About Quantum Computers

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... 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

Clear from previous use M 0 : β 0 : 12 mat

linfit modules

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 :

Applicable parts are: Optimiz "numeric" XY f φ β βlinfit 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 Gradient Matrix j 1 k range i 1 n range M i j el X i el β φ j 1 + el eval : for for Cholesky solver [LS] 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 :

XY 75274 - 100160 - 125104 - 150 71.5 - 200 35.2 - 250 16.2 - 300 4.2 - 4009500 16.9 600 21.3 70024112 mat :

data XY 1 col XY 2 col . 12 red plotG :

XY XY 111 range 12 range el :

order 4 :

X XY 1 col : Y XY 2 col : 21 line

x β p n 0 order range F 1 el 1 : n 0 ≡ F n 1 + el β n el 1 x / (n^* : cases for F 21 line :

Prepare the 'Unary β' i 1 order range β i el 1 : for

β transpose 111114 mat

3. Collect  the model function x β f x β p n el n 1 order 1 + sum 11 line :

x c 175 x ≤ (x 750 ≤ (& cases :

set 'n' to length β n β rows :

vector gradient x β φ x β f n φ :

The "linfit" coefficients s XY f φ β βlinfit :

CWD C:\SmathFile CurrentDirectory :

s CWD linfit wfile 1

s CWD linfit rfile :

x G s m el 1 x / (m^* m 1 order sum :

x G 0 ≡ x 300350 solve 305.7315

u deriv u G u diff :

linfit rational to Broyden data set

x G x c * data 2 1 sys

s 24757.9902 1.0351 107^* - 9.5765 108^* 3.2761 1010^* - 41 mat

x G x diff x c * 75 10 75 1 - 2 2 mat 2 1 sys

75 deriv 9.1

x G x 400700 int 4641