quilc charges double for `RY(pi)`

[braised-babbage]

A single RY gate translates to two RX gates, when we could get away with just one.

QUIL> (print-parsed-program (compiler-hook (parse-quil "RY(pi) 0") (build-nq-linear-chip 2)))
RZ(2.2216554087607694) 0                # Entering rewiring: #(0 1)
RX(pi/2) 0
RZ(pi) 0
RX(-pi/2) 0
RZ(2.2216554087607694) 0
HALT                                    # Exiting rewiring: #(0 1)
NIL

[braised-babbage]

Just a couple of notes from inspection of *compiler-noise*

• The addressor can currently do no better than translate RY(pi) to use two RX gates.
• The compressor, when doing algebraic rewriting, tries peephole optimization of the two RX program against peephole optimization of its decompiled equivalent. The decompilation uses the Euler compiler, but here the specific choice of translation (in apply-translation-compilers) is simply the first that works. This means the last definition from euler-compile.lisp, namely euler-zyz-compiler.
• We can't recover RY structure during algebraic rewriting, so we the only viable peephole option for decompiled code is to expand the above RY gate into another XZX triple. This has the same fidelity as the original sequence, and the compressor breaks the tie by picking it.

Here are three ways to get the shorter decomposition (there may be more):

1.

(define-compiler Y-to-ZXZ ((y-gate ("RY" (#.pi) q)))
  (inst "RZ" '(#.-pi/2) q)
  (inst "RX" '(#.pi) q)
  (inst "RZ" '(#.pi/2) q))

will allow the addresser to emit better code for the chip. The compressor will subsequently respect this, since it only uses decompiled code if it's no worse than the original.

2. (Not suggesting this is a good idea) If we get rid of all but euler-zxz-compiler, then the compressor uses this for decompilation, which happens to be the preferred method for this chip.

3. We could add some rewriting rules that are tailored to standard patterns that occur in compiler outputs (e.g. a ZXZXZ sequence) and check conditions on the angles to reduce these to known, simpler sequences. I am not a huge fan of this, but it's at least of the flavor of "adding more information" to quilc.

[braised-babbage]

For what it's worth, I don't view the current behavior as being a real problem, in the sense that I know that on typical programs the overhead will not be a big deal (I nice guarantee from any flavor of Euler decompilation). However, it's a special enough case that people will naturally try it, so it would be nice for quilc to get it right. I think the way in which things go awry in the above example is interesting in the sense that it's a reminder of how some of this machinery fits together, and where things can get lost at the seams.

[markasoftware]

I ultimately agree that it doesn't seem to be a major issue -- usually the ZXZ decomposition is not applicable.

[markasoftware]

For anyone interested in how the compiler chooses which Euler decompositions to support: At the time the chip-spec is constructed, the compiler tries to find the best way to compile an arbitrary gate down to native gates (see compute-applicable-compilers and find-shortest-compiler-path). This happens to be the ZYZ Euler decomposition, followed by an RY-to-XZX decomposition to eliminate the inner Y.

[markasoftware]

After thinking more, adding a Y-to-ZXZ compiler as Erik suggested seems the best solution in my eyes. However, since Y-to-ZXZ is actually a special case of the Euler ZXZ transform, it may be valuable to add a general mechanism for creating specialized versions of a compiler. Eg:

(define-compiler FOO-to-BAR
    ((my-gate ("FOO" (theta) q))
     :specialize '((FOO-to-BAR-2pi (("FOO" (#.2pi) q)))
                   (FOO-to-BAR-pi (("FOO" (#.pi) q)))))
  (inst "BAR" (/ theta 2) q))

Would also define compilers FOO-to-BAR-2pi and FOO-to-BAR-pi, with outputs precomputed according to the input gates specified.

Then one could specialize the Euler compilers to add special cases for RY(pi) and similar.

The nativization will pick up the specialized compilers because their output may lie in the target gateset even when the more generic compiler's output does not.

Any thoughts?