Add documentation for quantum state tomography and performance features

[arnavk23]

This PR adds new documentation to the tutorials, focusing on:

• Quantum State Tomography:
  Introduces a new section with an example of simulating homodyne measurements and reconstructing a Gaussian state from sampled data, including Wigner function visualization.

• Performance Features:
  Adds sections on GPU Acceleration, Multithreading, and Benchmarking/Profiling, with practical examples and usage notes for each.

CHANGELOG notes:

• Added quantum state tomography example to tutorials.
• Added documentation for GPU acceleration, multithreading, and benchmarking/profiling.

Checklist:

• The code is properly formatted and commented.
• Substantial new functionality is documented within the docs.
• All new functionality is tested.
• All of the automated tests on github pass.
• Formatting checks have been considered for new code.

[github-actions]

Benchmark Results (Julia v1)

Time benchmarks

	main	dfeed77...	main / dfeed77...
operations/channel product/10	4.83 ± 1.1 μs	4.54 ± 0.73 μs	1.06 ± 0.29
operations/channel product/100	0.689 ± 0.063 ms	0.695 ± 0.048 ms	0.992 ± 0.11
operations/channel product/2	1.37 ± 0.11 μs	1.35 ± 0.1 μs	1.01 ± 0.11
operations/channel product/200	3.52 ± 0.19 ms	3.55 ± 1.5 ms	0.992 ± 0.43
operations/channel product/50	0.243 ± 0.019 ms	0.241 ± 0.022 ms	1.01 ± 0.12
operations/partial trace/10	1.29 ± 0.12 μs	1.34 ± 0.14 μs	0.962 ± 0.13
operations/partial trace/100	9.32 ± 1.5 μs	9.73 ± 1.3 μs	0.957 ± 0.2
operations/partial trace/2	0.932 ± 0.069 μs	0.902 ± 0.061 μs	1.03 ± 0.1
operations/partial trace/200	24.7 ± 3.2 μs	24.9 ± 3.1 μs	0.99 ± 0.18
operations/partial trace/50	5.25 ± 0.88 μs	5.24 ± 0.68 μs	1 ± 0.21
operations/tensor product/10	2.16 ± 0.4 μs	2.33 ± 0.32 μs	0.927 ± 0.21
operations/tensor product/100	0.152 ± 0.015 ms	0.152 ± 0.015 ms	1 ± 0.14
operations/tensor product/2	0.882 ± 0.051 μs	0.852 ± 0.059 μs	1.04 ± 0.093
operations/tensor product/200	0.797 ± 0.087 ms	0.809 ± 0.23 ms	0.985 ± 0.3
operations/tensor product/50	30.5 ± 11 μs	31.1 ± 11 μs	0.983 ± 0.5
operations/unitary product/10	3.64 ± 0.35 μs	3.66 ± 0.32 μs	0.994 ± 0.13
operations/unitary product/100	0.644 ± 0.029 ms	0.644 ± 0.025 ms	1 ± 0.06
operations/unitary product/2	1.2 ± 0.059 μs	1.16 ± 0.05 μs	1.04 ± 0.068
operations/unitary product/200	3.43 ± 0.092 ms	3.43 ± 0.097 ms	1 ± 0.039
operations/unitary product/50	0.225 ± 0.015 ms	0.226 ± 0.017 ms	0.997 ± 0.1
time_to_load	0.219 ± 0.0013 s	0.218 ± 0.0022 s	1.01 ± 0.012

Memory benchmarks

	main	dfeed77...	main / dfeed77...
operations/channel product/10	17 allocs: 10.2 kB	17 allocs: 10.2 kB	1
operations/channel product/100	17 allocs: 0.919 MB	17 allocs: 0.919 MB	1
operations/channel product/2	14 allocs: 0.891 kB	14 allocs: 0.891 kB	1
operations/channel product/200	19 allocs: 3.67 MB	19 allocs: 3.67 MB	1
operations/channel product/50	17 allocs: 0.231 MB	17 allocs: 0.231 MB	1
operations/partial trace/10	14 allocs: 0.672 kB	14 allocs: 0.672 kB	1
operations/partial trace/100	15 allocs: 2.79 kB	15 allocs: 2.79 kB	1
operations/partial trace/2	14 allocs: 0.672 kB	14 allocs: 0.672 kB	1
operations/partial trace/200	15 allocs: 5.04 kB	15 allocs: 5.04 kB	1
operations/partial trace/50	14 allocs: 1.69 kB	14 allocs: 1.69 kB	1
operations/tensor product/10	9 allocs: 13.1 kB	9 allocs: 13.1 kB	1
operations/tensor product/100	10 allocs: 1.22 MB	10 allocs: 1.22 MB	1
operations/tensor product/2	8 allocs: 0.797 kB	8 allocs: 0.797 kB	1
operations/tensor product/200	10 allocs: 4.89 MB	10 allocs: 4.89 MB	1
operations/tensor product/50	9 allocs: 0.307 MB	9 allocs: 0.307 MB	1
operations/unitary product/10	14 allocs: 6.95 kB	14 allocs: 6.95 kB	1
operations/unitary product/100	14 allocs: 0.614 MB	14 allocs: 0.614 MB	1
operations/unitary product/2	12 allocs: 0.688 kB	12 allocs: 0.688 kB	1
operations/unitary product/200	16 allocs: 2.45 MB	16 allocs: 2.45 MB	1
operations/unitary product/50	14 allocs: 0.155 MB	14 allocs: 0.155 MB	1
time_to_load	0.145 k allocs: 11 kB	0.145 k allocs: 11 kB	1

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
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Additional details and impacted files

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