Target-adapted chains and the buffer

Fix an integer $n\ge 1$. Install a chain of qubit registers $Q_0,\dots ,Q_n$ at

Here $Q_0$ is a temporary register at $A$; $Q_n$ is the input register at $B$. A separate qubit $P$ is the input at $A$. Initialize $Q_0,\dots ,Q_{n-1}$ in $|0⟩$.

Let

During the inbound interval of length $D$, use $n$ successive content exchanges

each of duration $D/n$, realized by opposite causal carriage of the two contents along the regular axial segment. Their physical dimensionless speed is $v_{\ast }/4<1$.

The unknown qubit reaches $A$ by

Both matter qubits then remain stored at $A$. Destroy the two clock qubits in two local slots of duration $1/64$, from $\tau =-1/32$ to $0$. The complete record is available at $\tau =0$.

Wait until $\tau =1/16$. Run the nine event-code gates, three local CNOTs implementing ${\mathrm{SWAP}}_{P,Q_0}$, and the classical-record controlled gate ${Z_P}^{a_1}$. The thirteen local slots each have duration $1/208$, so they finish at $\tau =1/8$.

Finally move $Q_0$'s content outward by the $n$ successive exchanges

Allow duration $D/n$ per outbound stage. Its first half copies the five-bit classical word

into the next site's blank record buffer by five sequential classical CNOTs. Each copy slot has positive duration $D/(10n)$. The second half carries the qubit exchange and the copied record over the segment of length $L/n$. The communication speed is $v_{\ast }/2<1$.

All records and payloads arrive by

Wait at the destination ports until ${\tau }_{\mathrm{out}}$. Records at earlier sites are retained, not reset.