About Quantum Computers

0d0770ac-5f3c-4066-9481-5713802b0e75 148 8 12 decimal

&[DATE] &[TIME] - &[FILENAME]

... GR-50-AA ... Ge Ω °K 35000 0.05 2320 0.1 364.6 0.2 164 0.3 73.75 0.5 33.55 1 24.73 1.4 19.32 2 13.66 4.2 102 mat :

Germanium RTD

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°C 1 :

https://www.lakeshore.com/Documents/LSTC_Germanium_l.pdf Lake Shore germanium resistance temperature sensors are recognized as “Secondary Standard Thermometers” and have been employed in the measurement of temperature from 0.05 K to 30 K for more than 40 years.

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

Ge Ge 210 range 12 range el :

About Quantum Computers

Quantum computing requires extremely cold temperatures, as sub-atomic particles must be as close as

possible to a stationary state to be measured. The cores of D-Wave quantum computers operate at -273 °C,

which is 0.02 °C away from absolute zero.Feb 23, 2018

Reduction of the temperature of the computing environment below approximately 80mK is required for

the processor to function, and generally performance increases as temperature is lowered -

the lower the temperature, the better. The latest generation D-Wave 2000Q system has an operating

temperture of about 15 millikelvin. The QPU and parts of the input/output (I/O) system, comprising

roughly 10kg of material, is cooled to this temperature, which is approximately 180 times colder than

interstellar space! Most of the physical volume of the current system is due to the large size of the

refrigeration system. The refrigeration system used to cool the processors is known as a

dilution refrigerator.

To reach the near-absolute zero temperatures at which the system operates, the refrigerators use liquid

helium as a coolant. The type of refrigerator inside the D-Wave system is known as a "dry" dilution

refrigerator. This means that all the liquid helium resides inside a closed cycle system, where it is

recycled and recondensed using a pulse-tube technology. This makes them suited to remote deployment,

as there is no requirement for liquid helium replenishment on-site.

The specialized equipment to allow cooling to these temperatures is available commercially and runs

reliably. The refrigeration technology is also mature enough that the system has a turnkey operation.

The computer can be cooled down to operating temperature within several hours, and once this temperature

is reached remain cold for months or years.

]]> Genfit Utilities

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

Error stem plot for QuickPlot unicolor data Error stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 line :

L H N xd U 0 : dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 41 line :

Module xd(L,H,N) is a discretiser for use in-situ [user spec's]: range [L,H], density [N].

Applicable parts are: Optimiz "numeric" XY f φ β Minimize X XY 1 col : Y XY 2 col : n XY rows : k x β φ length 1 - : vx-> raw initial vector fit i 1 X length range vx i el X i el β f eval : for M-> Cholesky GradientMatrix j 1 k range i 1 n range M i j el X i el β φ j 1 + el eval : for for CholeskySolver LeastSquares Φ M transpose M * : d M transpose Y vx - (* : Δβ Φ 1 -^eval d * : b β Δβ + : 131 line :

Vector gradient ... Optimiz Symbolic x β f n φ ct 1 : i 1 n range PD ct el x β f (β ct el diff : stack f(x,β) & PD V 1 el x β f : V i 1 + el PD i el : 21 line ct ct 1 + : 41 line for V 31 line :

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

Genfit Germanium

x α f α 1 el α 2 el x 1.125^/ + α 3 el x 2.25^/ + α 4 el x 3.375^/ + α 5 el x 1^/ + α 6 el x 0.5^/ + α 7 el x 0.25^/ + α 8 el x 0.125^/ + :

<= ConjugateGradient Vector Fnct x α φ x α f 8 φ :

X Ge 1 col : Y Ge 2 col : 12 mat XY X Y augment : data Ge o 7 black plot : n Ge rows : x c 1 13.66 x ≤ (x 35000 ≤ (& cases : 51 sys

α α 1 el 1111111118 mat transpose : iter 9 : i 1 : i iter ≤ α i 1 + el XY f φ α i el Minimize : i i 1 + : 21 line while α α iter el : 51 line :

assign to isolate α α :

α α 4 round vectorize : 3.844 - 2401.821 5401.639 - 52172.807 1901.257 - 172.7 82.887 - 33.532 81 mat

Conformity from absolute residuals δ i 1 Ge rows range Δ i el Y i el X i el α f - 3 round eval : for Ge X Y Δ augment : Header Ω °K Δ°K 13 mat : Header Ge stack 41 line :

Observe . . . @ 4.2 °K, switch to

GR-300-AA . . . Pt100 subcryo .

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Observe . . .

Thiele extrapolates both ends... Data set rectified

below to escape glitch [24.71 ... 19.34]

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Quick linfit GR-50-AA ... a most remarkable fit ± 0.001°K

data x α f x c * 2 1 sys

δ Ω °K Δ°K 35000 0.05 02320 0.1 0 364.6 0.2 0164 0.3 0.001 73.75 0.5 0.001 - 33.55 1 0.001 24.73 1.4 0.001 - 19.32 20 13.66 4.2 0103 mat

X i el α f 4 round

Genfit Utilities

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

Error stem plot for QuickPlot unicolor data Error stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 line :

L H N xd U 0 : dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 41 line :

Module xd(L,H,N) is a discretiser for use in-situ [user spec's]: range [L,H], density [N].

Applicable parts are: Optimiz "numeric" XY f φ β Minimize X XY 1 col : Y XY 2 col : n XY rows : k x β φ length 1 - : vx-> raw initial vector fit i 1 X length range vx i el X i el β f eval : for M-> Cholesky GradientMatrix j 1 k range i 1 n range M i j el X i el β φ j 1 + el eval : for for CholeskySolver LeastSquares Φ M transpose M * : d M transpose Y vx - (* : Δβ Φ 1 -^eval d * : b β Δβ + : 131 line :

Vector gradient ... Optimiz Symbolic x β f n φ ct 1 : i 1 n range PD ct el x β f (β ct el diff : stack f(x,β) & PD V 1 el x β f : V i 1 + el PD i el : 21 line ct ct 1 + : 41 line for V 31 line :

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

Genfit Germanium

x β f β 1 el β 2 el x 1.125^/ + β 3 el x 2.25^/ + β 4 el x 3.375^/ + β 5 el x 1^/ + β 6 el x 0.5^/ + β 7 el x 0.25^/ + β 8 el x 0.125^/ + β 9 el x 0.0625^/ + β 10 el x 0.03125^/ + :

<= ConjugateGradient Vector Fnct x β φ x β f 10 φ :

.. GR-300-AA .. Ge Ω °K 35180 0.3 5443 0.5 875.7 1 448.6 1.4 248.8 2 94.46 4.2 33.2 10 7.79 40 3.5 77.4 2.72 100112 mat :

Ge Ge 211 range 12 range el : X Ge 1 col : Y Ge 2 col : 12 mat XY X Y augment : data Ge o 7 black plot : n Ge rows : x c 1 2.72 x ≤ (x 35000 ≤ (& cases : 61 sys

β β 1 el 1111111111110 mat transpose : iter 9 : i 1 : i iter ≤ β i 1 + el XY f φ β i el Minimize : i i 1 + : 21 line while β β iter el : 51 line :

assign to isolate β β :

β β 4 round vectorize : 21757.055 - 21745.606 6122.318 - 5997.393 22769.638 - 9717.895 23136 - 64140.236 1.206 105^* - 95360.029 101 mat

Conformity from absolute residuals δ i 1 Ge rows range Δ i el Y i el X i el β f - 2 round eval : for Ge X Y Δ augment : Header Ω °K Δ°K 13 mat : Header Ge stack 41 line :

1.760129 β f 273.150

x β f 273.15 - 0 ≡ x 1.5 2 solve 1.760129

Quick linfit GR-300-AA ... a most remarkable fit ± 0.01°K

data x β f x c * 2 1 sys

δ Ω °K Δ°K 35180 0.3 05443 0.5 0 875.7 1 0.01 - 448.6 1.4 0.01 248.8 2 0.01 - 94.46 4.2 0 33.2 100 7.79 400 3.5 77.4 0 2.72 1000113 mat

range GR-300-AA 0.3 273.15 - 100 273.15 - 21 mat °C 272.85 - 173.15 - 21 mat

Pt100 subCryo [-273.15 . . . -189. 3442 °C]

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Smath al_nleqsolve λ 4.582374490 0.689736236 - 4.153686384 - 50.944725014 - 41 mat :

... exact eit90 inverse in the subCryo  [-259.3467...-189.3442] x λ subCryo λ 1 el x λ 3 el - (λ 2 el x *^(* 1 x ln + x λ 3 el - (- exp + λ 4 el + (* :

abs 0.00006230541 :

eit90 °C Ω 273.15 - abs 268.935 - 0.00015549 259.3467 - 0.00119007 248.5939 - 0.00844974 218.7916 - 0.09171804 189.3442 - 0.21585975 38.8344 - 0.84414211 0.01 1 29.7646 1.11813889 156.5985 1.60980185 231.928 1.89279768 419.527 2.5689173 660.323 3.3760086 961.78 4.28642053 1064.43 4.57255961 1084.5 4.62715523 172 mat :

eit90 eit90 217 range 12 range el : data eit90 2 col eit90 1 col augment : fixed data o 7 black plot : x sub 1 0.00006230541 x ≤ (x 0.21585975 ≤ (& cases : 41 sys

abs λ subCryo 0.00015549 λ subCryo 0.00119007 λ subCryo 0.00844974 λ subCryo 0.09171804 λ subCryo 0.21585975 λ subCryo 61 mat 273.15 - 268.9349 - 259.3467 - 248.5939 - 218.7916 - 189.3442 - 61 mat

eit90 solved solved exact exact exact exact 61 sys ≡

just an image

GR-50-AA 273.15 - 0.05 + 273.15 - 4.2 + 21 mat 273.1 - 268.95 - 21 mat

HeNBP 0.000155487 :

fixed x λ subCryo x sub * HeNBP HeNBP λ subCryo + 20 blue 1 5 mat 3 1 sys

HeNBP Ω 21 mat 268.935 - 0.000155487 21 mat ≡

...GR-50-AA ...

.. GR-300-AA .. Ge Ω °K 35000 0.05 2320 0.1 364.6 0.2 164 0.3 73.75 0.5 33.55 1 24.71 1.4 19.34 2 13.66 4.2 102 mat :

LakeShore Ω °K 35000 0.05 2320 0.1 364.6 0.2 164 0.3 73.75 0.5 33.55 1 24.73 1.4 19.32 2 13.66 4.2 102 mat ≡

Ge Ge 210 range 12 range el : X Ge 1 col : Y Ge 2 col : 12 mat data Ge : 31 sys

plotG(vx,vy,char,size,color)

vx vy char size color plotG n vx length : plot vx 1 el vy 1 el char size color augment : i 2 n range plot plot vx i el vy i el char size color augment stack : for plot 41 line :

Thiele(X,Y,Δ)

X Y Δ Thiele ε 1018 -^: n X rows : i 1 n range M i 1 el Y i el : for j 2 n range i j n range dM M i j 1 - el M j 1 - j 1 - el - : dM dM abs ε < ε M i j el X i el X j 1 - el - dM / : if : 21 line for for i 1 n range c i 1 el X i el : c i 2 el M i i el : 21 line for Δ 0 ≡ c M if 61 line :

data List collects index list select 12345678919 mat : ct 1 : i select a ct el data i 1 el : b ct el data i 2 el : ct ct 1 + : 31 line for a b augment 51 line :

select the support points XY data List :

XY 35000 0.05 2320 0.1 364.6 0.2 164 0.3 73.75 0.5 33.55 1 24.71 1.4 19.34 2 13.66 4.2 92 mat

length Thiele j XY rows : 9

Cfr(K,X,x) ... recast ... support

Thiele on length of support points 'j' K X x Cfr N j 1 + el K j 1 + el : c j el N j el : a j el K j el : jj j 1 - (0 range c jj el a jj 1 + el : a jj el K jj el x X jj el - c jj el / + : 21 line for a 1 el 51 line :

recast the Cf on the system  [K,X,x] x Cf K X x Cfr :

data set vx data 1 col : vy data 2 col : 21 sys

support points X XY 1 col : Y XY 2 col : 21 sys

support X Y + 15 green plotG : data vx vy . 10 black plotG : 21 line

K X Y 0 Thiele 2 col :

x c 112 x ≤ (x 40000 ≤ (& cases :

data x Cf x c * support 3 1 sys

.. GR-300-AA .. Ge Ω °K 35000 0.05 2320 0.1 364.6 0.2 164 0.3 73.75 0.5 33.55 1 24.71 1.4 19.34 2 13.66 4.2 102 mat :

Ge Ge 210 range 12 range el : X Ge 1 col : Y Ge 2 col : 12 mat 21 sys

Conformity @ suupport points δ i 1 Ge rows range Δ i el Y i el X i el Cf - 3 round eval : for Ge X Y Δ augment : Header Ω °K Δ°K 13 mat : Header Ge stack 41 line :

δ Ω °K Δ°K 35000 0.05 02320 0.1 0 364.6 0.2 0164 0.3 0 73.75 0.5 0 33.55 10 24.71 1.4 0 19.34 20 13.66 4.2 0103 mat

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

LaheShore 24.73 Cf 19.32 Cf 21 mat 1.40 2.00 21 mat

Tabulate a generalized function

f L H N Myfnct i 1 N range ω i 1 + el L H L - N / (i * + : ω 1 el L : 21 line for ω j 2 ω rows range U j el ω j el f : U 1 el L f : 21 line for ω U 4 round vectorize augment 41 line :

L 13 : H 183 : N 340 : 13 mat

User fnct to tabulate within limits x f x Cf :

Table f L H N Myfnct : vx Table 1 col : vy Table 2 col (: 12 mat x interpolated vx vy x linterp : 31 sys

u 15 :

Table 1 row Table N 1 + row 21 mat 13 4.8852 12 mat 183 0.2822 12 mat 21 mat

u interpolated 3.291

data n Decimate collect every 'n' pairs range 1 data rows n range : k 1 : i range u k el data i 1 el : v k el data i 2 el : k k 1 + : 31 line for u v augment 51 line :

disabled
after use New Table 11 Decimate : New New o 5 black plot : 21 sys

support 13.66 4.2 + 20 blue 19.32 2 + 20 blue 24.73 1.4 + 20 blue 33.55 1 + 20 blue 73.75 0.5 + 20 blue 164 0.3 + 20 blue 65 mat :

New1 ... New2

New1 13 4.885 o 5 black 15 3.291 o 5 black 17 2.518 o 5 black 19 2.06 o 5 black 21 1.757 o 5 black 23 1.541 o 5 black 25 1.379 o 5 black 27 1.253 o 5 black 29 1.152 o 5 black 31 1.07 o 5 black 33 1.004 o 5 black 35 0.938 o 5 black 37 0.889 o 5 black 39 0.845 o 5 black 41 0.806 o 5 black 43 0.772 o 5 black 45 0.741 o 5 black 47 0.713 o 5 black 49 0.688 o 5 black 51 0.666 o 5 black 53 0.645 o 5 black 55 0.626 o 5 black 57 0.608 o 5 black 59 0.592 o 5 black 61 0.576 o 5 black 63 0.562 o 5 black 65 0.549 o 5 black 67 0.537 o 5 black 69 0.525 o 5 black 71 0.514 o 5 black 73 0.504 o 5 black 315 mat :

New2 78 0.48 o 5 black 83 0.46 o 5 black 88 0.442 o 5 black 93 0.426 o 5 black 98 0.411 o 5 black 103 0.398 o 5 black 108 0.386 o 5 black 113 0.375 o 5 black 118 0.365 o 5 black 123 0.356 o 5 black 128 0.347 o 5 black 133 0.339 o 5 black 138 0.332 o 5 black 143 0.325 o 5 black 148 0.318 o 5 black 153 0.312 o 5 black 158 0.306 o 5 black 175 mat :

New1 Table support New2 4 1 sys

Thiele Cryogenic °K . . . export formula

. . . check/adapt K coefficients wrt support Y's

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GR-50-AA 273.15 - 0.05 + 273.15 - 4.2 + 21 mat °C 273.1 - 268.95 - 21 mat

Thiele 'K' fit to GR-50-AA K K 8 round vectorize :

268.935 - Helium NBP ≡

K 1 el x X 1 el - K 2 el x X 2 el - K 3 el x X 3 el - K 4 el x X 4 el - K 5 el x X 5 el - K 6 el x X 6 el - K 7 el x X 7 el - K 8 el x X 8 el - K 9 el / + / + / + / + / + / + / + / +

Ω °K 35000 0.05 2320 0.1 364.6 0.2 164 0.3 73.75 0.5 33.55 1 24.71 1.4 19.34 2 13.66 4.2 102 mat

K 0.05 653600 - 0.00462601 - 462702 - 0.00145151 - 225158 - 0.00086475 540.8 0.00130983 - 91 mat ≡

Sensible remark . . . Pt100

eit90 °C vs Wr data are experimental. Their polynomials representation excludes extrapolation

as they are not a represntative model. In fact, eit90 is representable in three segments of

same model, allowing low/high range extrapolation. RemToFind parametric global model.

What happens to Pt100 @ Helium NBP -268.935 °C ? evaporates/explodes . . .

Clearly: the 4 points exact fit 4 parameters tracks below eit90 -259.3467 °C.

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Resume/Export ...GR-50-AA

Thiele continued fraction GR-50-AA ... 'K's' adapted x Cf K 1 el x X 1 el - K 2 el x X 2 el - K 3 el x X 3 el - K 4 el x X 4 el - K 5 el x X 5 el - K 6 el x X 6 el - K 7 el x X 7 el - K 8 el x X 8 el - K 9 el / + / + / + / + / + / + / + / + :

K 0.05 653600 - 0.00462601 - 462700 - 0.00145151 - 225158 - 0.00086475 541 0.00130983 - 91 mat :

Ge Ω °K 35000 0.05 2320 0.1 364.6 0.2 164 0.3 73.75 0.5 33.55 1 24.71 1.4 19.34 2 13.66 4.2 102 mat :

Ge Ge 210 range 12 range el : X Ge 1 col : Y Ge 2 col : 12 mat 21 sys

Conformity @ suupport points δ i 1 Ge rows range Δ i el Y i el X i el Cf - 4 round eval : for Ge X Y Δ augment : Header Ω °K Δ°K 13 mat : Header Ge stack 41 line :

δ Ω °K Δ°K 35000 0.05 02320 0.1 0 364.6 0.2 0164 0.3 0 73.75 0.5 0 33.55 10 24.71 1.4 0 19.34 20 13.66 4.2 0103 mat

Thiele continued fraction converted to J_Frac ... collected coeff's x J 0.0434774 243.079 x 2291.11 + 847382 x 409.59 + 2301.44 x 36.3758 + 0.384546 x 33.7423 - / + / - / - / + :

Conformity @ suupport points Jδ i 1 Ge rows range Δ i el Y i el X i el J - 5 round eval : for Ge X Y Δ augment : Header Ω °K Δ°K 13 mat : Header Ge stack 41 line :

Jδ Ω °K Δ°K 35000 0.05 02320 0.1 0 364.6 0.2 0164 0.3 0 73.75 0.5 0 33.55 10 24.71 1.4 0 19.34 20 13.66 4.2 0103 mat

x J

LakeShore 24.73 19.32 21 mat 1.4 221 mat ≡

ITS_90 273.15 - 268.935 - 259.3467 - 248.5939 - 218.7916 - 189.3442 - 38.8344 - 0.01 29.7646 156.5985 231.928 419.527 660.323 961.78 1064.43 1084.5 161 mat_NBP Helium TP Hydrogen TP Neon TP Oxygen TP Argon TP Mercury TP Water MP Gallium FP Indium FP Tin FP Zinc FP Aluminum FP Silver FP Gold FP Copper 161 mat 12 mat ≡

jmGiraud: 20190202