Quantum Bayesian Networks

March 5, 2019

The iSWAP, sqrt(iSWAP) and other up-and-coming quantum gates

Filed under: Uncategorized — rrtucci @ 8:28 am

The writing is on the wall. The engineers behind the quantum computers at Google, Rigetti, IonQ, etc., are using, more and more, certain variants of the simple SWAP gate, variants that are more natural than the SWAP for their devices, variants with exotic, tantalizing names like the iSWAP, and sqrt(iSWAP). In the last day or two, I decided to bring Qubiter up-to-date by adding to its arsenal of gates, a gate that I call the SWAY. SWAY is very general. It includes the humble SWAP and all its other variants too. So, what is this SWAY, you ask?

Let \sigma_X, \sigma_Y, \sigma_Z be the Pauli Matrices.

Recall that the swap of two qubits 0, 1, call it SWAP(1, 0), is defined by

SWAP = diag(1, \sigma_X, 1)

NOTE: SWAP is qbit symmetric, meaning that SWAP(0,1) = SWAP(1,0)

We define SWAY by

SWAY = diag(1, U2, 1)

where U2 is the most general 2-dim unitary matrix satisfying \sigma_X U2 \sigma_X=U2. If U2 is parametrized as

U2 = \exp(i[ \theta_0 + \theta_1\sigma_X + \theta_2\sigma_Y + \theta_3\sigma_Z])

for real \theta_j, then

\theta_2=\theta_3=0.

NOTE:SWAY is qbit symmetric (SWAY(0,1)=SWAY(1,0)) iff \sigma_X U2 \sigma_X=U2 iff \theta_2=\theta_3=0

The Qubiter simulator can now handle a SWAY with zero or any number of controls of type T or F. Very cool, don’t you think?

Here is a jupyter notebook that I wrote to test Qubiter’s SWAY implementation

https://github.com/artiste-qb-net/qubiter/blob/master/qubiter/jupyter_notebooks/unusual_gates_like_generalized_swap.ipynb

2 Comments »

  1. IBM’s quantum volume idea is several years old. This science journalist is pretty dopey, presenting 2 year old news as if it just happened.

    Comment by rrtucci — March 5, 2019 @ 9:59 am


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