Add analytical decomposition for synthesis of single qubit unitaries generated by Clifford and T gates.

[tanujkhattar]

Is your feature request related to a use case or problem? Please describe. One of the promising gatesets for fault tolerant regime is the Clifford + T gateset, where executing T gates is significantly slower than executing Cliffords and therefore it's often desired to minimize the T-count of the compiled circuits. Cirq currently does not have any analytical decompositions for synthesizing arbitrary 1/2q unitaries in terms of Clifford + T gateset.

Describe the solution you'd like Fast and efficient exact synthesis of single qubit unitaries generated by Clifford and T gates provides an efficient algorithm for synthesis of arbitrary single qubit rotations in terms of Clifford + T gates. The feature request is to implement the described algorithm as an analytical decomposition in Cirq

What is the urgency from your perspective for this issue? Is it blocking important work? P2 - we should do it in the next couple of quarters

cc @augustehirth This would need documentation once we get this done.

[tanujkhattar]

A related recent paper for decomposing arbitrary n-qubit unitaries, which is probably out of scope for this feature request but can be done as a follow-up if we have enthusiastic contributors.

https://link.springer.com/article/10.1007/s11128-020-02816-0

[aksaw]

I'd be very interested in giving this a shot. From cirq cync, it seems that this should be a good first issue given I'm comfortable with the math but not extremely familiar with the cirq library.

[NoureldinYosri]

@aksaw Is there progress on this? I will need this soon.

[aksaw]

Yes, I had started working on this already. I can try to finish it up in the next couple of weeks.

[tanujkhattar]

@aksaw Are you still working on this?

[mhucka]

@aksaw Are you still interested in working on this?

[aksaw]

Sorry, this slipped through the cracks. I have too much on my plate and will not be able to work on this at the moment.