MEASURED DATA (9 runs: ibm_fez 371, ibm_kingston 392/721/722/723, ibm_boston 441/711/712/713; mean of runs): own -0.00136 r90 -0.00138 r300 -0.00101 | below-extrap share 0.79 mean R30 0.846 R90 0.644 run 371 ibm_fez own -0.00182 r90 -0.00231 r300 -0.00247 run 392 ibm_kingston own -0.00198 r90 -0.00178 r300 -0.00104 run 441 ibm_boston own -0.00139 r90 -0.00148 r300 -0.00139 run 711 ibm_boston own -0.00154 r90 -0.00127 r300 -0.00120 run 712 ibm_boston own -0.00080 r90 -0.00074 r300 -0.00056 run 713 ibm_boston own -0.00063 r90 -0.00048 r300 -0.00024 run 721 ibm_kingston own -0.00114 r90 -0.00125 r300 -0.00059 run 722 ibm_kingston own -0.00134 r90 -0.00158 r300 -0.00082 run 723 ibm_kingston own -0.00161 r90 -0.00152 r300 -0.00077 (note: mean over runs of single-run slopes) SYNTHETIC: PERFECT X gates (zero cost). 300 noise seeds per row; noise = real per-qubit shot errors; anchor = each qubit's R300. Slope is mean over the 9 runs; "seed sd" is the sd of that 9-run mean over seeds. (a) single exponential exp own +0.00018 (seed sd 0.00009) r90 +0.00005 r300 +0.00002 | below-extrap share 0.50 mean R30 0.874 R90 0.673 (b) T1 mixture: rate varies shot-to-shot (lognormal sigma), persists through a whole circuit mixture sigma=0.3 own -0.00081 (seed sd 0.00009) r90 -0.00084 r300 -0.00055 | below-extrap share 0.66 mean R30 0.866 R90 0.662 mixture sigma=0.6 own -0.00347 (seed sd 0.00009) r90 -0.00333 r300 -0.00227 | below-extrap share 0.93 mean R30 0.843 R90 0.630 mixture sigma=0.9 own -0.00679 (seed sd 0.00009) r90 -0.00673 r300 -0.00486 | below-extrap share 1.00 mean R30 0.805 R90 0.590 mixture sigma=1.2 own -0.00956 (seed sd 0.00008) r90 -0.01018 r300 -0.00777 | below-extrap share 1.00 mean R30 0.760 R90 0.551 mixture sigma=1.5 own -0.01127 (seed sd 0.00008) r90 -0.01319 r300 -0.01054 | below-extrap share 1.00 mean R30 0.713 R90 0.517 mixture sigma=2.0 own -0.01224 (seed sd 0.00009) r90 -0.01705 r300 -0.01438 | below-extrap share 1.00 mean R30 0.643 R90 0.474 (b2) T1 drifts circuit-to-circuit (every circuit has its own T1), exponential otherwise drift per circuit sigma=0.1 own +0.00018 (seed sd 0.00012) r90 +0.00005 r300 +0.00001 | below-extrap share 0.50 mean R30 0.874 R90 0.674 drift per circuit sigma=0.3 own +0.00018 (seed sd 0.00026) r90 +0.00004 r300 -0.00004 | below-extrap share 0.50 mean R30 0.875 R90 0.678 drift per circuit sigma=0.6 own +0.00019 (seed sd 0.00049) r90 +0.00002 r300 -0.00021 | below-extrap share 0.50 mean R30 0.878 R90 0.694 (c) stretched exponential, hazard keyed to time since circuit start (abs0) / since first X (abs30) / restarted at each X (renew) stretch beta=0.8 clock=abs0 own -0.00749 (seed sd 0.00008) r90 -0.00649 r300 -0.00435 | below-extrap share 1.00 mean R30 0.809 R90 0.607 stretch beta=0.9 clock=abs0 own -0.00411 (seed sd 0.00009) r90 -0.00330 r300 -0.00214 | below-extrap share 0.97 mean R30 0.844 R90 0.641 stretch beta=1.0 clock=abs0 own +0.00018 (seed sd 0.00009) r90 +0.00005 r300 +0.00002 | below-extrap share 0.50 mean R30 0.874 R90 0.673 stretch beta=1.2 clock=abs0 own +0.01019 (seed sd 0.00011) r90 +0.00700 r300 +0.00407 | below-extrap share 0.00 mean R30 0.918 R90 0.731 stretch beta=1.4 clock=abs0 own +0.02032 (seed sd 0.00013) r90 +0.01392 r300 +0.00770 | below-extrap share 0.00 mean R30 0.947 R90 0.781 stretch beta=0.8 clock=abs30 own -0.01049 (seed sd 0.00008) r90 -0.00949 r300 -0.00735 | below-extrap share 1.00 mean R30 0.809 R90 0.607 stretch beta=0.9 clock=abs30 own -0.00534 (seed sd 0.00009) r90 -0.00454 r300 -0.00337 | below-extrap share 0.97 mean R30 0.844 R90 0.641 stretch beta=1.0 clock=abs30 own +0.00018 (seed sd 0.00009) r90 +0.00005 r300 +0.00002 | below-extrap share 0.50 mean R30 0.874 R90 0.673 stretch beta=1.2 clock=abs30 own +0.01137 (seed sd 0.00011) r90 +0.00818 r300 +0.00525 | below-extrap share 0.00 mean R30 0.918 R90 0.731 stretch beta=1.4 clock=abs30 own +0.02147 (seed sd 0.00013) r90 +0.01507 r300 +0.00885 | below-extrap share 0.00 mean R30 0.947 R90 0.781 stretch beta=0.8 clock=renew own +0.00010 (seed sd 0.00008) r90 +0.00111 r300 +0.00324 | below-extrap share 1.00 mean R30 0.809 R90 0.607 stretch beta=0.9 clock=renew own +0.00014 (seed sd 0.00009) r90 +0.00095 r300 +0.00211 | below-extrap share 0.97 mean R30 0.844 R90 0.641 stretch beta=1.0 clock=renew own +0.00018 (seed sd 0.00009) r90 +0.00005 r300 +0.00002 | below-extrap share 0.50 mean R30 0.874 R90 0.673 stretch beta=1.2 clock=renew own +0.00025 (seed sd 0.00011) r90 -0.00294 r300 -0.00587 | below-extrap share 0.00 mean R30 0.918 R90 0.731 stretch beta=1.4 clock=renew own +0.00032 (seed sd 0.00013) r90 -0.00608 r300 -0.01230 | below-extrap share 0.00 mean R30 0.947 R90 0.781 (c2) stretched with each qubit's OWN measured beta (3-point fit of ln(-ln R) vs ln t, clipped 0.8-1.4) stretch per-qubit beta clock=abs0 own -0.00201 (seed sd 0.00009) r90 -0.00191 r300 -0.00148 | below-extrap share 0.75 mean R30 0.852 R90 0.652 stretch per-qubit beta clock=abs30 own -0.00314 (seed sd 0.00009) r90 -0.00304 r300 -0.00261 | below-extrap share 0.75 mean R30 0.852 R90 0.652 stretch per-qubit beta clock=renew own +0.00015 (seed sd 0.00009) r90 +0.00025 r300 +0.00068 | below-extrap share 0.75 mean R30 0.852 R90 0.652 (d) timing: finite X-gate duration (each excited segment is 30+g us, reference waits are 30), exponential and mixture decay exp, gate g=0.035 us own +0.00019 (seed sd 0.00009) r90 +0.00006 r300 +0.00003 | below-extrap share 0.50 mean R30 0.874 R90 0.673 exp, gate g=0.100 us own +0.00021 (seed sd 0.00009) r90 +0.00009 r300 +0.00005 | below-extrap share 0.50 mean R30 0.874 R90 0.673 exp, gate g=0.500 us own +0.00035 (seed sd 0.00009) r90 +0.00023 r300 +0.00019 | below-extrap share 0.50 mean R30 0.874 R90 0.673 exp, gate g=1.000 us own +0.00052 (seed sd 0.00009) r90 +0.00040 r300 +0.00036 | below-extrap share 0.50 mean R30 0.874 R90 0.673 mixture sigma=1.2, gate g=0.035 us own -0.00956 (seed sd 0.00008) r90 -0.01018 r300 -0.00777 | below-extrap share 1.00 mean R30 0.760 R90 0.551 mixture sigma=1.2, gate g=0.100 us own -0.00956 (seed sd 0.00008) r90 -0.01017 r300 -0.00777 | below-extrap share 1.00 mean R30 0.760 R90 0.551 NOISE-FREE (infinite shots, exact expectations; slope of the estimator on the true curves; exp baseline must be 0): exp own +0.00000 r90 +0.00000 r300 -0.00000 mixture sigma=0.4 own -0.00171 r90 -0.00157 r300 -0.00102 mixture sigma=0.5 own -0.00260 r90 -0.00241 r300 -0.00159 mixture sigma=1.2 own -0.00964 r90 -0.01022 r300 -0.00779 CONTROL mixture re-drawn every wait sigma=0.5 own +0.00000 r90 +0.00020 r300 +0.00101 CONTROL mixture re-drawn every wait sigma=1.2 own +0.00000 r90 -0.00059 r300 +0.00185 stretch beta=0.9 renew own +0.00000 r90 +0.00090 r300 +0.00209 stretch beta=0.9 abs0 own -0.00424 r90 -0.00335 r300 -0.00215 exp gate g=0.035 own +0.00001 r90 +0.00001 r300 +0.00001 exp gate g=0.1 own +0.00004 r90 +0.00004 r300 +0.00004 PER-QUBIT own-interval slope, binned by non-exponentiality d = R300^(1/10) - R30 (9 runs pooled). cells: n qubits, mean slope bins of d: [-inf,-0.03) [-0.03,0.00) [0.00,0.03) [0.03,0.06) [0.06,0.10) [0.10,inf) MEASURED 6:+0.0067 279:+0.0015 666:-0.0013 226:-0.0028 80:-0.0040 70:-0.0062 synthetic exp (perfect X) 1390:+0.0029 25289:+0.0012 25091:-0.0009 1293:-0.0013 17:+0.0011 0:+nan synthetic mixture sigma=0.43 92:+0.0036 11041:+0.0001 32454:-0.0023 7564:-0.0029 1691:-0.0008 238:+0.0004 MIXTURE (T1 varies shot to shot, sigma = lognormal width of the rate) -- parameter matched PER RUN so the synthetic share below the 300-us extrapolation equals that run's real share: run chip param | real share | real slope own/r90/r300 | model slope own/r90/r300 | mean N2,N6,N10 real vs model 371 ibm_fez 0.428 | 0.92 | -0.00182 -0.00231 -0.00247 | -0.00203 -0.00221 -0.00227 | real 0.2354 0.4307 0.5024 model 0.2156 0.4078 0.4840 392 ibm_kingston 0.502 | 0.85 | -0.00198 -0.00178 -0.00104 | -0.00251 -0.00235 -0.00147 | real 0.1612 0.3249 0.4073 model 0.1426 0.3014 0.3851 441 ibm_boston 0.383 | 0.74 | -0.00139 -0.00148 -0.00139 | -0.00137 -0.00131 -0.00081 | real 0.1501 0.3019 0.3889 model 0.1305 0.2864 0.3738 711 ibm_boston 0.389 | 0.74 | -0.00154 -0.00127 -0.00120 | -0.00145 -0.00139 -0.00084 | real 0.1471 0.2989 0.3883 model 0.1304 0.2867 0.3744 712 ibm_boston 0.333 | 0.68 | -0.00080 -0.00074 -0.00056 | -0.00101 -0.00101 -0.00059 | real 0.1370 0.2904 0.3803 model 0.1224 0.2761 0.3656 713 ibm_boston 0.404 | 0.76 | -0.00063 -0.00048 -0.00024 | -0.00155 -0.00149 -0.00087 | real 0.1388 0.2932 0.3860 model 0.1283 0.2829 0.3704 721 ibm_kingston 0.421 | 0.77 | -0.00114 -0.00125 -0.00059 | -0.00175 -0.00166 -0.00100 | real 0.1487 0.3102 0.3947 model 0.1316 0.2880 0.3745 722 ibm_kingston 0.457 | 0.80 | -0.00134 -0.00158 -0.00082 | -0.00201 -0.00192 -0.00115 | real 0.1539 0.3140 0.3994 model 0.1362 0.2937 0.3787 723 ibm_kingston 0.486 | 0.83 | -0.00161 -0.00152 -0.00077 | -0.00226 -0.00216 -0.00135 | real 0.1534 0.3137 0.3974 model 0.1381 0.2935 0.3773 MEAN of 9 runs: real own -0.00136 r90 -0.00138 r300 -0.00101 model own -0.00177 r90 -0.00172 r300 -0.00115 (model/real own = 1.30) STRETCHED, clock since circuit start (beta<1 side only) -- parameter matched PER RUN so the synthetic share below the 300-us extrapolation equals that run's real share: run chip param | real share | real slope own/r90/r300 | model slope own/r90/r300 | mean N2,N6,N10 real vs model 371 ibm_fez 0.933 | 0.92 | -0.00182 -0.00231 -0.00247 | -0.00195 -0.00202 -0.00189 | real 0.2354 0.4307 0.5024 model 0.1955 0.3855 0.4670 392 ibm_kingston 0.939 | 0.85 | -0.00198 -0.00178 -0.00104 | -0.00255 -0.00203 -0.00126 | real 0.1612 0.3249 0.4073 model 0.1289 0.2849 0.3732 441 ibm_boston 0.965 | 0.74 | -0.00139 -0.00148 -0.00139 | -0.00148 -0.00115 -0.00070 | real 0.1501 0.3019 0.3889 model 0.1229 0.2770 0.3671 711 ibm_boston 0.965 | 0.74 | -0.00154 -0.00127 -0.00120 | -0.00153 -0.00120 -0.00074 | real 0.1471 0.2989 0.3883 model 0.1226 0.2771 0.3676 712 ibm_boston 0.974 | 0.68 | -0.00080 -0.00074 -0.00056 | -0.00103 -0.00079 -0.00046 | real 0.1370 0.2904 0.3803 model 0.1172 0.2695 0.3610 713 ibm_boston 0.962 | 0.76 | -0.00063 -0.00048 -0.00024 | -0.00161 -0.00124 -0.00073 | real 0.1388 0.2932 0.3860 model 0.1203 0.2729 0.3633 721 ibm_kingston 0.958 | 0.77 | -0.00114 -0.00125 -0.00059 | -0.00177 -0.00137 -0.00084 | real 0.1487 0.3102 0.3947 model 0.1227 0.2769 0.3666 722 ibm_kingston 0.949 | 0.80 | -0.00134 -0.00158 -0.00082 | -0.00212 -0.00166 -0.00102 | real 0.1539 0.3140 0.3994 model 0.1254 0.2803 0.3692 723 ibm_kingston 0.945 | 0.83 | -0.00161 -0.00152 -0.00077 | -0.00234 -0.00183 -0.00113 | real 0.1534 0.3137 0.3974 model 0.1255 0.2784 0.3665 MEAN of 9 runs: real own -0.00136 r90 -0.00138 r300 -0.00101 model own -0.00182 r90 -0.00148 r300 -0.00098 (model/real own = 1.34) STRETCHED, clock restarted at each X (physically: each flip re-excites) -- parameter matched PER RUN so the synthetic share below the 300-us extrapolation equals that run's real share: run chip param | real share | real slope own/r90/r300 | model slope own/r90/r300 | mean N2,N6,N10 real vs model 371 ibm_fez 0.933 | 0.92 | -0.00182 -0.00231 -0.00247 | +0.00009 +0.00002 +0.00015 | real 0.2354 0.4307 0.5024 model 0.2127 0.4201 0.5006 392 ibm_kingston 0.939 | 0.85 | -0.00198 -0.00178 -0.00104 | +0.00016 +0.00068 +0.00144 | real 0.1612 0.3249 0.4073 model 0.1396 0.3121 0.4055 441 ibm_boston 0.965 | 0.74 | -0.00139 -0.00148 -0.00139 | +0.00014 +0.00046 +0.00091 | real 0.1501 0.3019 0.3889 model 0.1286 0.2921 0.3857 711 ibm_boston 0.965 | 0.74 | -0.00154 -0.00127 -0.00120 | +0.00012 +0.00045 +0.00091 | real 0.1471 0.2989 0.3883 model 0.1284 0.2925 0.3866 712 ibm_boston 0.974 | 0.68 | -0.00080 -0.00074 -0.00056 | +0.00018 +0.00042 +0.00075 | real 0.1370 0.2904 0.3803 model 0.1212 0.2803 0.3746 713 ibm_boston 0.962 | 0.76 | -0.00063 -0.00048 -0.00024 | +0.00015 +0.00053 +0.00104 | real 0.1388 0.2932 0.3860 model 0.1263 0.2891 0.3835 721 ibm_kingston 0.958 | 0.77 | -0.00114 -0.00125 -0.00059 | +0.00017 +0.00057 +0.00110 | real 0.1487 0.3102 0.3947 model 0.1297 0.2953 0.3891 722 ibm_kingston 0.949 | 0.80 | -0.00134 -0.00158 -0.00082 | +0.00016 +0.00062 +0.00126 | real 0.1539 0.3140 0.3994 model 0.1340 0.3026 0.3960 723 ibm_kingston 0.945 | 0.83 | -0.00161 -0.00152 -0.00077 | +0.00016 +0.00066 +0.00136 | real 0.1534 0.3137 0.3974 model 0.1348 0.3026 0.3957 MEAN of 9 runs: real own -0.00136 r90 -0.00138 r300 -0.00101 model own +0.00015 r90 +0.00049 r300 +0.00099 (model/real own = -0.11) CONTROL: mixture re-drawn at every wait -- parameter matched PER RUN so the synthetic share below the 300-us extrapolation equals that run's real share: run chip param | real share | real slope own/r90/r300 | model slope own/r90/r300 | mean N2,N6,N10 real vs model 371 ibm_fez 0.428 | 0.92 | -0.00182 -0.00231 -0.00247 | +0.00011 -0.00007 -0.00013 | real 0.2354 0.4307 0.5024 model 0.2156 0.4217 0.5011 392 ibm_kingston 0.502 | 0.85 | -0.00198 -0.00178 -0.00104 | +0.00015 +0.00031 +0.00119 | real 0.1612 0.3249 0.4073 model 0.1426 0.3145 0.4063 441 ibm_boston 0.383 | 0.74 | -0.00139 -0.00148 -0.00139 | +0.00017 +0.00023 +0.00073 | real 0.1501 0.3019 0.3889 model 0.1305 0.2934 0.3861 711 ibm_boston 0.389 | 0.74 | -0.00154 -0.00127 -0.00120 | +0.00015 +0.00021 +0.00076 | real 0.1471 0.2989 0.3883 model 0.1304 0.2939 0.3872 712 ibm_boston 0.333 | 0.68 | -0.00080 -0.00074 -0.00056 | +0.00014 +0.00015 +0.00057 | real 0.1370 0.2904 0.3803 model 0.1224 0.2811 0.3748 713 ibm_boston 0.404 | 0.76 | -0.00063 -0.00048 -0.00024 | +0.00015 +0.00021 +0.00083 | real 0.1388 0.2932 0.3860 model 0.1283 0.2905 0.3840 721 ibm_kingston 0.421 | 0.77 | -0.00114 -0.00125 -0.00059 | +0.00013 +0.00022 +0.00088 | real 0.1487 0.3102 0.3947 model 0.1316 0.2967 0.3895 722 ibm_kingston 0.457 | 0.80 | -0.00134 -0.00158 -0.00082 | +0.00020 +0.00029 +0.00106 | real 0.1539 0.3140 0.3994 model 0.1362 0.3043 0.3964 723 ibm_kingston 0.486 | 0.83 | -0.00161 -0.00152 -0.00077 | +0.00017 +0.00027 +0.00108 | real 0.1534 0.3137 0.3974 model 0.1381 0.3051 0.3967 MEAN of 9 runs: real own -0.00136 r90 -0.00138 r300 -0.00101 model own +0.00015 r90 +0.00020 r300 +0.00077 (model/real own = -0.11)