Surface Code Quantum Communication

Quantum communication typically involves a linear chain of repeater stations, each capable of reliable local quantum computation and connected to their nearest neighbors by unreliable communication links. The communication rate of existing protocols is low as two-way classical communication is used. By using a surface code across the repeater chain and generating Bell pairs between neighboring stations with probability of heralded success greater than 0.65 and fidelity greater than 0.96, we show that two-way communication can be avoided and quantum information can be sent over arbitrary distances with arbitrarily low error at a rate limited only by the local gate speed. This is achieved by using the unreliable Bell pairs to measure nonlocal stabilizers and feeding heralded failure information into post-transmission error correction. Our scheme also applies when the probability of heralded success is arbitrarily low.

Figure 1

A surface code logical qubit. Stabilizers $ZZZZ$ ($XXXX$) are associated with the data qubits (open circles) around each face (vertex). Syndrome qubits (dots) measure stabilizers using the indicated sequences of gates. Logical operators $Z_L,X_L$ connect opposing boundaries.

Figure 2

Monolithic surface code quantum communication. (a) Monolithic lattice of qubits with source logical qubit $|{\Psi }_L⟩$, initial measurement pattern for the intermediate region, and destination area initialized to $|0_L⟩$. (b) Circuits used in parallel to prepare for stabilizer measurement. Numbers indicate the timing of gates. (c) Intermediate stabilizer measurements. (d) Final stabilizer measurement and communicated state.

Figure 3

Repeater-based surface code quantum communication. The qubit pattern in each quantum repeater (ovals) is for $d=3$. The pattern width is independent of $d$.

Figure 4

If the probability of heralded success is sufficiently high, qubit $A$ can be interacted with its neighboring data qubits and measured before the entangling pulse or photon even reaches its destination. Error correction takes care of heralded failures, including loss during transmission.

Figure 5

Average number of error correction rounds before logical failure versus Bell pair error rate $p_B$ and code distance. Inset: Magnification of high $p_B$ region.

Figure 6

Average number of error correction rounds before logical failure versus loss and code distance.

Figure 7

Probability of logical error per link for a variety of loss and Bell error rates.