Teleportation is real — information can be transmitted from one location to another without passing through a physical medium (e.g. wires, radio waves, or light waves). However, teleporting matter is still bound in the realm of science fiction. In late 2019, researchers realized teleportation between two quantum compute chips.
This article will explain how a quantum internet may be constructed using teleportation to network information among quantum computers. This article assumes that you have a familiarity of the following quantum computing topics: qubits, superposition, and entanglement. I have written a crash course on these topics here: Quantum Computer Programming, As Fast As Possible.
Classical Internet
Today, we use the word internet synonymously with large-scale TCP/IP computer networking. For the remainder of this article, we will refer to this as the classical internet to disambiguate it from a quantum internet. The classical internet is an architecture for a communication network among classical computers. At an extremely high-level, binary bits are transmitted from one computer to another through a network of routers.
There’s obviously a lot more that goes into the design and implementation of the classical internet, but I have specifically brought up routers because they have two responsibilities that are impossible to implement in a quantum network:
- Inspecting the an incoming packet to determine its intended destination.
- “Amplifying” the degraded incoming physical signal by synthesizing a new, full-strength physical signal.
Quantum Internet
Measuring a qubit irreversibly collapses its superposition state into a classical state. Therefore, a quantum internet can not route qubits in the same way that the classical internet routes bits because:
- The intended destination of a qubit can not be determined through inspection (i.e. measurement) without destroying its state.
- Qubits can not be read (i.e. measured) and re-synthesized for purposes of strengthening the qubits’ physical implementation.
Quantum Teleportation
Qubits are notoriously difficult to keep stable even in a stationary environment. Any exposure to the external world (i.e. unintentional measurements) will immediately destabilize a qubit. Reliably moving a stable qubit over a large distance would be a monumentally difficult task. Instead, we can teleport the state of an arbitrary qubit to a different qubit to avoid the need for physically moving qubits.
Let’s consider the scenario where Alice wants to teleport an arbitrary qubit, q0, to Bob. The algorithm has four primary steps:
Step #1: A pair of entangled qubits are distributed to Alice and Bob, q1 and q2 respectively.
Step #2: Alice locally entangles q0 with q1.
Step #3: Alice measures q0 and q1 and sends her two measured classical states to Bob over a classical communication channel.
Step #4: Bob uses the measurements of q0 and q1 from Alice to transform q2 into the arbitrary superposition state that q0 originally existed in.
At the end of the algorithm, the original quantum state in Alice’s q0 has been teleported to Bob’s q2 — in other words: the arbitrary quantum state that originally existed in q0 now exists in q2 without having moved through a physical medium.
The arbitrary starting state in q0 is destroyed before the state has been teleported into q2. This adheres to the no-cloning theorem that prohibits cloning the state of q0 into q2.
The no-cloning theorem states that it is impossible to create an identical copy of an arbitrary unknown quantum state.
The algorithm depends on two classical communication channels, limiting algorithm’s speed of communication to the speed of light. This is an important consideration because communication speeds exceeding the speed of the light would be in violation of Newton’s Theory of Special Relativity. In step #1, a classical physical medium must be used to distribute the entangled qubits to Alice and Bob. In step #3, Alice uses a physical medium to communicate her measurement results to Bob.
For clarification, let’s individually consider each of the four steps:
Step #1. You might be curious why we physically move the entangled qubits (q1 and q2) from some third-party distributor to Alice and Bob. After all, the intent of the teleportation algorithm is to avoid moving q0. The distinction here is that q0 is in an arbitrary state while q1 and q2 are known. If the physical transmission fails for either q1 or q2, step 1 may be repeated. If we attempted and failed to physically move q0, its state is irreversibly lost. The no-cloning theorem prohibits us from creating clones of q0 and retrying on a failed transmission. In 2017, it was demonstrated that known (bell-state) entangled photons could be distributed over 1200km using satellites.
Step #2. At this step, qubits q1 and q2 are entangled to be manifestations of the same entity. Alice entangles q0 with q1 to create a 3-qubit system state. q0, q1, and q2 are now manifestations of the same entity. This is the “magic” that allows the state of q0 to be “reconstructed” at q2. The qubit states are no longer independent, even at arbitrarily long distances. The state of q0 has been introduced into the entangled system and may be extracted from any of the qubits by “canceling out” the known states of q1 and q2.
Step #3. This step serves two purposes. It allows Bob to know that Alice has entangled and measured q0. Additionally, it provides Bob with enough information to transform q2 back into the original superposition state of q0.
Step #4. Bob receives one-of-four possible measurements of q0 and q1 from Alice: |00⟩, |01⟩, |10⟩, or |11⟩. Depending on the measurement, Bob applies one-of-four transformations to q2 using trivial quantum gates:
- For |00⟩, apply the identity gate to q2.
- For |01⟩, apply the not gate to q2.
- For |10⟩, apply the Pauli-Z gate to q2.
- For |11⟩, apply the not gate followed by the Pauli-Z gate to q2.
At this point, the probabilistic starting states of q1 and q2 have been eliminated from q2 — leaving only the original, superposition state of q0.
Quantum Internet (Continued)
Using teleportation, we now know that it is possible to move arbitrary qubits over long distances with the caveat that we must employ some form of classical communication. The quantum internet envisioned in the white paper Towards Large-Scale Quantum Networks calls for routers that are both quantum-compute capable and classical-compute capable. We’ll just refer to these as quantum routers.
Quantum routers that have both a classical network link and a quantum network link lend themselves well to the teleportation algorithm covered in this article. The quantum link would be used to distribute the entangled qubit pairs (q1 and q2 in the above example) and the classical link would be used for transmitted the measurement results from Alice to Bob. These two links between quantum routers are sufficient to teleport qubits from one router to another.
Additionally, the classic link would still allow for TCP/IP networking between routers. Although the routers can not inspect the qubits for routing information, classical network sessions could be established to carry the metadata required for routing the qubits to their intended destination.
Putting it all together, transmitting a qubit from one computer to another may look like the following on a quantum internet:
