2021 Quantum Hackathon

Quantum Hackathon Korea 2021

Entanglement Swapping Protocol

 

1. Abstraction

 In quantum physics there is a peculiar phenomenon called quantum entanglement, which is a close connection between qubits that makes them react to the change of the other’s state instantaneously. This property was originally proposed from Einstein, Bohr, and many others. Although it is such a counterintuitive phenomenon, if this is possible to exploit, it could potentially revolutionize our methods of communication.

 In theory, quantum entanglement can happen between any two qubits in the world. Of course in reality, the further the two qubits are the less accurate this phenomenon will occur, due to various disturbance present in the gap between them.

 Therefore, to avoid such inaccuracies, we use Quantum Teleportation. By stacking multiple entangled qubits together in a range they can be reliably entangled, it is possible to connect those entanglements to achieve connection between the first qubit and the last. This is a very rough description of quantum teleportation, which we will explore further into our paper. 

 Our first objective is to build an entanglement swapping protocol for four-qubit system. This is to check if our small unit of teleportation is operational.

 Our second objective is to expand this protocol into a 10-qubit system. This is to check if expansion of the protocol is possible, and to analyze how it affects the result.

 Our third objective is to compare two quantum hardware available in the market. This is to check which hardware is better suited for quantum teleportation protocol we built.

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2. Implement Entanglement Swapping Protocol Circuit

Problem 1) Design entanglement swapping protocol for 4-qubit system

 Firstly, we built a four-qubit circuit. In the circuit, each qubits have the name q0, q1, q2, q3. In this protocol, we assume q0 and q3 have never met. So, we make quantum entanglement between q0 and q1, and between q2 and q3. Let ‘s say entanglement state between q0 and q1 is |e1>, and q2 and q3 is |e2>. Then |e1> and |e2> can be represented as follow.

Let’s denote each qubit in A, B, C and D. Then, we can represent final state as follow.

 From this result, we were able to find out which gate should be applied to q0 and q3 to perform Entanglement Swapping Protocol. If q1 is measured by 1, Z gate should be applied to q0. So, we use Controlled Z gate between q1 and q0. If q2 is measured by 1, X gate should be applied to q3. So, we use Controlled NOT gate between q2 and q3.

When this process finish, we can see Entanglement Swapping Protocol. This means that even if q0 and q3 do not contact, q0 and q3 are always measured at the same value.

Problem 2) Extend the protocol up to 10 qubits

 Before extending to 10 qubits, we performed the protocol for 6 qubits. Firstly, we build the 6 Qubit circuit in the similar way as Problem 1. Compared to Problem 1, we created an |e3> state in which q4 and q5 were entangled. Then we can represent the state before the farthest two points will be measured as follow.

Let’s denote each qubit in A, B, C, D, E and F. To find out the state of the farthest two points (A and F), we wrote qubits state in the following format : |BCDE>(|AF> + |AF>)

 From this result, we can find out that if q2 or q4 qubit is measure by 1, we should apply NOT gate to q5 and if q1 or q3 qubit is measured by 1, we should apply Z gate to q0. So, we apply CNOT gate from q2 and q4 to q5 and apply Controlled Z gate from q1 and q3 to q0. When this process finish, we can see 6-Qubit Entanglement Swapping Protocol. This means that even if the farthest two points do not contact each other, q0 and q5 are always measured at the same value. From this result, we can find out the pattern of the protocol. To extend the protocol, after makes an entanglement, an odd-numbered qubit applies Controlled Z gate to the first qubit. Similarly, an even-numbered qubit applies CNOT gate to the last qubit.

According to this process, we can extend the protocol up to 10 qubits. Furthermore, it can be applied on even number of qubits.

 

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3. Additional Research

Currently there are two hardware available in the market.

1.IBM Quantum Computer uses superconductivity in temperature as low as 100K to enact quantum environment.

2. IonQ Quantum Computer traps atoms in 3D space to produce naturally occurring quantum systems.

It is natural to think mechanism difference between the two hardware will yield subtly different result. Our team was curious which hardware produced more accurate result in the case of Entanglement Swapping protocol. The result of error rate is as follows.

	4-Qubit	6-Qubit	8-Qubit	10-Qubit
IBM	20.508%	50.586%	48.145%	48.926%
IonQ	9.668%	19.824%	15.984%	18.551%

 Contrary to our expectation that the difference would be subtle, the error rate was close to 2 times larger in IBM compared to IonQ. This result clearly shows ionic trap hardware is preferrable when entangling qubits with our devised protocol. The IBM error rates shows us close to 50% starting from 6 qubit entanglement, which shows quantum teleporting protocol is not currently viable in IBM quantum computer.

 Another interesting characteristic was the error rate yielded similar result starting from 6 qubits. We have confirmed this pattern to the extent of our provided qubits(IBM: 15 , IonQ : 11). Although the number of our sample is trivial at best, it illuminates a possible pattern that quantum teleportation accuracy is quite resilient to the number of qubits used. This assumption, if correct, leads to the conclusion that quantum teleportation is a solid candidate for quantum computing based communication.

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4. Conclusion

   Our purpose in this paper was to devise a quantum teleportation protocol that could be applied in quantum networking. The reason this technology is noteworthy is because it does not lose its quantum property when relaying information. Although our research results show relatively high error rates, this is due to the quantum hardware technology being young, and will no doubt improve in near future. It is our hope that with this research we have contributed to the possibility of quantum teleportation based networking, and that we shed a light to where it needs improvement.

 

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5. Reference

1. https://qiskit.org/textbook/ch-algorithms/teleportation.html

2. https://ionq.com/docs/get-started-with-qiskit

 

6. Thanks to

1. JoonSik Yu (ChungAng univerisity)

2. JunYoung Kim (Hanyang university)