Pan Jianwei team of University of science and technology of China put forward the scheme of fault-tolerant all-optical quantum repeater
In 2019, academician Pan Jianwei of the university of science and technology of china and his colleagues Chen yuao and Xu feihu achieved the principle verification of all-optical quantum repeaters for the first time in the world[1], which in principle makes quantum memory no longer a necessary condition for building quantum repeaters, and opens up new ways for the research of practical quantum repeaters.
On this basis, Pan Jianwei, Chen Yuao, and others published "Loss-tolerant all-photonic quantum repeater with generalized Shor code" in the latest issue of Optica, an authoritative journal of international optics[2]. This achievement is an important step towards practical all-optical quantum repeaters, enriching the study of quantum error correction codes.
Advantages and disadvantages of all-optical quantum repeater
In the process of long-distance quantum communication, the quantum state transmitted by the channel tends to decrease exponentially with the increase of the communication distance, which greatly limits the effective transmission distance of quantum communication. how to achieve long-distance quantum communication has always been a hot topic in international research. there are currently two main solutions.
One is to use satellites to expand quantum communication distances in outer space, which is almost vacuum and has very little quantum signal loss; mozi has successfully verified the feasibility of this scheme. the second is the use of quantum repeaters in optical fiber networks to divide a long-distance fiber channel into a multi-segment short channel, so that the quantum signal no longer decays exponentially with the increase of distance, thereby expanding the quantum communication distance.
Traditional quantum repeaters require three essential technologies based on entanglement exchange, entanglement purification, and quantum storage.
However, current quantum storage performance is limited, and it will take time to realize a practical quantum repeater. the all-optical quantum relay scheme can theoretically implement quantum repeaters without quantum storage, providing another feasible solution in principle for the use of quantum repeaters to achieve long-distance optical fiber quantum communication networks.
All-optical quantum repeater (apqr) eliminates the need for quantum memory by connecting the repeater node with the graph state (RGS) of the all-optical repeater. For practical apqr, an essential requirement is the robustness of RGS to photon loss.
However, in previous proofs of principle, the Greenberger-Horne-Zeilingerr (GHZ) state was used as RGS (Naked GHZ RGS), which could disrupt the repeater scheme because the GHZ state cannot tolerate photon loss. Therefore, to date, there is no practical fault tolerance scheme to protect APQR from photon loss.
To this end, Pan Jianwei's team proposed a new fault-tolerant scheme, applying the generalized Shor code to RGS, and experimentally verifying it with existing technology.
Fault-tolerant all-optical quantum repeater scheme
To protect quantum information from environmental noise, quantum error correction codes (QECC) play an important role in many areas of fault-tolerant quantum information processing. Quantum parity codes (QPCs) have been widely studied to protect quantum states, especially in quantum networks, because of their strong robustness to the loss of physical qubits. As a representative of QPC, the nine-qubit Shor code designs a combination of a three-qubit bit-flip and a phase flip code that encodes a single qubit state |φ⟩ = α|0⟩ + β|1⟩ into a logical state:
where (|000⟩±|111⟩) represents a code block.
If a physical qubit is lost, the block of code affected by the loss becomes a mixed block of code, but the effect is local and limited to that block. As long as there are photons in the block of code affected by photon loss, the overall entanglement structure of the three blocks of code will not be broken, and the entanglement between the physical qubits in the remaining two complete blocks of code will continue. Thanks to strong loss tolerance, nine-qubit Shor codes can be used to protect bare GHZ RGS from photon loss.
Specifically, since the three code blocks of the nine-qubit Shor code are arranged in a GHZ type structure, it is natural to apply them to the bare GHZ RGS and encode each qubit of the GHZ state into a logical qubit with a code block:
|0⟩↦|0⟩l=1/√2(|000⟩+|111⟩)
|1⟩↦|1⟩l=1/√2(|000⟩−|111⟩)
As a result, the bare GHZ RGS is encoded into a nine-qubit Shor code state with strong loss tolerance.
Encoded n-logic qubit RGS can be seen as a generalized Shor code state with n blocks of code. The effects of photon loss will be limited to a given loss-affected logical qubit, which will not break the overall entangled chain encoding the RGS. In addition, since it is encoded by a full-featured QECC, the encoded RGS naturally has the robustness to resist arbitrary single-qubit errors.
Photon loss tolerance successfully verified
In this work, by manipulating a ten-photon interferometer, the team prepared a nine-qubit Shor code and studied the feasibility of their APQR fault tolerance scheme.
To verify the nine-qubit Shor code they prepared, they encoded and read out six different states and verified its robustness to qubit loss and its ability to recognize arbitrary single-qubit errors. They then applied QPC to bare GHZ RGS, prepared partially encoded RGS, and demonstrated the most simplified entanglement connection process for fault-tolerant APQR.
Fig. 2 Experimental apparatus and its characterization. (a) Schematic diagram of the experimental apparatus. The order of the entanglement sources is arranged according to the circuit in Figure 1(b). SC−YVO4 and TC−YVO4 represent space- and temporally compensated yttrium-yttrium vanadate crystals, respectively. (b) The reconstructed density matrix ρ of the code block in the first quantum encoder. Spaces and boxes indicate ideal and experimental results, respectively. (c) Logical Shor code state | D⟩l is in the | The polarization distribution in the H/V ⟩ base.
Ultimately, the effectiveness of the fault-tolerant scheme was verified. In addition, based on the prepared nine-qubit Shor code, the loss tolerance of the encoded RGS when a photon loss occurs at the third logical qubit by measuring the entanglement between two complete logic qubits. The results show that the entanglement between the two logical qubits can be well maintained in an encoded RGS affected by photon loss, so the loss tolerance of the encoded RGS is also verified.
As shown in Figure 3(b), the overall fidelity is 0.64±0.05 at no loss, 0.67±0.05 at a single-photon loss, and 0.71±0.05 at a two-photon loss. When the photon loss occurs continuously in the third logic qubit, the entanglement fidelity of the two photons of the two complete logic qubits remains good, indicating the effectiveness of the entanglement protection of the encoded RGS fault tolerance scheme.
Figure 3 is used to illustrate the results of a fault-tolerant APQR scenario. (a) Results of verifying the effectiveness of fault tolerance schemes. (b) Encode the RGS | Results of the G⟩l loss tolerance study.
Link:
[1]https://www.nature.com/articles/s41566-019-0468-5
[2]https://opg.optica.org/optica/fulltext.cfm?uri=optica-9-2-152&id=469063
