Quantum Experience Hadamard test investigation

This document discusses tests with 4 Hadamard gates and 3 Hadamard gates.
The line marked "value" shows the value between 0 and 1

1. 4 gates Simulated Results 100 shots

   Measured values:

   bits	00000	00001	00010	00011	00100	00101	00110	00111	01000	01001	01010	01011	01100	01101	01110	01111
   value	0.090	0.050	0.060	0.070	0.060	0.030	0.090	0.090	0.060	0.060	0.100	0.090	0.030	0.080	0.010	0.030
   %	9	5	6	7	6	3	9	9	6	6	10	9	3	8	1	3

   Frequency distribution:

   %	1	2	3	4	5	6	7	8	9	10
   	1		3		1	4	1	1	4	1

2. 4 gates Simulated Results 1024 shots

   Measured values:

   bits	00000	00001	00010	00011	00100	00101	00110	00111	01000	01001	01010	01011	01100	01101	01110	01111
   value	0.070	0.067	0.061	0.055	0.053	0.053	0.062	0.071	0.061	0.069	0.066	0.067	0.062	0.061	0.059	0.064
   %	7	6.7	6.1	5.5	5.3	5.3	6.2	7.1	6.1	6.9	6.6	6.7	6.2	6.1	5.9	6.4

   Frequency distribution:

   %	1	2	3	4	5	6	7	8	9	10	11	12
   					4	10	2

3. 4 gates Run 2017-02-17 07:52:12

   Measured values:

   bits	00000	00001	00010	00011	00100	00101	00110	00111	01000	01001	01010	01011	01100	01101	01110	01111
   value	0.070	0.074	0.058	0.074	0.059	0.065	0.068	0.057	0.075	0.053	0.057	0.068	0.060	0.058	0.066	0.038
   %	7	7.4	5.8	7.4	5.9	6.5	6.8	5.7	7.5	5.3	5.7	6.8	6	5.8	6.6	3.8

   Frequency distribution:

   %	1	2	3	4	5	6	7	8	9	10
   #			1		6	5	4

4. 4 gates Run 2017-04-19 04:26:28

   Measured values:

   bits	00000	00001	00010	00011	00100	00101	00110	00111	01000	01001	01010	01011	01100	01101	01110	01111
   value	0.080	0.071	0.066	0.063	0.044	0.041	0.100	0.070	0.061	0.063	0.080	0.049	0.033	0.026	0.071	0.082
   %	8	7.1	6.6	6.3	4.4	4.1	10	7	6.1	6.3	8	4.9	3.3	2.6	7.1	8.2

   Frequency distribution:

   %	1	2	3	4	5	6	7	8	9	10
   #		1	1	3		4	3	3		1

5. 3 gates Simulated Results 100 shots

   Measured values:

   bits	00000	00001	00010	00011	00100	00101	00110	00111
   value	0.120	0.130	0.090	0.110	0.150	0.180	0.130	0.090
   %	12	13	9	11	15	18	13	9

   Frequency distribution:

   %	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
   #									2		1	1	2		1			1

6. 3 gates Simulated Results 1024 shots

   Measured values:

   bits	00000	00001	00010	00011	00100	00101	00110	00111
   value	0.144	0.114	0.120	0.115	0.114	0.127	0.146	0.120
   %	14,4	11,4	12	11,5	11,4	12,7	14,6	12

   Frequency distribution:

   %	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
   #											3	3		2

7. 3 gates - Run 2017-01-26 13:10:12

   Measured values:

   bits	00000	00001	00010	00011	00100	00101	00110	00111
   value	0.141	0.165	0.118	0.133	0.117	0.125	0.101	0.101
   %	14.1	16.5	11.8	13.3	11.7	12.5	10.1	10.1

   Frequency distribution:

   %	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
   #										2	2	1	1	1		1

8. 3 gates - Run 2017-03-07 18:08:32

   Measured values:

   bits	00000	00001	00010	00011	00100	00101	00110	00111
   value	0.148	0.139	0.142	0.105	0.123	0.121	0.109	0.112
   %	14.8	13.9	14.2	10.5	12.3	12.1	10.9	11.2

   Frequency distribution:

   %	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
   #										2	1	2	1	2

9. 3 gates - Run 2017-03-07 5:27:51

   Measured values:

   bits	00000	00001	00010	00011	00100	00101	00110	00111
   value	0.154	0.118	0.143	0.125	0.127	0.094	0.129	0.110
   %	15.4	11.8	14.3	12.5	12.7	9.4	12.9	11

   Frequency distribution:

   %	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
   #									1		2	3		1	1

The following 3 tables show summary data:

• Table 1A shows summary data of the above 9 tests.
  The column QC indicates if the Quantum Computer is used. Y means Yes. Blank means simulated.
• Table 1B shows the results of the same 9 tests simulated on a digital computer.
• Table 1C shows the same results as of 1B for 9 more tests.

test nqbits Shots QC Average variance Std dev 1 4 100 6.250 6.813 2.610 2 4 1024 6.256 0.301 0.549 3 4 1024 Y 6.250 0.854 0.924 4 4 1024 Y 6.250 3.628 1.905 5 3 100 12.500 8.000 2.828 6 3 1024 12.500 1.498 1.224 7 3 1024 Y 12.513 3.981 1.995 8 3 1024 Y 12.488 2.324 1.524 9 3 1024 Y 12.500 3.025 1.739 Table 1A

test nqbits Shots Average variance Std dev 1 4 100 6.250 5.938 2.437 2 4 1024 6.250 0.755 0.869 3 4 1024 6.250 1.284 1.133 4 4 1024 6.250 0.756 0.869 5 3 100 12.500 5.000 2.236 6 3 1024 12.500 1.388 1.178 7 3 1024 12.500 1.879 1.371 8 3 1024 12.500 0.405 0.637 9 3 1024 12.500 2.096 1.448 Table 1B

test variance Std dev 1 5.813 2.411 2 0.371 0.609 3 0.726 0.852 4 0.255 0.505 5 11.750 3.428 6 0.472 0.687 7 1.233 1.110 8 1.261 1.123 9 1.199 1.095 Table 1C

• Tests 3 and 4 are QC tests done with 4 Hadamard's
  The two standard deviation values 0.924 and 1.905 in Table 1A are on average slightly higher than the corresponding values (1.133, 0.869, 0.852 and 0.505) in the tables 1B and 1C. This means that the QC is not performing as expected.
• The test 7, 8 and 9 are also performed on a QC, but now with 3 Hadamard's.
  Also in this case the standard deviation values are higher for a QC than in the case when a DC is used.

Reflection 1

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