strong simulation / bitstring probability

[ajavadia]

Problem or motivation

Thanks for developing this nice simulator.

I would like to propose strong simulation as a useful feature. Currently I use Quizx or TSim for this task, but since Clifft seems to be faster than those (at least at sampling), it would be great if this feature was available too.

The task is to query the exact probability of a specified measurement outcome $x$, i.e. $p(x)=|\langle x|\psi\rangle|^2$. This would make Clifft useful not only as a weak simulator, but also for tasks such as validating individual output probabilities.

Proposed solution

This could be exposed with an interface like clifft.amplitude(program, bitstring) or clifft.probability(program, bitstring).

A possible route is to propagate the computational-basis effect $\langle x|$ backward through the Clifford frame and projector/Pauli structure, reducing the query to an overlap with only the active state $|\phi\rangle_A$.

Alternatives considered

In tsim this would be via probability_of.

[bachase]

Hi @ajavadia -- great suggestion and I agree it shouldn't be too challenging to add.

Clifft currently supports an EXP_VAL instruction that lets you query the expectation value of a a Pauli string at an arbitrary point in the circuit. For small enough circuits, we could decompose the bitstring in terms of Pauli strings. But we can do better in the general case by tracking the bitstring through the frames directly as you note.

From an implementation perspective, based on your use cases/workflows:

1. Do you typically want to query many independent bitstrings at once? Thinking of the right interface to batch the query most efficiently.
2. Do you ever want to query the bitstring mid-circuit? That was why we added EXP_VAL as an instruction instead of a query at the end of the simulation. But I can also imagine its cleaner for users to not "dirty" their circuit with these queries.

[ajavadia]

1- Yes it would be very useful to query probabilities of many independent bitstrings at once (an example usecase would be computing cross entropy of some sampled measurement outcomes).

2- For my usecase I only need this at the end of the circuit. I guess one could compute an outcome probability for any set of measurements in the circuit regardless of where they are, but having it work for final measurements is already a great start.