Month: June 2018

QCJC: Linke 2017

Among potential experimental realizations of scalable quantum computing (QC), superconducting qubits of various kinds have received the bulk of the public’s attention. In addition to their promise, this is largely because IBM and Google have both chosen to pour money and resources into developing superconducting devices for QC. As massive tech companies, they are both well-known to the public and have some experience in developing and scaling the fabrication methods used to make superconducting circuits. This expertise made superconducting their natural technology of choice and since then has stimulated rapid progress, another reason for so much press coverage.

Meanwhile, trapped ions, another candidate for scalable QC, has reached a similar level of maturity while receiving much less attention. Instead of the “artificial atoms” engineered in superconducting circuits, trapped ions do computation using the energy levels of an actual atom that has been ionized so that it can be trapped by electric (and/or magnetic, depending on your trap architecture) fields.

One example of such a qubit is the two hyperfine-split ground state levels of an Ytterbium-171 ion. Hyperfine splitting of an energy level is due to the interaction between the total electron angular momentum and the nuclear spin. Yb-171 has a nuclear spin of 1/2 so each of its energy levels, including the ground state, is split into two different levels, one for spin up and one for spin down. By labeling one of these states |0> and the other |1>, we have ourselves a qubit. I won’t talk much more about how these qubits are implemented and controlled here because hopefully I’ll cover that in future posts.

Instead, I figured there would be no better way to start off my QCJC contributions than by comparing trapped ions with superconducting qubits. Thus far, QCJC (at least the experimental posts) has predominantly been about superconducting qubits because, duh, Chunny works in a superconducting lab. Norbert Linke and Chris Monroe, on the other hand, do not. Instead, Chris Monroe is the PI of a trapped ion group at UMD and Norbert Linke is a research scientist in that group.

Last year, along with collaborators from inside and outside their group, they published a comparison of a five-qubit trapped-ion quantum computer that they built with the five-qubit superconducting quantum computer made publicly available online by IBM. Both systems are full-stack, fully-programmable universal quantum computers, but they are also both noisy. This means that their qubits decohere over time and their gates are not perfectly implemented.

To avoid decoherence, it is important that gate times are much shorter than the decoherence time so that all of the gates required for an algorithm can be performed without having to worry about the quality of the qubit degrading. Superconducting devices decohere through state relaxation (T1 = 60 us) and dephasing (T2* = 60 us) while trapped ions only decohere via dephasing (T2* = 0.5 s). Although superconducting qubits decohere much more quickly than hyperfine qubits do, they also have much faster gate times at 130 ns for one-qubit gates and between 250 and 450 ns for two-qubit gates compared to 20 us and 250 us for one- and two-qubit gates, respectively.

Gate time is not the only consideration for avoiding decoherence since different numbers of gates may be needed in each architecture due to different sets being available. Trapped ions can implement arbitrary rotations on single qubits and XX entangling gates on two qubits. IBM makes the Clifford+T gate set available in their interface and have a compiler that optimizes the actual implementation of whatever algorithm one gives. Using fewer gates decreases the total time needed for the calculation, thus preventing more decoherence, but it also decreases the impact of gate errors because there are less chances for them to occur.

The final important difference between the two architectures is their level of connectivity. Currently, not all superconducting qubits on the IBM chip are able to interact directly because they are confined to a planar geometry and a direct connection is need to apply a two-qubit gate. two non-connected qubits can still become entangled by using an intermediary qubit, but this requires the use of extra gates, which takes time and gives more opportunities for errors to creep in. In contrast, any two ions in the same trap can interact by using the collective motion of all the ions as an information bus (I need to read the paper that proposes this and write a QCJC submission on it in the future because I don’t really understand it).

With all of this in mind, Linke and his team first implemented a Margolus gate on both systems. This gate is the same as a Toffoli gate except that it introduces a phase on the |001> state and can be implemented with fewer elementary gates. In particular, the star-shaped connectivity graph of the superconducting system does not require any extra gates to implement it. The IBM system completed this circuit with a success probability of 74.1(7)% and the trapped ion system had a success probability of 90.1(2)%. For full Toffoli gates, the success probabilities were 52.6(8)% and 85.0(2)%. All of these figures are based on state tomography done after the gates were implemented.

Next, they ran an algorithm to find the c of a black box that implements a function f(x) = x • c. Known as the Bernstein-Vazirani problem, this requires multiple queries to the function oracle for classical systems but can be completed in one query by a quantum computer. This particular algorithm maps well onto the star-shaped connectivity architecture of the IBM chip. The success probabilities for completing this algorithm were 72.8(5)% for superconducting and 85.1(1)% for trapped ions.

Finally, the two systems were made to solve the hidden shift problem, in which an oracle calculates a known function f(x) but with a “hidden shift”: f(x + s). The idea of the algorithm is to find this hidden shift s. This algorithm is not nearly so kind to IBM’s connectivity graph, resulting in a success probability of only 35.1(6)% compared to 77.1(2) for the trapped ion quantum computer.

Overall, this may seem like a victory for trapped ions, but we have no way of knowing how these comparisons will change as both systems are further developed and scaled up. Neither has hit any fundamental obstacles to scaling yet. Both are still promising technologies with their own strengths and weaknesses and there is a reason that Google and IBM have chosen to focus on superconducting circuits. With their expertise in fabrication and scaling technologies, rapid progress that outpaces trapped ions could be on the horizon. Or, it might be the case that using the two together, or one with some other technology, will prove to be the architecture of the future.

Source: Linke, N. M., et al. Experimental Comparison of Two Quantum Computing Architectures PNAS 114 (13) 3305-3310 (2017)

QCJC: Minev 2018 – Finding new islands of predictability in a sea of uncertainty

Imagine that your fourteen-year-old daughter, Alice, has been arguing with you day and night for the past week about going out with friends to party. Every night, you tell her no, and every night, you hear her groaning and complaining in her room. One night as you are washing the dishes, you notice that the house is quiet – too quiet. You run up to Alice’s room and fling open the door, catching Alice just as she is climbing out the window to freedom. Determining if a teenager is about to sneak out of the house may be difficult, but even more unpredictable than a disgruntled teenager is a quantum system, where artificial atoms can jump between different levels with complete randomness. However, recent research from the Devoret Lab at Yale has shown that there may be a way to predict, catch, and even reverse such a jump, even if the atom is partway through its daring escape.

While it is obvious why you care about catching escaping teenage delinquents, understanding tiny quantum systems can have even greater reward. One of the hallmarks of quantum mechanics is the absolute randomness present within a quantum system. Such limits, derived by physicists like Heisenberg and Schrodinger, show that even if you knew how every single particle in the universe moved, you would still be unable to predict what happens in certain quantum systems. This uncertainty can create problems for quantum computing, as it makes it especially different to prevent errors in the system from accumulating. To attack this problem, the Devoret Lab created a quantum system that they could finely control and test out a new way of predicting errors.

Designing a quantum system that can be carefully probed and measured is not easy, but Zlatko Minev, an applied physics graduate student at Yale, has plenty of experience. His previous work was in a quantum system of superconducting circuits that is often referred to as an artificial atom, because like an atom, the system has different energy levels that it can jump between with complete randomness. These energy levels are similar to the states that the teenage daughter can occupy – in her bedroom, on her phone, or going out the window. At any time, it is possible for the daughter to make a leap away from talking on the phone and bolt for the window. For the artificial atom, it can jump between a ground state to either an excited state or a dark state.

Unlike a regular atom, an artificial atom can be very carefully controlled using microwave signals and measured using highly sensitive photon detectors. Both these properties were crucial for this experiment’s success: the microwave control allows the experimenters to freeze the status of the atom at different points to look more closely at it, while the sensitive photon detectors allow for the detection of the tiniest signals.

When the quantum system is turned on, it must always be jumping to one of its excited states. Every time it makes the jump between the excited state and the ground state, the system emits a photon that can then be measured with high precision by the experimenters. However, the dark state is isolated and cannot be directly measured in the same way. Instead, the experimenters can deduce that the atom is now jumping back and forth from the dark state to the ground by looking for an absence of signal in the excited state transition. This is analogous to the daughter talking on her telephone: every time she speaks, her parents can hear her and know that she is in her room, while a prolonged silence would indicate that she has escaped.

Minev’s experiment hinges on a prediction made by Quantum Jump Theory, which governs the random probability of making hops from the ground to the excited state to making hops from the ground to the dark state. Although this theory predicts that it is impossible to directly predict when the atom would suddenly start jumping to the dark states, it does provide a loophole to peer into this bizarre world. The experimenters can determine that the atom is about to make the transition if they observe a warning signal. This warning signal comes from a prolonged gap in the signal from the excited state, like how it may take time for the daughter to hang up the phone before she is able to leap out the window.

This warning signal may seem like a simple concept, but it is incredibly hard to measure. To begin, the normal photon signal from the excited state is not continuous, meaning that there are natural breaks in seeing photons. To properly predict a transition to the dark state, the experimenters need to tell the difference between a natural lull in and a warning signal. In addition, both natural lulls and warning signals require incredible precision to measure, equivalent to not missing a single signal within one hundred thousand. Such a measurement can perhaps only be done accurately in a superconducting system, and not in a natural atom system.

Although building a superconducting system is difficult, the payoff is great: Minev’s team was able to predict the atom jumps before they happened. Using the microwave control signals, they were able to freeze the system to observe exactly how far the atom had jumped at several different time steps, and by reversing the control signals, they can even force the atom to jump backwards halfway through a jump. These measurements not only show the validity of the quantum jump theory, they also provide new insights into the nature of randomness.

In the future, the group hopes to use this powerful warning signal to understand other quantum behaviors and to correct for errors before they even happen. Sitting on a stable island amidst a sea of chaos, there is hope yet ahead for a fully implementable quantum computer.

Source: Minev, Z. et al. To catch and reverse a quantum jump mid-flight arXiv 1803.00545 (2018)

QCJC: Wallraff 2004

Welcome to the new season of QCJC! It’s still more or less the same as before, but instead of exclusively broadcasting to myself, I think there will be a few friends joining soon :)

Today’s paper will be Wallraff’s 2004 paper – it’s also Professor Schoelkopf’s most widely cited paper, and the first paper to show that superconducting circuits could be coupled to photon resonators for readout and control. It is very much an experimental paper, as the researchers were showing that this kind of coupling was not only true in theory, in the way that they can describe a Hamiltonian with mixing terms, but that they were able to observe avoided crossings through a special design of the architecture. As the authors state, “to our knowledge, our experiments constitute the first experimental observation of strong coupling cavity QED…”, which is really quite incredibly.

One of the key aspects of this experiment is achieving the “strong coupling regime” of coupling between the photon resonator and the superconducting qubit. By using a capacitor, they tune the coupling strength g of the system such that it is greater than than the photon decay rate and the qubit decay rate. This means that the photon and the qubit are able to interact with one another before either the photon dissipates or the qubit decoheres. Having a strong coupling strength means that the Jaynes-Cummings Hamiltonian, which is as follows:

H_{JC} = H_r + H_a + \hbar g (a^\dagger \sigma^- + a \sigma^+)

where a^\dagger is the creation operator for photons in the resonator, a is the destruction operator for photons, $\sigma^-$ is the annihilation operators for cavity excitations, and $\sigma^+$ is the creation operator for excitations in the qubit. As an aside, the superconducting qubit that they use is called a Cooper Box here, but I believe that with the addition of the coupling capacitors, this is what is commonly refered to as a transmon today.

Therefore, as you can see from H_{JC}, there is an interaction between the resonator and the qubit. A photon can disappear in the resonator and result in an excitation in the qubit, or vice versa. This is significant because it leads to certain kinds of control in the qubit, where microwave signals can be used to manipulate the photon number in the resonator without destroying the fragile state of the superconducting qubit itself.

One significant aspect is that the primary source of dissipation is through the resonator losing photons, which is limited by the quality factor Q. In the paper, the initial choice is Q = 10,000, resulting in a photon lifetime of $0.1 \mu$s. This helps explain some of the work in my lab as being focused on resonator design and making sure that there is an incredibly high quality factor for them. The Cooper Box itself is created using two Josephson Junctions, and is shown to be fabricated on a silicon chip using optical lithography.

In addition, there is explanation for why the cryostat needs to be kept at such a low temperature. I had been puzzled for some time about this, as it seems that the critical temperature for aluminum is T_c = 1.2K – and this is for the material we currently use in the lab, while the original paper uses niobium which has an even higher critical temperature at T_c = 9.26K! Therefore, why does the system need to be cooled down to 20mK? It seems that this drastic cooling is to prevent thermal fluctuations from occurring in the resonator cavity. The temperature needs to be less than the operating temperature of the resonator so that it remains in its ground state. The paper computes that \hbar \omega_r / k_B = 300mK for their resonator, so therefore they need to achieve a temperature lower than that. Thus, the mean photon number inside the cavity is n = 0.6.

To execute their experiment, the group carried out spectroscopy on the cavity resonator in order to determine known properties of the superconducting qubit. By examining the phase and the transmission coefficients of the superconducting cavity using the resonator as a mediator, they were able to find that there was a faithful measurement conducted.

Afterwards, the group also use the resonator as a manner to control the qubit, first by tuning the qubit so that it is in resonance with the resonator. This is done by changing the magnetic flux bias that passes through the qubit, as shown in Figure 4. They are able to observe an anti-crossing between the resonator and the qubit, which agrees with theory!

So this is the paper that launched a thousand ships… and may a thousand more set sail!

Source: Wallraff, A. et al. Strong Couping of a Single Photon to a Superconducting Qubit using Circuit Quantum Electrodynamics Nature 431 162-167 (2004)