multiple systems, eg all systems in the provider:
backends = provider.backends()
mm.best_overall_layout(small_qc, backends)that returns a tuple with the target layout, system name, and the computed cost:
([5, 3, 2, 1, 0, 4], 'ibm_hanoi', 0.08603879221106037)Alternatively, we can ask for the best mapping on all systems, yielding a list sorted in order from best to worse:
mm.best_overall_layout(small_qc, backends, successors=True)[([5, 3, 2, 1, 0, 4], 'ibm_hanoi', 0.08603879221106037),
([36, 51, 50, 49, 48, 55], 'ibm_washington', 0.09150102196508092),
([21, 23, 24, 25, 22, 26], 'ibm_auckland', 0.09666750964284976),
([5, 8, 11, 14, 16, 13], 'ibmq_montreal', 0.1010191806180305),
([21, 23, 24, 25, 22, 26], 'ibm_cairo', 0.10310508869235013),
([6, 5, 3, 1, 0, 2], 'ibm_lagos', 0.10806691390621592),
([16, 19, 22, 25, 24, 26], 'ibmq_mumbai', 0.11927719515976587),
([24, 25, 22, 19, 20, 16], 'ibmq_toronto', 0.13724935147063222),
([24, 29, 30, 31, 32, 39], 'ibmq_brooklyn', 0.1537915794715058),
([13, 14, 11, 8, 5, 9], 'ibmq_guadalupe', 0.1575476343119544),
([4, 5, 3, 1, 0, 2], 'ibmq_casablanca', 0.17901628434617056),
([6, 5, 3, 1, 0, 2], 'ibm_perth', 0.18024603271960626),
([4, 5, 3, 1, 2, 0], 'ibmq_jakarta', 0.1874412047495625)]Because of the stochastic nature of the SWAP mapping, the optimal sub-graph may change over repeated compilations.
Because the SWAP mappers in Qiskit are stochastic, the number of inserted SWAP gates can vary with each run. The spread in this number can be quite large, and can impact the performance of your circuit. It is thus beneficial to transpile many instances of a circuit and take the best one. For example:
trans_qc_list = transpile([qc]*20, provider.get_backend('ibm_auckland'), optimization_level=3)
best_cx_count = [circ.count_ops()['cx'] for circ in trans_qc_list]
best_cx_count[10, 6, 10, 7, 10, 11, 8, 8, 8, 10, 8, 13, 10, 7, 10, 5, 8, 10, 7, 11]We obviously want the one with minimum CNOT gates here:
best_idx = np.argmin(best_cx_count)
best_qc = trans_qc_list[best_idx]We can then use this best mapped circuit to find the ideal qubit candidates via mapomatic.
best_small_qc = mm.deflate_circuit(best_qc)
mm.best_overall_layout(best_small_qc, backends, successors=True)[([3, 2, 4, 1, 0], 'ibm_hanoi', 0.07011500213196731),
([51, 50, 48, 49, 55], 'ibm_washington', 0.07499096356285917),
([14, 11, 5, 8, 9], 'ibmq_montreal', 0.08633597995021536),
([3, 5, 11, 8, 9], 'ibm_auckland', 0.0905845988548658),
([5, 3, 0, 1, 2], 'ibm_lagos', 0.09341441561338637),
([23, 24, 22, 25, 26], 'ibm_cairo', 0.09368920161042149),
([19, 22, 24, 25, 26], 'ibmq_mumbai', 0.10338126987554686),
([25, 22, 16, 19, 20], 'ibmq_toronto', 0.12110219482337559),
([5, 3, 0, 1, 2], 'ibm_perth', 0.1283276775628739),
([14, 13, 15, 12, 10], 'ibmq_guadalupe', 0.12860835365491008),
([13, 14, 24, 15, 16], 'ibmq_brooklyn', 0.13081072372091407),
([5, 3, 0, 1, 2], 'ibmq_jakarta', 0.14268582212594894),
([5, 3, 0, 1, 2], 'ibmq_casablanca', 0.15103780612586304),
([4, 3, 0, 1, 2], 'ibmq_belem', 0.1574210243350943),
([4, 3, 0, 1, 2], 'ibmq_quito', 0.18349713324910477),
([4, 3, 0, 1, 2], 'ibmq_lima', 0.1977398974865432)]You can define a custom cost function in the following manner
def cost_func(circ, layouts, backend):
"""
A custom cost function that includes T1 and T2 computed during idle periods
Parameters:
circ (QuantumCircuit): circuit of interest
layouts (list of lists): List of specified layouts
backend (IBMQBackend): An IBM Quantum backend instance
Returns:
list: Tuples of layout and cost
"""
out = []
props = backend.properties()
dt = backend.configuration().dt
num_qubits = backend.configuration().num_qubits
t1s = [props.qubit_property(qq, 'T1')[0] for qq in range(num_qubits)]
t2s = [props.qubit_property(qq, 'T2')[0] for qq in range(num_qubits)]
for layout in layouts:
sch_circ = transpile(circ, backend, initial_layout=layout,
optimization_level=0, scheduling_method='alap')
error = 0
fid = 1
touched = set()
for item in sch_circ._data:
if item[0].name == 'cx':
q0 = sch_circ.find_bit(item[1][0]).index
q1 = sch_circ.find_bit(item[1][1]).index
fid *= (1-props.gate_error('cx', [q0, q1]))
touched.add(q0)
touched.add(q1)
elif item[0].name in ['sx', 'x']:
q0 = sch_circ.find_bit(item[1][0]).index
fid *= 1-props.gate_error(item[0].name, q0)
touched.add(q0)
elif item[0].name == 'measure':
q0 = sch_circ.find_bit(item[1][0]).index
fid *= 1-props.readout_error(q0)
touched.add(q0)
elif item[0].name == 'delay':
q0 = sch_circ.find_bit(item[1][0]).index
# Ignore delays that occur before gates
# This assumes you are in ground state and errors
# do not occur.
if q0 in touched:
time = item[0].duration * dt
fid *= 1-idle_error(time, t1s[q0], t2s[q0])
error = 1-fid
out.append((layout, error))
return out
def idle_error(time, t1, t2):
"""Compute the approx. idle error from T1 and T2
Parameters:
time (float): Delay time in sec
t1 (float): T1 time in sec
t2, (float): T2 time in sec
Returns:
float: Idle error
"""
t2 = min(t1, t2)
rate1 = 1/t1
rate2 = 1/t2
p_reset = 1-np.exp(-time*rate1)
p_z = (1-p_reset)*(1-np.exp(-time*(rate2-rate1)))/2
return p_z + p_resetYou can then pass this to the layout evaluation steps:
mm.best_overall_layout(small_qc, backends, successors=True, cost_function=cost_func)[([4, 0, 1, 2, 3], 'ibm_hanoi', 0.1058869747468042),
([0, 2, 1, 3, 5], 'ibm_lagos', 0.15241444774632107),
([0, 2, 1, 3, 5], 'ibm_perth', 0.16302150717418362),
([0, 2, 1, 3, 5], 'ibmq_casablanca', 0.18228556142682584),
([4, 0, 1, 2, 3], 'ibmq_mumbai', 0.19314785746073515),
([0, 2, 1, 3, 4], 'ibmq_quito', 0.20388545685291504),
([4, 0, 1, 2, 3], 'ibmq_montreal', 0.20954722547784943),
([0, 2, 1, 3, 4], 'ibmq_belem', 0.22163468736634484),
([5, 11, 4, 3, 2], 'ibmq_brooklyn', 0.23161086629870287),
([0, 2, 1, 3, 5], 'ibmq_jakarta', 0.23215575814258282),
([4, 0, 1, 2, 3], 'ibm_auckland', 0.2448657847182769),
([4, 0, 1, 2, 3], 'ibmq_guadalupe', 0.3104200973685135),
([0, 2, 1, 3, 4], 'ibmq_lima', 0.31936325970774426),
([5, 15, 4, 3, 2], 'ibm_washington', 0.35009793314185045),
([4, 0, 1, 2, 3], 'ibmq_toronto', 0.39020468922200047),
([4, 0, 1, 2, 3], 'ibm_cairo', 0.4133587550267118)]If you use mapomatic in your research, we would be delighted if you cite it in your work using the included BibTeX file.