## Quantifying quantum speedups: improved classical simulation from tighter magic monotones

Code accompanying the manuscript PRX Quantum **2**, 010345 (2021) (arXiv:2002.06181).

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The code implements several of the measures considered in the manuscript, in particular the robustness of magic $\mathcal{R}$, the generalised robustness of magic $\Lambda^+$, and the dyadic negativity $\Lambda$. The functions take two arguments: one is the density matrix `rho`

, and one is a list of pure stabiliser states in the given dimension, given as a matrix `T`

whose columns are the state vectors. The `T`

matrices for 1-4 qubits (expressed in the computational basis) are provided above. Each function returns the value of the measure as well as the optimal decomposition (as a `k`

-dimensional vector in the case of the robustness measures or a `k`

x`k`

-dimensional matrix in the case of the dyadic negativity, where `k`

is the number of stabiliser states in the given dimension). The implementation requires CVX.

### Robustness of magic

```
function [cvx_optval, x] = RobMag(rho, T)
k = size(T,2);
cvx_begin quiet
variable x(k)
rho == T*diag(x)*T'
minimize norm(x,1)
cvx_end
end
```

### Generalised robustness of magic

```
function [cvx_optval, x] = RobMagG(rho, T)
k = size(T,2);
cvx_begin sdp quiet
variable x(k) nonnegative
rho <= T*diag(x)*T'
minimize sum(x)
cvx_end
end
```

### Dyadic negativity

```
function [cvx_optval, X] = Lambda(rho, T)
k = size(T,2);
cvx_begin quiet
variable X(k,k) complex
rho == T*X*T'
minimize sum(sum(abs(X)))
cvx_end
end
```