Reverse Endianness

[swernli]

Based on feedback, we are reversing the endianness of ket displays from the QDK along with associated code. This includes reversing the display for state dumps from within Q#, in the debugger, and in Jupyter output. Included in this change is the revert of updates to kata content that tried to accomodate the different ordering between exercise text and the state display. The change also includes update to the new dump_operation in Python so that it is consistent with the endianness and outputs matrices that match the same conventions.

[minestarks]

@swernli Shouldn't we reverse the order of the formatted tables as well so they still go from 00001 => 11111?

[ScottCarda-MS]

@swernli Shouldn't we reverse the order of the formatted tables as well so they still go from 00001 => 11111?

Yes I think that is what I'm seeing here as well.

[swernli]

@swernli Shouldn't we reverse the order of the formatted tables as well so they still go from 00001 => 11111?

No, because that is the correct order for what those entries are. |10⟩ is the first entry in the state vector, |01⟩ is the second entry, etc.

If there were 4 qubits in equal superposition, it would go:

|0000⟩
|1000⟩
|0100⟩
|1100⟩
|0010⟩
|1010⟩
|0110⟩
|1110⟩
|0001⟩
|1001⟩
|0101⟩
|1101⟩
|0011⟩
|1011⟩
|0111⟩
|1111⟩

[github-actions]

Benchmark for 9daf12d

Click to view benchmark

Test	Base	PR	%
Array append evaluation	878.1±14.74µs	868.1±31.81µs	-1.14%
Array update evaluation	953.9±4.27µs	932.7±4.37µs	-2.22%
Deutsch-Jozsa evaluation	31.3±0.23ms	31.5±1.62ms	+0.64%
Large file parity evaluation	36.0±0.23ms	35.9±0.11ms	-0.28%
Large input file	38.8±2.21ms	38.0±0.55ms	-2.06%
Standard library	21.3±0.59ms	20.8±0.20ms	-2.35%
Teleport evaluation	103.9±1.98µs	106.1±1.97µs	+2.12%

[tcNickolas]

The order of the printed entries is the second part of our discussion today, do we interpret bit strings as integers using little endian (least significant bit first) or big endian (most significant bit first)? For the CNOT matrix to have the right ("textbook") shape, we need to use big endian, so it makes sense to have the same for ordering the entries. (|0000⟩ then |0001⟩ then |0010⟩ etc.)

[ScottCarda-MS]

@swernli Shouldn't we reverse the order of the formatted tables as well so they still go from 00001 => 11111?

No, because that is the correct order for what those entries are. |10⟩ is the first entry in the state vector, |01⟩ is the second entry, etc.

If there were 4 qubits in equal superposition, it would go:

|0000⟩
|1000⟩
|0100⟩
|1100⟩
|0010⟩
|1010⟩
|0110⟩
|1110⟩
|0001⟩
|1001⟩
|0101⟩
|1101⟩
|0011⟩
|1011⟩
|0111⟩
|1111⟩

Is there something imposing a particular order other than what we want to display? Displaying the kets in that order seems confusing to me.

[github-actions]

Benchmark for 5b3dab7

Click to view benchmark

Test	Base	PR	%
Array append evaluation	859.5±7.82µs	878.6±24.81µs	+2.22%
Array update evaluation	935.2±8.90µs	952.4±9.75µs	+1.84%
Deutsch-Jozsa evaluation	31.3±0.26ms	31.2±0.17ms	-0.32%
Large file parity evaluation	35.9±0.10ms	36.0±0.18ms	+0.28%
Large input file	39.9±1.05ms	39.3±0.86ms	-1.50%
Standard library	21.6±0.44ms	21.4±0.40ms	-0.93%
Teleport evaluation	102.2±1.56µs	105.5±2.51µs	+3.23%

[swernli]

Given the feedback and sticking with the theme of trying to make things less confusing, I'll make sure the state display is sorted according to the display format rather than the original state vector ordering.

[billti]

No, because that is the correct order for what those entries are. |10⟩ is the first entry in the state vector, |01⟩ is the second entry, etc.

Is this correct? If |01> is the tensor product of |0> and |1>, then it is [1, 0]T x [0, 1]T which is [0, 1, 0, 0]T. In other words, the kets should be ordered from |00>, |01>, |10>, |11> to map to the way state vectors are typically ordered as sequential entries of [1, 0, 0, 0]T, [0, 1, 0, 0]T, [0, 0, 1, 0]T, and [0, 0, 0, 1]T.

[github-actions]

Benchmark for b096d88

Click to view benchmark

Test	Base	PR	%
Array append evaluation	860.0±19.22µs	864.8±5.59µs	+0.56%
Array update evaluation	933.6±5.90µs	935.6±15.54µs	+0.21%
Deutsch-Jozsa evaluation	31.2±0.19ms	31.5±0.92ms	+0.96%
Large file parity evaluation	35.9±0.14ms	36.2±0.27ms	+0.84%
Large input file	37.6±0.74ms	38.3±1.17ms	+1.86%
Standard library	21.2±0.59ms	20.9±0.27ms	-1.42%
Teleport evaluation	102.5±1.90µs	104.7±2.46µs	+2.15%

[swernli]

Now all the endianness matches and the ordering of the state entries are also sequential:

The state display in the debugger also matches this too.

[minestarks]

Phew, looks pretty thorough. Thanks!