mehulpandita / sg-grand-challenge-final
Publicq register, and rebased to
the H2 native gateset before submission.EP must use the sparse inter-degree
Carleman couplings.
Thus the mathematical algorithm and terminating path sum are
multidimensional, but the present explicit pytket multiplexor is
only the scalar small-instance circuit. A scalable non-scalar
implementation requires structured sparse/arithmetic block
encodings for the blocks; this notebook does not hide that
additional circuit-design requirement.AP by a
controlled single-qubit rotation, while its complex phase is
attached to the same branch. The selected block of
is implemented in two pieces:
for . The coefficient rotation is followed by the
one-step system shift. This is the explicit joint block encoding
of ; it is not an oracle placeholder.
Path value activates exactly the first EP stages. A
common final then produces in circuit-time
order.
PREPARE(J,Q) loads
A diagonal operation supplies . After SELECT, the
inverse preparation makes the amplitude equal to
the weighted sum of all selected paths. Postselecting every
operator ancilla in zero gives
S, then jointly prepare J,Q.J,Q so the different finite-sum terms interfere.J,Q and every operator ancilla in zero.S=0 and reconstruct .EP ancillas, and one P ancilla. The current pytket
implementation deliberately compiles controlled multiplexors
explicitly. It is a rigorous small-instance demonstration, not a
claim that dense multiplexor synthesis is asymptotically optimal;
a larger solver would replace it with sparse arithmetic/oracle
constructions that exploit the banded Carleman structure.Rz, PhasedX, and ZZPhase
rotations; it does not execute a Clifford+ gate set. A
-count is therefore meaningful only after choosing a
fault-tolerant rotation-synthesis precision.
For this estimate, the fully decomposed logical circuit is rebased
to CX, Rz, and Rx. Angles that are multiples of one half-turn
are Clifford operations. Odd quarter-turns require one exact
or . Every remaining arbitrary axial rotation is
synthesized independently using the standard leading-order
estimate
This is a transparent planning estimate, not a compiler-certified
optimum: the additive term, cancellations
between neighboring rotations, magic-state factory overhead, and
surface-code cost are not included.cAEP0 cAP cJ cQ cS
0 0 000 0 *
cS=0.
In the 1,000-shot H2-1E run, the exact target key
0 0 000 0 0 occurred 433 times. Thirteen further shots passed
all operator/LCU postselections but ended in cS=1. Thus 446 shots
were accepted and 433 were target events.
The high conditional fraction shows that the
shape inside the accepted subspace is close to the intended first
Carleman component. However, the total target probability is
suppressed from the ideal to . Increasing shots
narrows statistical uncertainty, but shot noise alone cannot
explain this discrepancy. The recorded data do not isolate
emulator noise from compilation or implementation effects.page_size to embed more in the static export.