# Inconsistent results between Yao and Qiskit

**URL:** <https://discourse.julialang.org/t/inconsistent-results-between-yao-and-qiskit/63363>\
**Category:** Quantum\
**Tags:** quantum-circuits\
**Created:** [June 22, 2021, 1:15pm UTC](https://discourse.julialang.org/t/inconsistent-results-between-yao-and-qiskit/63363 "2021-06-22T13:15:29Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![rmedinar](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rmedinar/32/25263_2.png) [@rmedinar](https://discourse.julialang.org/u/rmedinar)\
**Post date:** [June 22, 2021, 1:15pm UTC](https://discourse.julialang.org/t/inconsistent-results-between-yao-and-qiskit/63363/1 "2021-06-22T13:15:29Z")

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Hi everyone. I have been trying to simulate the growth of entanglement entropy in random unitary circuits using Yao for a while now. When comparing with old results from my Qiskit code I found out about some inconsistencies in the results, even though I basically translated my Qiskit code to Yao. Moreover, when sampling over unitaries, I get NaNs for the entropy. I think this could be associated with some precision issues but I don’t know how to tackle them. Let me explain with a small example code:

```julia
using Yao, YaoExtensions
using Random
using QuantumInformation, SharedArrays, Statistics, Distributed

function entropy(psi, n, nA)
    state = svdvals(reshape(psi, (2^nA, 2^(n-nA)))) .^ 2
    return -sum( state.*log.(state) )
end

# Circuit definition: 1.) Random single-qubit rotation gates and 2.) Controlled-Z gates as entanglers
# I used periodic boundary conditions in this particular case

function ruc(n::Int, θ::Array{Float64, 1})
    U = chain(n)
    append!(U, chain(n, put(n, loc=>chain(rand(rng,randG)( θ[loc] ))) for loc = 1:n))
    for j = 1:n-1
         append!(U, chain(n, cz(n, j, j+1)))
    end
    append!(U, chain(n, cz(n, 1)))
    return U
end

# pmax = circuit depth, n = num of qubits, nA=2, and eps controls the angles of
# the single-qubit rotation gates

function entropyEvolution(pmax::Int, n::Int, nA::Int, eps::Float64 )
    ψ = Yao.uniform_state(n)
 
    ent = Float64[]
    θ = (2*rand(n) .- 1)*(π*eps)
    
    for t in 1:pmax
        
        U = ruc(n, θ)
        ψ |> U
        
        push!(ent, entropy(state(ψ), n, nA))
    end
   ent
end

test_cz = SharedArray{Float64, 2}(100, p);
test_cz_ϵ = SharedArray{Float64, 2}(100, p);

@distributed for i in 1:100
    test_cz[i,:] = entropyEvolution(p, 10, 2, 1.0)
end

@distributed for i in 1:100
    test_cz_ϵ[i,:] = entropyEvolution(p, 10, 2, 0.05)
end

```

After running this code I get something like this for the entanglement entropy  
 ![Screenshot 2021-06-22 at 15.12.08](https://global.discourse-cdn.com/julialang/original/3X/9/1/91ed99d0f30bf8facff890d853b7ffc6c547c9c9.png)  
However, running the same code in Qiskit doesn’t show such oscillations in the entropy as well as no NaN values. Am I missing something here? Any help in immensely appreciated.

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**Author:** ![Roger-luo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/roger-luo/32/3399_2.png) [@Roger-luo](https://discourse.julialang.org/u/Roger-luo)\
**Post date:** [June 29, 2021, 12:33am UTC](https://discourse.julialang.org/t/inconsistent-results-between-yao-and-qiskit/63363/2 "2021-06-29T00:33:14Z")

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from a first glance, your `randG` seems to be something missing, I assume it’s a random gate set. not sure which gate set it is, but if you are not using a constant gate set, then this could be the problem since you aren’t actually sampling random distributed arbitrary unitaries but just a list of gates.

But again (like your previous questions…), your code doesn’t run, I’m not sure where does the NaNs actually come from.

* * *

update: by setting `const randG = [Rx, Ry, Rz]` and `p = 10` I can run your code, but this doesn’t give me NaNs, the results do not contain `NaN`, I’m not sure about the oscillations due to unfamiliarity of what you are doing however

```julia
julia> any(isnan.(test_cz_ϵ))
false

julia> any(isnan.(test_cz))
false

```

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**Author:** ![rmedinar](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rmedinar/32/25263_2.png) [@rmedinar](https://discourse.julialang.org/u/rmedinar)\
**Post date:** [July 16, 2021, 8:40am UTC](https://discourse.julialang.org/t/inconsistent-results-between-yao-and-qiskit/63363/3 "2021-07-16T08:40:04Z")

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Sorry again, I seem to always forget to add some variable declaration so that the code runs without issue. At the moment, I don’t have any explanation for the oscillations in the entanglement. Regarding the NaNs, I definitely continued getting them in my simulations. Now, since their appearance is always at a small circuit depth, I thought this could be associated with numerical precision. For example, if I get two pure build-in states in Yao:

```julia
using Yao, LinearAlgebra

function entropy(psi, n, nA)
    state = svdvals(reshape(psi, (2^nA, 2^(n-nA)))) .^ 2
    return -sum( state.*log.(state) )
end

ψ1= Yao.zero_state(12)
ψ2 = Yao.uniform_state(12)

@show entropy(ψ1, 12, 2)
@show entropy(ψ2, 12, 2)

```

I get a NaN as result in the first case and a very small negative value for the second state. As a simple test, I just redefined the entropy function such that only singular values above a certain threshold are considered, which luckily seems to fix the NaN issue.

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**Author:** ![1115](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/1115/32/4465_2.png) [@1115](https://discourse.julialang.org/u/1115)\
**Post date:** [April 24, 2022, 5:02pm UTC](https://discourse.julialang.org/t/inconsistent-results-between-yao-and-qiskit/63363/4 "2022-04-24T17:02:11Z")

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Did it fix the oscillation problem for you?

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<div class="post-metadata">

**Author:** ![rmedinar](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rmedinar/32/25263_2.png) [@rmedinar](https://discourse.julialang.org/u/rmedinar)\
**Post date:** [May 4, 2022, 3:27pm UTC](https://discourse.julialang.org/t/inconsistent-results-between-yao-and-qiskit/63363/5 "2022-05-04T15:27:56Z")

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Yes, it did 😌 (sorry for the late reply)