Update QV test for Qiskit 1.1 (#1443)

### Summary

This PR updates the stored probabilities in
`test_qv_ideal_probabilities` after the randomization update in
Qiskit/qiskit#12097.

test/library/quantum_volume/qv_ideal_probabilities_qiskit_1_1.json

@@ -0,0 +1 @@
+[[0.02110822695364887, 0.013936320980929177, 0.06762829067477494, 0.05640378028262168, 0.019434855941263804, 0.01254494041140876, 0.3597504343657043, 0.44919315038964813], [0.1722976165549457, 0.029841680707019494, 0.015656642181112637, 0.22730547539691617, 0.12732050329410488, 0.06013320751345239, 0.23738660274412582, 0.13005827160832278], [0.025330413591789218, 0.05365793634629424, 0.005510054610574176, 0.2659480366696103, 0.06644689405510834, 0.16522547308232338, 0.06550526962201847, 0.35237592202228174], [0.03752531358760119, 0.0639087743319445, 0.05174568892966019, 0.026258899708790133, 0.06025270407432933, 0.4752249297421205, 0.17263176026475763, 0.11245192936079637], [0.31320609444467884, 0.0064025098682649, 0.2454242441765262, 0.11834874135446874, 0.1410876641286843, 0.016731059242565263, 0.09755353034344483, 0.06124615644136609], [0.019448190781865507, 0.05499334515101417, 0.13640962401919648, 0.027348070327303475, 0.048411270171909986, 0.16728339683880306, 0.3206808043538741, 0.225425298356034], [0.00960924565105907, 0.5136650426998607, 0.0011415111620172156, 0.020066510917153436, 0.0010864777624874085, 0.12088859340271874, 0.003926145584809557, 0.32961647281989354], [0.0033843151967825605, 0.0904375862783492, 0.14082024165587934, 0.028700581811163736, 0.5206374518621331, 0.1449007040623369, 0.020747488106116044, 0.050371631027239266], [0.02953881873020507, 0.16412229218641006, 0.0044071010350494825, 0.2837594965902758, 0.015330305509777008, 0.10239055990425917, 0.02799467182995681, 0.37245675421406627], [0.1322823017311934, 0.4458209485696668, 0.0, 0.0, 0.048864936086664826, 0.3730318136124744, 0.0, 0.0], [0.08168205214501269, 0.014301663582061402, 0.031796449397294785, 0.030646878482070747, 0.03347798878280955, 0.30568913585068463, 0.48978086811193544, 0.012624963648130906], [0.10270572333629126, 0.2054021653045906, 0.3214150326296182, 0.06540473121561362, 0.030757362188421174, 0.2211717639672315, 0.04658693468342603, 0.006556286674807662], [0.15936994988625908, 0.10431864042664502, 0.08299765915752665, 0.02804542799741586, 0.06960987222202304, 0.15337460586250898, 0.0958361933378381, 0.3064476511097831], [0.004950387743443303, 0.036932489074513596, 0.03652458327201384, 0.2650570018042196, 0.009291507543548598, 0.10388620362313436, 0.1691098123043206, 0.37424801463480634], [0.05972657537009159, 0.19914118274809703, 0.08779406969022188, 0.25663496507647837, 0.12477975035159891, 0.1996292453671398, 0.012677912029188738, 0.059616299367184024], [0.4809352140937508, 0.1984839027335819, 0.08741344211264122, 0.01856979807616571, 0.020353167602611928, 0.06987732405489348, 0.02366752222163191, 0.10069962910472299], [0.08304167605222394, 0.04112711434346582, 0.06461187209953644, 0.29581303509821427, 0.1801493690994243, 0.15019357344113535, 0.03342178624142832, 0.1516415736245708], [0.11034335151398833, 0.1535142244794561, 0.010924645942967047, 0.1595660489816288, 0.012260755380658836, 0.2373347471191917, 0.25694446799872295, 0.05911175858338647], [0.144941751473959, 0.009237621811653846, 0.016193183621015943, 0.015626036290447263, 0.07939130818210129, 0.1282415772050653, 0.522578062681002, 0.08379045873475498], [0.12323459136182116, 0.04647043553049166, 0.36115923872923944, 0.06606545697235076, 0.14875149834994203, 0.016170939689423118, 0.22211811256352207, 0.01602972680320908]]

test/library/quantum_volume/test_qv.py

@@ -25,6 +25,7 @@
 from qiskit_experiments.framework import ExperimentData
 from qiskit_experiments.library import QuantumVolume
 from qiskit_experiments.framework import ExperimentDecoder
+from qiskit_experiments.framework.package_deps import version_is_at_least
 
 SEED = 42
 
@@ -88,7 +89,10 @@ def test_qv_ideal_probabilities(self):
         )
         # compare to pre-calculated probabilities
         dir_name = os.path.dirname(os.path.abspath(__file__))
-        probabilities_json_file = "qv_ideal_probabilities.json"
+        if version_is_at_least("qiskit", 1.1):
+            probabilities_json_file = "qv_ideal_probabilities_qiskit_1_1.json"
+        else:
+            probabilities_json_file = "qv_ideal_probabilities.json"
         with open(
             os.path.join(dir_name, probabilities_json_file), "r", encoding="utf-8"
         ) as json_file: