QCJC: Chou 2018

A key component of quantum computation is the ability for modularity in the construction of data and communication qubits. That is, it’s rather useless to have to reinvent the wheel for every single new qubit that is introduced to the system. It would require an obscene amount of engineering to program new types of quantum gates for each different architecture. That is why the authors of this article so strongly tout the idea of using quantum teleportation to enable communication between multiple qubits.

To begin with, we need to understand how the quantum system in question operates. As with most systems in RSL, we have a transmon qubit that is strongly coupled to a seamless microwave cavity. As per the paper, the cavity operates as a “data qubit” that is able to store information for a long period of time. Part of the rationale for using a circuit QED architecture is that cavities can be designed with a very high quality factor, ranging in the upper millions of Q. That means that after a certain number of photons have entered the cavity, they would not easily leak out. In addition, there are “communication qubits” that are transmon circuits. These circuits are able to be controlled by microwave pulses and are coupled to the microwave cavities, such that an action on one will be felt by the other, and vice versa. These transmons are also coupled to a low-Q stripline resonator, which acts as a “quantum bus” for information to travel. Physically, this bus is a cavity mode within the resonator, but we can conceptualize it as some way that allows different “communication” qubits to talk to each other, or transfer data from one place to the other.

A diagram of the different qubits discussed above. From Chou 2018, Fig 1(d).

The primary accomplishment of this paper is demonstrating how the two communication qubits along with the quantum bus were able to enact a CNOT gate between the two data qubits. In addition, they remark that this was conducted on “logical” states in the qubits – where the “data” qubits were placed in a “first-level bosonic binomial quantum code” that allows for basic quantum error correction. This is characterized by the Wigner function, which is a probability distribution that describes quantum states. As show in Fig 2(b), it is really quite obvious when a qubit goes from one state to another!

In order to satisfy the requirements that this would fulfill some kind of future modular architecture, and thus have qubits that are far away from each other, the paper makes the following argument. First, they argue that the two logical qubits would not be able to interfere with each other – they have an “immeasurably small direct coupling” that is smaller than the smallest decay rate in the system. Therefore, we are confident that results are truly because of actions through the quantum bus and not through some mere accidental effect through proximity. Next, the paper justifies that their CNOT gate works through the generation of an entangled Bell state, allowing for the two communication gates to be spatially separated at far distances. Finally, the paper argues that the implementation of feed-forward operations, where the measurements of the communication qubits and use of classical information is incorporated into the CNOT gate, allows for the maintenance of a deterministic operation that always works, rather than some kind of probabilistic operation that had been demonstrated in the past.

And the results are really pretty! Here it is – just a standard truth table, but made to be much more fancy :) You can see that the gate has an effect – the pictures from the output state look decidedly less “sharp” than the input state. What this actually means, I’m hesitant to say, but it does seem to say something…

The logic table for the CNOT gate using the quantum bus. From Chou 2018 Fig 2(b).

The rest of the paper seems primarily focused on characterizing the CNOT gate. Which it seems to do well!

The main thing that I want to still learn more about here is how this differs from other uses of the quantum bus. I mean, the technology has been around since… 2014, right? So what were the uses of it prior to this? Wasn’t the purpose of the quantum bus to do exactly this? I want to chat with some of the authors and figure this out more soon!

Reference: Chou, K. S. et al. Deterministic Teleportation of a Quantum Gate between Two Logical Qubits Nature (2018)

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