Alright, as you might have noticed that my updates are … sporadic … at best right now. To that I say:
I am currently on vacation in Oregon! We’re spending 10 days in this state, and so far it has been beautiful. But being the primary driver on a 1800 mile trip is a bit tiring, so my updates are a bit slower than usual :)
But anyways, while I have time, let’s try to digest DiCarlo’s 2009 paper! This seems to be an early paper from the Schoelkopf lab, as it was published only 2 years after the transmon qubit was actually implemented. The overall idea is using a cavity bus to perform two-qubit interactions, conducting a proof-of-concept demonstration with the Grover search algorithm and the Deutsch-Jozsa algorithm, which allows for the determination of either a balanced or unbalanced function.
The paper begins by defining what the quantum bus architecture is. The bus uses a transmission line cavity to couple, control, and measure qubits. They are able to perform tomography on the two transmon qubit states to determine the final results. In order to entangle the qubits, the qubit frequencies themselves are tuned and adjusted.
I am not entirely sure what it means to tune the qubit frequencies themselves, since our quantum class primarily discussed how to use an external magnetic field to interact with the resonances of spins. However, from the Reed 2012 paper, it appears that transmon qubits, and other superconducting qubits, have characteristic frequencies for each of their excited states. These states can then be adjusted and tuned to different frequencies. With this bus architecture, it appears that there are microwave pulses at resonant frequencies to perform the standard x and y rotations, while another pulsed measurement performs the readout. Now, there are two additional ports that create “local magnetic fields that tune the qubit transition frequency.” I think this has to do more with electrical engineering, where the Josephson junctions are controlled by the voltages.
The paper spends some time discussing several different regions where they can tune the qubits, such that the qubits become more or less coupled to the cavity. For instance, at one point the qubits are detuned from the cavity and detuned from each other. That means that each qubit does not strongly interact with any part of their environment. The paper remarks that this state is especially good for state preparation, which makes sense. If you have a state where there is little interaction, that would likely mean that you have more control in staying at a stable state.
The paper then implements the Controlled Phase, or CPhase, gate using the avoided crossing. As I had previously discussed with the Reed 2012 paper, avoided crossings are basically magic. But, the basic idea is that as the two qubits are reaching a degenerate frequency, they are prevented from directly interacting, and instead “swap’ states. This allows for some special entangling procedure to occur. The CPhase gate is very important, because using the CPhase gate, we are able to implement a CNOT gate, one of the gates needed (along with X/Z rotations) to complete a universal set of gates for quantum computing.
This paper is mostly experimental, so after they implement the CPhase and implementation gates, they perform quantum tomography to demonstrate that the qubits are in the proper states. And they are in the proper states! The group then implement both the two-qubit Grover search algorithm, and the two-qubit Deutsch-Jozsa algorithm, with between 80% and 90% fidelity. I think I will need another blog post (perhaps the original Grover and/or Deutcsh-Jozsa papers?!) to explain these two algorithms in depth.
I think the most interesting part of this paper is the ability to demonstrate several quantum algorithms with experiments, not just through theory. I need to read more papers, but it feels like this is a fairly early demonstration of quantum algorithms with superconducting qubits, opening the way to further algorithm implementations today. By demonstrating the results step by step through use of quantum tomography, and showing that the results are much better than random chance, it shows that the quantum algorithms are working!
Reference: DiCarlo, L., Chow, J. M., et al. Demonstrations of Two-Qubit Algorithms with a Superconducting Quantum Processor Nature 460 240-244 (2012)