diamond distance is not symmetric #53

benkj · 2019-03-13T22:03:53Z

Consider the following:

p=0.2
AD=KrausOperators([[1 0; 0 sqrt(p)], [0 sqrt(1-p); 0 0]])
AD2=KrausOperators([[1 0; 0 sqrt(2p)], [0 sqrt(1-2p); 0 0]])
println(diamond_distance(AD,AD2))
println(diamond_distance(AD2,AD))

The first line outputs ~0.17 while the second line outputs ~0.40.
This is a bug, since the diamond distance is symmetric

The text was updated successfully, but these errors were encountered:

lpawela · 2019-03-13T23:43:36Z

@pgawron does this indicate some problem with conversion?

lpawela · 2019-03-13T23:50:38Z

@benkj just run the code on my machine, seems to work fine

julia> println(diamond_distance(AD,AD2))
0.3999999603826285

julia> println(diamond_distance(AD2,AD))
0.4000000254778498

pgawron · 2019-03-13T23:54:23Z

@lpawela conversion is suspicious then.

lpawela · 2019-03-13T23:55:15Z

@pgawron can you replicate this behavior?

pgawron · 2019-03-13T23:59:41Z

@lpawela I can. On release version of the package I obtain:

AD=convert(DynamicalMatrix{Matrix{Float64}},KrausOperators([[1 0; 0 sqrt(p)], [0 sqrt(1-p); 0 0]]))
AD2=convert(DynamicalMatrix{Matrix{Float64}},KrausOperators([[1 0; 0 sqrt(2p)], [0 sqrt(1-2p); 0 0]]))

println(diamond_distance(AD,AD2))
# 0.17161841986966694
println(diamond_distance(AD2,AD))
# 0.39999997855290215

lpawela · 2019-03-14T00:05:46Z

@pgawron still can't reproduce. Just to verify I'm on the same version

p=0.2
AD=KrausOperators([[1 0; 0 sqrt(p)], [0 sqrt(1-p); 0 0]])
AD2=KrausOperators([[1 0; 0 sqrt(2p)], [0 sqrt(1-2p); 0 0]])
println(diamond_distance(AD,AD2))
ERROR: MethodError: no method matching DynamicalMatrix{Array{Float64,2}}(::KrausOperators{Array{Float64,2}})

as expected. Now lunching your code

AD=convert(DynamicalMatrix{Matrix{Float64}},KrausOperators([[1 0; 0 sqrt(p)], [0 sqrt(1-p); 0 0]]))
AD2=convert(DynamicalMatrix{Matrix{Float64}},KrausOperators([[1 0; 0 sqrt(2p)], [0 sqrt(1-2p); 0 0]]))
println(diamond_distance(AD,AD2))
# 0.3999999603826285
println(diamond_distance(AD2,AD))
# 0.4000000254778498

My installed packages

(v1.0) pkg> status
    Status `~/.julia/environments/v1.0/Project.toml`
  [c7e460c6] ArgParse v0.6.2
  [c52e3926] Atom v0.7.15
  [8e7c35d0] BlockArrays v0.7.0
  [f65535da] Convex v0.11.1
  [5789e2e9] FileIO v1.0.5
  [033835bb] JLD2 v0.1.2
  [e5e0dc1b] Juno v0.5.5
  [b964fa9f] LaTeXStrings v1.0.3
  [2fda8390] LsqFit v0.7.3
  [15e1cf62] NPZ v0.3.0
  [91a5bcdd] Plots v0.23.1
  [438e738f] PyCall v1.90.0
  [3c0b384b] QuantumInformation v0.4.4
  [c946c3f1] SCS v0.5.1
  [2913bbd2] StatsBase v0.29.0
  [10745b16] Statistics

pgawron · 2019-03-14T00:08:18Z

My status

(v1.1) pkg> status
    Status `~/.julia/environments/v1.1/Project.toml`
  [ca501d18] AcausalNets v0.0.0 #master (https://github.com/mikegpl/AcausalNets.jl)
  [c52e3926] Atom v0.7.15
  [b4f34e82] Distances v0.8.0
  [e5e0dc1b] Juno v0.5.5
  [c36e90e8] PowerModels v0.9.4
  [438e738f] PyCall v1.90.0
  [d330b81b] PyPlot v2.8.0
  [3c0b384b] QuantumInformation v0.4.4

lpawela · 2019-03-14T00:09:35Z

@benkj can you post your status and julia versions?
@pgawron I don't see Convex and SCS in your packages

pgawron · 2019-03-14T00:10:52Z

@pgawron I don't see Convex and SCS in your packages

I wonder why diamond_norm even works in this case.

lpawela · 2019-03-14T00:17:01Z

@pgawron I noticed you're using v1.1, mine is v1.0. After update I get

(v1.1) pkg> status
    Status `~/.julia/environments/v1.1/Project.toml`
  [c52e3926] Atom v0.7.15
  [15e1cf62] NPZ v0.3.0
  [438e738f] PyCall v1.90.0
  [d330b81b] PyPlot v2.8.0
  [3c0b384b] QuantumInformation v0.4.4

It simply doesn't show dependencies. The result is still the same

println(diamond_distance(AD,AD2))
# 0.3999999603826285

println(diamond_distance(AD2,AD))
# 0.4000000254778498

Maybe this behavior is somehow related to #50 and jump-dev/Convex.jl#274

pgawron · 2019-03-14T00:18:38Z

@pgawron I noticed you're using v1.1, mine is v1.0. After update I get

I've just tested for version difference. in both versions i get the same buggy result.

lpawela · 2019-03-14T00:25:30Z

Just tested on another machine v1.0.3, still the results agree. What is going on?

benkj · 2019-03-14T06:35:08Z

I'm running it on a OSX with

  [f65535da] Convex v0.11.1
  [3c0b384b] QuantumInformation v0.4.4 [`~/.julia/dev/QuantumInformation`]
  [c946c3f1] SCS v0.5.1

I find the same bug with or without conversions. This is really weird.

benkj · 2019-03-14T06:38:07Z

I changed the code putting verbose=1 in the SCSsolver and I get the following
ulia> println(diamond_distance(AD,AD2))

----------------------------------------------------------------------------
	SCS v2.0.2 - Splitting Conic Solver
	(c) Brendan O'Donoghue, Stanford University, 2012-2017
----------------------------------------------------------------------------
Lin-sys: sparse-indirect, nnz in A = 197, CG tol ~ 1/iter^(2.00)
eps = 1.00e-05, alpha = 1.50, max_iters = 5000, normalize = 1, scale = 1.00
acceleration_lookback = 20, rho_x = 1.00e-03
Variables n = 49, constraints m = 293
Cones:	primal zero / dual free vars: 137
	sd vars: 156, sd blks: 3
Setup time: 1.79e-04s
----------------------------------------------------------------------------
 Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)
----------------------------------------------------------------------------
     0| 2.69e+00  3.90e+01  9.88e-01 -5.19e+00  7.41e+01  0.00e+00  2.98e-04
   100| 5.59e-05  2.20e-04  5.58e-05 -2.81e-01 -2.81e-01  4.18e-16  1.14e-02
   120| 2.62e-07  1.82e-06  7.24e-07 -1.72e-01 -1.72e-01  1.70e-16  1.38e-02
----------------------------------------------------------------------------
Status: Solved
Timing: Solve time: 1.38e-02s
	Lin-sys: avg # CG iterations: 2.67, avg solve time: 5.95e-06s
	Cones: avg projection time: 5.91e-05s
	Acceleration: avg step time: 4.21e-05s
----------------------------------------------------------------------------
Error metrics:
dist(s, K) = 2.6859e-03, dist(y, K*) = 4.8922e-02, s'y/|s||y| = 1.3742e-06
primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.6203e-07
dual res:   |A'y + c|_2 / (1 + |c|_2) = 1.8192e-06
rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 7.2403e-07
----------------------------------------------------------------------------
c'x = -0.1716, -b'y = -0.1716
============================================================================
0.17161841986966694

julia> println(diamond_distance(AD2,AD))
----------------------------------------------------------------------------
	SCS v2.0.2 - Splitting Conic Solver
	(c) Brendan O'Donoghue, Stanford University, 2012-2017
----------------------------------------------------------------------------
Lin-sys: sparse-indirect, nnz in A = 197, CG tol ~ 1/iter^(2.00)
eps = 1.00e-05, alpha = 1.50, max_iters = 5000, normalize = 1, scale = 1.00
acceleration_lookback = 20, rho_x = 1.00e-03
Variables n = 49, constraints m = 293
Cones:	primal zero / dual free vars: 137
	sd vars: 156, sd blks: 3
Setup time: 8.63e-05s
----------------------------------------------------------------------------
 Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)
----------------------------------------------------------------------------
     0| 2.69e+00  3.90e+01  9.88e-01 -5.19e+00  7.41e+01  0.00e+00  2.17e-04
   100| 4.76e-04  2.56e-03  2.91e-04 -3.57e+00 -3.57e+00  2.87e-14  1.07e-02
   200| 2.85e-05  1.54e-04  4.32e-04 -3.38e-01 -3.38e-01  8.08e-04  2.35e-02
   300| 3.82e-04  2.16e-03  3.11e-04 -2.16e-02 -2.12e-02  3.10e-04  3.51e-02
   400| 1.37e-03  1.18e-02  6.30e-03 -1.83e-01 -1.74e-01  2.21e-02  4.83e-02
   500| 1.33e-03  6.41e-03  5.04e-03 -1.82e-01 -1.89e-01  9.15e-17  6.07e-02
   600| 7.72e-03  5.27e-02  7.13e-03 -1.64e-01 -1.74e-01  1.64e-15  7.26e-02
   700| 4.52e-05  2.59e-04  7.39e-05 -3.60e-01 -3.60e-01  4.00e-16  8.62e-02
   800| 1.52e-04  1.02e-03  1.54e-03 -4.04e-01 -4.07e-01  2.36e-03  9.92e-02
   860| 1.50e-08  6.94e-08  5.42e-09 -4.00e-01 -4.00e-01  8.92e-17  1.08e-01
----------------------------------------------------------------------------
Status: Solved
Timing: Solve time: 1.08e-01s
	Lin-sys: avg # CG iterations: 3.84, avg solve time: 7.58e-06s
	Cones: avg projection time: 6.47e-05s
	Acceleration: avg step time: 4.73e-05s
----------------------------------------------------------------------------
Error metrics:
dist(s, K) = 3.8501e-07, dist(y, K*) = 2.9020e-09, s'y/|s||y| = 1.0184e-08
primal res: |Ax + s - b|_2 / (1 + |b|_2) = 1.4951e-08
dual res:   |A'y + c|_2 / (1 + |c|_2) = 6.9402e-08
rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 5.4179e-09
----------------------------------------------------------------------------
c'x = -0.4000, -b'y = -0.4000
============================================================================
0.39999997855290215

lpawela · 2019-03-14T11:21:22Z

@benkj @pgawron please add printlnt(J) after line 8 in convex.jl and show the output.

lpawela · 2019-03-14T11:34:28Z

I can reproduce w somewhat similar behavior when I set eps=1e-4 in the SCSSolver(...) call. @benkj @pgawron could you set eps=1e-7 just to be sure?

benkj · 2019-03-14T12:19:37Z

eps=1e-7 in SCSSolver() seem to fix the bug for me.

lpawela · 2019-03-14T12:28:07Z

@pgawron could you confirm this? I wonder why the default setting doesn't work. @benkj did you compile julia or downloaded the release? Maybe in the manually compiled version some defaults are different.

benkj · 2019-03-14T12:29:03Z

I have a downloaded julia for OSX. All packages are installed with Pkg.add

* 'master' of https://github.com/ZKSI/QuantumInformation.jl: Fix iitis#53

benkj mentioned this issue Mar 13, 2019

calculate diamond norm using dual problem #54

Merged

pgawron added the bug label Mar 13, 2019

lpawela added this to the v0.5 milestone Mar 14, 2019

lpawela closed this as completed in b619397 Mar 14, 2019

benkj added a commit to benkj/QuantumInformation.jl that referenced this issue Mar 14, 2019

Merge branch 'master' of https://github.com/ZKSI/QuantumInformation.jl

15fd07b

* 'master' of https://github.com/ZKSI/QuantumInformation.jl: Fix iitis#53

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diamond distance is not symmetric #53

diamond distance is not symmetric #53

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diamond distance is not symmetric #53

diamond distance is not symmetric #53

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