Add Bloch-Messiah decomposition

[apkille]

No description provided.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Files with missing lines	Coverage Δ
src/Gabs.jl	100.00% <ø> (ø)
src/factorizations.jl	100.00% <100.00%> (ø)

[github-actions]

Benchmark Result

Judge result

Benchmark Report for /home/runner/work/Gabs.jl/Gabs.jl

Job Properties

• Time of benchmarks:

• Target: 25 Jan 2025 - 15:59
• Baseline: 25 Jan 2025 - 16:01

• Package commits:

• Target: 405ed5
• Baseline: d17bea

• Julia commits:

• Target: 4c16ff
• Baseline: 4c16ff

• Julia command flags:

• Target: None
• Baseline: None

• Environment variables:

• Target: None
• Baseline: None

Results

A ratio greater than 1.0 denotes a possible regression (marked with ❌), while a ratio less
than 1.0 denotes a possible improvement (marked with ✅). Only significant results - results
that indicate possible regressions or improvements - are shown below (thus, an empty table means that all
benchmark results remained invariant between builds).

ID	time ratio	memory ratio
["operations", "channel product", "50"]	3.80 (5%) ❌	1.00 (1%)
["operations", "partial trace", "200"]	1.19 (5%) ❌	1.00 (1%)
["operations", "partial trace", "50"]	0.92 (5%) ✅	1.00 (1%)
["operations", "tensor product", "10"]	0.87 (5%) ✅	1.00 (1%)
["operations", "tensor product", "100"]	0.90 (5%) ✅	1.00 (1%)
["operations", "tensor product", "50"]	1.16 (5%) ❌	1.00 (1%)

Benchmark Group List

Here's a list of all the benchmark groups executed by this job:

• ["operations", "channel product"]
• ["operations", "partial trace"]
• ["operations", "tensor product"]
• ["operations", "unitary product"]

Julia versioninfo

Target

Julia Version 1.10.8
Commit 4c16ff44be8 (2025-01-22 10:06 UTC)
Build Info:
 Official https://julialang.org/ release
Platform Info:
 OS: Linux (x86_64-linux-gnu)
 Ubuntu 24.04.1 LTS
 uname: Linux 6.8.0-1020-azure #23-Ubuntu SMP Mon Dec 9 16:58:58 UTC 2024 x86_64 x86_64
 CPU: AMD EPYC 7763 64-Core Processor: 
 speed user nice sys idle irq
 #1 3243 MHz 726 s 0 s 294 s 2882 s 0 s
 #2 3243 MHz 839 s 0 s 510 s 2591 s 0 s
 #3 3240 MHz 883 s 0 s 335 s 2690 s 0 s
 #4 3243 MHz 776 s 0 s 320 s 2827 s 0 s
 Memory: 15.61526870727539 GB (14206.16015625 MB free)
 Uptime: 400.76 sec
 Load Avg: 1.76 1.07 0.46
 WORD_SIZE: 64
 LIBM: libopenlibm
 LLVM: libLLVM-15.0.7 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)

Baseline

Julia Version 1.10.8
Commit 4c16ff44be8 (2025-01-22 10:06 UTC)
Build Info:
 Official https://julialang.org/ release
Platform Info:
 OS: Linux (x86_64-linux-gnu)
 Ubuntu 24.04.1 LTS
 uname: Linux 6.8.0-1020-azure #23-Ubuntu SMP Mon Dec 9 16:58:58 UTC 2024 x86_64 x86_64
 CPU: AMD EPYC 7763 64-Core Processor: 
 speed user nice sys idle irq
 #1 3242 MHz 1008 s 0 s 398 s 3476 s 0 s
 #2 3244 MHz 1271 s 0 s 648 s 3001 s 0 s
 #3 3248 MHz 1100 s 0 s 609 s 3180 s 0 s
 #4 3242 MHz 883 s 0 s 425 s 3596 s 0 s
 Memory: 15.61526870727539 GB (14173.91015625 MB free)
 Uptime: 499.01 sec
 Load Avg: 1.75 1.24 0.59
 WORD_SIZE: 64
 LIBM: libopenlibm
 LLVM: libLLVM-15.0.7 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)

---

Target result

Benchmark Report for /home/runner/work/Gabs.jl/Gabs.jl

Job Properties

• Time of benchmark: 25 Jan 2025 - 15:59
• Package commit: 405ed5
• Julia commit: 4c16ff
• Julia command flags: None
• Environment variables: None

Results

Below is a table of this job's results, obtained by running the benchmarks.
The values listed in the ID column have the structure [parent_group, child_group, ..., key], and can be used to
index into the BaseBenchmarks suite to retrieve the corresponding benchmarks.
The percentages accompanying time and memory values in the below table are noise tolerances. The "true"
time/memory value for a given benchmark is expected to fall within this percentage of the reported value.
An empty cell means that the value was zero.

ID	time	GC time	memory	allocations
["operations", "channel product", "10"]	2.847 μs (5%)		10.19 KiB (1%)	5
["operations", "channel product", "100"]	756.055 μs (5%)		941.17 KiB (1%)	8
["operations", "channel product", "2"]	497.974 ns (5%)		768 bytes (1%)	5
["operations", "channel product", "200"]	3.343 ms (5%)		3.67 MiB (1%)	8
["operations", "channel product", "50"]	324.693 μs (5%)		236.27 KiB (1%)	8
["operations", "partial trace", "10"]	458.959 ns (5%)		2.89 KiB (1%)	2
["operations", "partial trace", "100"]	35.245 μs (5%)		308.12 KiB (1%)	3
["operations", "partial trace", "2"]	76.332 ns (5%)		176 bytes (1%)	2
["operations", "partial trace", "200"]	158.264 μs (5%)		1.21 MiB (1%)	3
["operations", "partial trace", "50"]	7.778 μs (5%)		75.98 KiB (1%)	3
["operations", "tensor product", "10"]	956.667 ns (5%)		13.02 KiB (1%)	2
["operations", "tensor product", "100"]	106.207 μs (5%)		1.22 MiB (1%)	3
["operations", "tensor product", "2"]	125.384 ns (5%)		704 bytes (1%)	2
["operations", "tensor product", "200"]	645.239 μs (5%)		4.89 MiB (1%)	3
["operations", "tensor product", "50"]	22.993 μs (5%)		314.31 KiB (1%)	3
["operations", "unitary product", "10"]	2.448 μs (5%)		6.94 KiB (1%)	4
["operations", "unitary product", "100"]	700.211 μs (5%)		628.62 KiB (1%)	6
["operations", "unitary product", "2"]	420.528 ns (5%)		576 bytes (1%)	4
["operations", "unitary product", "200"]	3.431 ms (5%)		2.45 MiB (1%)	6
["operations", "unitary product", "50"]	314.445 μs (5%)		158.09 KiB (1%)	6

Benchmark Group List

Here's a list of all the benchmark groups executed by this job:

• ["operations", "channel product"]
• ["operations", "partial trace"]
• ["operations", "tensor product"]
• ["operations", "unitary product"]

Julia versioninfo

Julia Version 1.10.8
Commit 4c16ff44be8 (2025-01-22 10:06 UTC)
Build Info:
 Official https://julialang.org/ release
Platform Info:
 OS: Linux (x86_64-linux-gnu)
 Ubuntu 24.04.1 LTS
 uname: Linux 6.8.0-1020-azure #23-Ubuntu SMP Mon Dec 9 16:58:58 UTC 2024 x86_64 x86_64
 CPU: AMD EPYC 7763 64-Core Processor: 
 speed user nice sys idle irq
 #1 3243 MHz 726 s 0 s 294 s 2882 s 0 s
 #2 3243 MHz 839 s 0 s 510 s 2591 s 0 s
 #3 3240 MHz 883 s 0 s 335 s 2690 s 0 s
 #4 3243 MHz 776 s 0 s 320 s 2827 s 0 s
 Memory: 15.61526870727539 GB (14206.16015625 MB free)
 Uptime: 400.76 sec
 Load Avg: 1.76 1.07 0.46
 WORD_SIZE: 64
 LIBM: libopenlibm
 LLVM: libLLVM-15.0.7 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)

---

Baseline result

Benchmark Report for /home/runner/work/Gabs.jl/Gabs.jl

Job Properties

• Time of benchmark: 25 Jan 2025 - 16:1
• Package commit: d17bea
• Julia commit: 4c16ff
• Julia command flags: None
• Environment variables: None

Results

Below is a table of this job's results, obtained by running the benchmarks.
The values listed in the ID column have the structure [parent_group, child_group, ..., key], and can be used to
index into the BaseBenchmarks suite to retrieve the corresponding benchmarks.
The percentages accompanying time and memory values in the below table are noise tolerances. The "true"
time/memory value for a given benchmark is expected to fall within this percentage of the reported value.
An empty cell means that the value was zero.

ID	time	GC time	memory	allocations
["operations", "channel product", "10"]	2.768 μs (5%)		10.19 KiB (1%)	5
["operations", "channel product", "100"]	744.133 μs (5%)		941.17 KiB (1%)	8
["operations", "channel product", "2"]	507.731 ns (5%)		768 bytes (1%)	5
["operations", "channel product", "200"]	3.318 ms (5%)		3.67 MiB (1%)	8
["operations", "channel product", "50"]	85.409 μs (5%)		236.27 KiB (1%)	8
["operations", "partial trace", "10"]	478.631 ns (5%)		2.89 KiB (1%)	2
["operations", "partial trace", "100"]	36.588 μs (5%)		308.12 KiB (1%)	3
["operations", "partial trace", "2"]	75.919 ns (5%)		176 bytes (1%)	2
["operations", "partial trace", "200"]	133.498 μs (5%)		1.21 MiB (1%)	3
["operations", "partial trace", "50"]	8.496 μs (5%)		75.98 KiB (1%)	3
["operations", "tensor product", "10"]	1.101 μs (5%)		13.02 KiB (1%)	2
["operations", "tensor product", "100"]	117.929 μs (5%)		1.22 MiB (1%)	3
["operations", "tensor product", "2"]	122.804 ns (5%)		704 bytes (1%)	2
["operations", "tensor product", "200"]	656.009 μs (5%)		4.89 MiB (1%)	3
["operations", "tensor product", "50"]	19.817 μs (5%)		314.31 KiB (1%)	3
["operations", "unitary product", "10"]	2.382 μs (5%)		6.94 KiB (1%)	4
["operations", "unitary product", "100"]	695.913 μs (5%)		628.62 KiB (1%)	6
["operations", "unitary product", "2"]	427.884 ns (5%)		576 bytes (1%)	4
["operations", "unitary product", "200"]	3.405 ms (5%)		2.45 MiB (1%)	6
["operations", "unitary product", "50"]	305.127 μs (5%)		158.09 KiB (1%)	6

Benchmark Group List

Here's a list of all the benchmark groups executed by this job:

• ["operations", "channel product"]
• ["operations", "partial trace"]
• ["operations", "tensor product"]
• ["operations", "unitary product"]

Julia versioninfo

Julia Version 1.10.8
Commit 4c16ff44be8 (2025-01-22 10:06 UTC)
Build Info:
 Official https://julialang.org/ release
Platform Info:
 OS: Linux (x86_64-linux-gnu)
 Ubuntu 24.04.1 LTS
 uname: Linux 6.8.0-1020-azure #23-Ubuntu SMP Mon Dec 9 16:58:58 UTC 2024 x86_64 x86_64
 CPU: AMD EPYC 7763 64-Core Processor: 
 speed user nice sys idle irq
 #1 3242 MHz 1008 s 0 s 398 s 3476 s 0 s
 #2 3244 MHz 1271 s 0 s 648 s 3001 s 0 s
 #3 3248 MHz 1100 s 0 s 609 s 3180 s 0 s
 #4 3242 MHz 883 s 0 s 425 s 3596 s 0 s
 Memory: 15.61526870727539 GB (14173.91015625 MB free)
 Uptime: 499.01 sec
 Load Avg: 1.75 1.24 0.59
 WORD_SIZE: 64
 LIBM: libopenlibm
 LLVM: libLLVM-15.0.7 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)

---

Runtime information

Runtime Info
BLAS #threads	2
BLAS.vendor()	lbt
Sys.CPU_THREADS	4

lscpu output:

Architecture: x86_64
CPU op-mode(s): 32-bit, 64-bit
Address sizes: 48 bits physical, 48 bits virtual
Byte Order: Little Endian
CPU(s): 4
On-line CPU(s) list: 0-3
Vendor ID: AuthenticAMD
Model name: AMD EPYC 7763 64-Core Processor
CPU family: 25
Model: 1
Thread(s) per core: 2
Core(s) per socket: 2
Socket(s): 1
Stepping: 1
BogoMIPS: 4890.86
Flags: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ht syscall nx mmxext fxsr_opt pdpe1gb rdtscp lm constant_tsc rep_good nopl tsc_reliable nonstop_tsc cpuid extd_apicid aperfmperf pni pclmulqdq ssse3 fma cx16 pcid sse4_1 sse4_2 movbe popcnt aes xsave avx f16c rdrand hypervisor lahf_lm cmp_legacy svm cr8_legacy abm sse4a misalignsse 3dnowprefetch osvw topoext vmmcall fsgsbase bmi1 avx2 smep bmi2 erms invpcid rdseed adx smap clflushopt clwb sha_ni xsaveopt xsavec xgetbv1 xsaves user_shstk clzero xsaveerptr rdpru arat npt nrip_save tsc_scale vmcb_clean flushbyasid decodeassists pausefilter pfthreshold v_vmsave_vmload umip vaes vpclmulqdq rdpid fsrm
Virtualization: AMD-V
Hypervisor vendor: Microsoft
Virtualization type: full
L1d cache: 64 KiB (2 instances)
L1i cache: 64 KiB (2 instances)
L2 cache: 1 MiB (2 instances)
L3 cache: 32 MiB (1 instance)
NUMA node(s): 1
NUMA node0 CPU(s): 0-3
Vulnerability Gather data sampling: Not affected
Vulnerability Itlb multihit: Not affected
Vulnerability L1tf: Not affected
Vulnerability Mds: Not affected
Vulnerability Meltdown: Not affected
Vulnerability Mmio stale data: Not affected
Vulnerability Reg file data sampling: Not affected
Vulnerability Retbleed: Not affected
Vulnerability Spec rstack overflow: Vulnerable: Safe RET, no microcode
Vulnerability Spec store bypass: Vulnerable
Vulnerability Spectre v1: Mitigation; usercopy/swapgs barriers and __user pointer sanitization
Vulnerability Spectre v2: Mitigation; Retpolines; STIBP disabled; RSB filling; PBRSB-eIBRS Not affected; BHI Not affected
Vulnerability Srbds: Not affected
Vulnerability Tsx async abort: Not affected

Cpu Property	Value
Brand	AMD EPYC 7763 64-Core Processor
Vendor	:AMD
Architecture	:Unknown
Model	Family: 0xaf, Model: 0x01, Stepping: 0x01, Type: 0x00
Cores	16 physical cores, 16 logical cores (on executing CPU)
	No Hyperthreading hardware capability detected
Clock Frequencies	Not supported by CPU
Data Cache	Level 1:3 : (32, 512, 32768) kbytes
	64 byte cache line size
Address Size	48 bits virtual, 48 bits physical
SIMD	256 bit = 32 byte max. SIMD vector size
Time Stamp Counter	TSC is accessible via rdtsc
	TSC runs at constant rate (invariant from clock frequency)
Perf. Monitoring	Performance Monitoring Counters (PMC) are not supported
Hypervisor	Yes, Microsoft