Lattice Architecture Circuits

Lattice Architecture Circuits and Movies

These circuits and diagrams correspond to the work presented in "Noise Threshold for a Fault-tolerant Two-dimensional Lattice Architecture" by Krysta M. Svore, David P. DiVincenzo, and Barbara M. Terhal.

Each movie presented assumes that the first prepared ancilla always fails verification and the second and third ancillas always pass verification.

The a_pi/2 - and a_pi/4 - preparation movies assume that we must always apply the correction involved in the T or S gates. This may or may not be necessary, but we must assume that it needs to be done and allow for the appropriate time and space to do so.

Circuits

Error-Correction Circuitry

[[7,1,3]] Error-Correction Routine: Circuit (jpg)
Preparation (G) and Verification (V): Circuit (eps) Circuit (pdf)
Preparation (G) and Verification (V) with time steps: Circuit (jpg)
Syndrome Extraction for X-error correction (S_X): Circuit (eps) Circuit (pdf)
Syndrome Extraction for Z-error correction (S_Z): Circuit (eps) Circuit (pdf)

Circuitry for Implementation of S and T Gates

Implementation of S and T gate: Circuit (eps) Circuit (pdf)

Legend for Movies

Coloring

Red indicates data qubits. They are labeled d1--d7. In a two-qubit gate, we label them as dia and dib, for i=1,...,7, where a and b indicate logical qubits a and b.
Blue indicates verification qubits. They are labeled v1,v2,v3. In a two-qubit gate, we label them as via and vib, for i=1,...,7, where a and b indicate logical qubits a and b. During special ancilla preparation for the S and T gates, we label them as vid and via, indicating verification of data qubits (d) and verification of ancilla qubits (a), for i=1,...,7.
Green indicates ancilla qubits. They are labeled a1--a7. In a two-qubit gate, we label them as aia and aib, for i=1,...,7, where a and b indicate logical qubits a and b.

Location Symbols

Location	Symbol	Location	Symbol
CNOT	controltarget	CZ
SWAP		Hadamard
CNOT then SWAP	controltarget	CZ + SWAP
Wait	Nothing occurs on the qubit	Waitm	Nothing occurs on the qubit
X-measurement		Z-measurement
\|+>-preparation		\|0>-preparation
a_pi/2 - preparation (for S gate)		a_pi/4 - preparation (for T gate)