January 29, 2020 | Written by: Baleegh Abdo
Categorized: Quantum Computing
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A key pillar for deploying IBM Quantum systems into the cloud is the ability to read out quantum states with high fidelity in real time. This critical capability is made possible using special kinds of low-noise microwave amplifiers, known as quantum-limited amplifiers (QLAs). In this post, we will shed light on these quantum devices and their role in enabling cloud-based IBM quantum systems. However, before we introduce QLAs, let’s explain why they are needed in the first place.
Superconducting qubits, like other quantum platforms, suffer from an inherent tradeoff between isolation and access. On the one hand, to achieve long coherence, qubits need to be isolated from the noisy environment; on the other hand, if they are too isolated, it is difficult to control and measure them.
Therefore, for superconducting qubits to be in the superconducting state, have low noise environment, and large isolation from the external world, they are cooled down to ultra-low temperatures, i.e., about 20 millikelvin above absolute zero (which is colder than any temperature in nature, including outer space). This is done using special cryogenic, high-vacuum systems called dilution fridges (shown in the left photo of figure 1). However, to control and read out these qubits, mounted at the base-temperature stage of dilution fridges, microwave signals need to communicate between the qubits and the classical electronics controlling them at room temperature. These microwave signals are carried by input and output chains devised to minimize qubits’ exposure to noise. Such chains typically run through the different temperature stages of the dilution fridge and include multiple microwave components, such as coaxial lines, filters, attenuators, isolators, and low-noise amplifiers (as seen in the right photo of figure 1).
Figure 1. Photos of a dilution fridge that houses and cools down superconducting quantum processors. The left photo shows an outside view of the dilution fridge. The right photo shows an exemplary wiring inside the dilution fridge and four of its temperature stages (4 K, 1 K, 0.1 K, 0.02 K).
To understand how QLAs fit in this big picture, let us examine the readout problem confronting superconducting qubits.
The common method for reading out quantum states of superconducting qubits in a non-destructible manner is to probe coupled readout resonators with very weak microwave signals, e.g., around 7 GHz, that contain a few microwave photons. However, since the power of these readout signals is extremely small on the order of 10-16 W or less, it is unfeasible to measure them with room-temperature equipment without significantly boosting their energy, using high-gain amplifiers in the output chain. However, since amplifiers, in general, add noise of their own, that is on top of the input noise accompanying the weak signals, this solution comes at the cost of adding appreciable noise to the amplified output. This could be problematic because the noise added by state-of-the-art, commercial, high-gain, low-noise semiconductor-based amplifiers, can be overwhelming: about 10-20 times larger than the quantum signal itself! Hence, to measure the quantum signal under these noisy conditions is like finding a needle in a haystack (see the top illustration of qubit readout in figure 2).
Fortunately, there is a solution to this readout problem. It entails using quantum-limited amplifiers as the first-stage amplification in the output chain. These microwave amplifiers are quantum-limited because they add only the minimum amount of noise required by quantum mechanics to the input signal, which equals to the ambient quantum noise, i.e., a half of a photon at the signal frequency. This means that in the ideal case, the signal-to-noise ratio at the output of the QLA is only degraded by a factor of two (since the added noise and input noise are equal).
Figure 2. Illustrations showing the advantage of using QLAs for qubit readout. The top scheme shows a qubit readout chain that only uses a state-of-the-art semiconductor-based Low Noise Amplifier (LNA) without any QLAs. Due to the relatively large added noise by the LNA compared to the weak readout signal probing the qubit state, the phase shift of the output signal, which indicates whether the qubit is in the ground (|𝑔⟩) (blue) or excited (|𝑒⟩) (red) states is completely blurred and difficult to resolve. The magnification factors above/below the signals indicate the signal power gain compared to the original input readout pulse. In the bottom scheme, which uses QLAs as the first amplification stage before the LNA, the phase of the amplified readout signal at the output of the chain is easy to resolve and the ratio of the signal to noise is similar to that of the signal leaving the qubit chip.
Another advantage of using these ultra-low noise amplifiers as first-stage amplifiers is that the signal-to-noise ratio of the whole amplification chain is, to a large extent, preserved following the first stage (see the bottom illustration of the qubit readout in figure 2). This is due to the helpful fact that the noise performance of a cascade of microwave amplifiers is primarily set by the noise characteristics of the first amplification stage (given it provides enough power gain).
Now, let’s turn our attention to QLAs’ basic building blocks, physics, and performance metrics.
Since they operate at the quantum limit, QLAs are built of the same circuit elements as superconducting qubits, namely, Josephson junctions (which function as lossless nonlinear inductors), superconducting capacitors, and superconducting linear inductors. The main differences between qubits and QLAs lie in the parameter values of these circuit elements, their emergent properties, and their mode of operation.
Figure 3. Illustration of signal amplification in QLAs. A strong coherent microwave tone, known as Pump, drives the lossless nonlinear medium that lies at the heart of QLAs (built out of Josephson junction circuits). As a result, a wave-mixing process takes place in the device, in which weak input quantum signals get amplified at the output by receiving a (small) portion of the pump energy.
One simple way to think about QLAs is that they contain a lossless nonlinear electromagnetic medium, whose physical properties, such as resonance frequencies or mutual couplings, are parametrically modulated by a strong coherent microwave tone called the pump (which serves as the energy source for the amplification). As a result of this modulation, parametric amplification occurs in the device via a wave-mixing process, in which a portion of the pump photons is converted to signal and idler photons, whose frequencies (or at least one of them) coincide with those of the input-weak quantum signals. In the illustration of figure 3, the signal and idler signals are represented by red and blue arrows, respectively. Owing to this coherent energy transfer occurring in the device, the quantum signals are considerably amplified at the output (see the illustration shown in figure 3).
QLAs, like superconducting qubits, come in different flavors. They tend to vary in their realization, the nonlinear interaction they implement, the operation conditions they require, and the performance metrics they achieve. In IBM Quantum systems, we use two kinds of QLAs, Josephson Traveling Wave Parametric Amplifiers (JTWPAs) and Josephson Parametric Converters (JPCs). Both amplifiers can achieve a gain factor of 100, which is enough to dilute the noise contribution of the following amplifiers. The JTWPA is better suited, at present, for frequency-multiplexed qubit readout since it has a higher saturation power (-103 dBm vs. -125 dBm) and larger instantaneous bandwidth (2 GHz vs. 10 MHz). On the other hand, JPCs have their own strengths, such as negligible insertion loss, higher fabrication yield, and spatial (i.e., physical) and spectral (i.e., frequency) separation between the pump drive and the weak quantum signals.
There are a few readout metrics commonly used to characterize qubit readout chains, mainly, readout fidelity and readout efficiency. Here, we will focus on the former metric measured in IBM Quantum systems.
Simply put, readout fidelity represents the probability of a successful determination of the qubit state. Typically, this metric is characterized by a real number between 0.5 and 1, where 1 represents no readout error (we know the qubit state with certainty) and where 0.5 represents a complete lack of knowledge about the qubit state. This metric is usually inferred from the separation or alternatively the overlap between the measurement histograms of the readout signal, which correspond to the qubit being initialized in the ground (|g〉) and excited (|e〉) states.
Figure 4. Readout fidelity measured for two qubits in the IBM Rochester quantum system (53 qubit processor). The measurements are examples of bad and good readout fidelities (i.e., F=0.6 and F=0.97, shown in the left and right side graphs) measured with nonworking and working QLAs, respectively. The blue and red dots, plotted in the two quadrature plane of microwave signals, i.e., I and Q, are readout data points, which correspond to instances in which the qubit is initialized in the ground (|𝑔⟩) and excited (|𝑒⟩) state, respectively. By plotting a histogram of the data across the x-axis, we obtain gaussian distributions characterized by mean values (representing the signal strength) and standard deviations (representing the noise level). In essence, readout fidelities is a measure of how much the readout histograms are separated (distinguishable).
As seen in figure 4, when applying many of these readout measurements, the resultant readout histograms follow gaussian distributions, which can be characterized by mean values and standard deviations. In this picture, if the two distributions lie on top of each other, the readout fidelity would be 0.5, and if they are completely separated, the fidelity would be very close to 1. In general, the separation between the means depends on the strength of the probe signal (e.g., the number of photons used in the readout signal and the total gain of the output chain), while the standard deviation, representing the measurement noise, depends on the noise in the output chain as well as the averaging time.
Following this standard readout fidelity measurement, qubit states are generally determined in real time during readout based on whether the measured values lie above or below a discriminating threshold that is typically set in the middle between the two distributions (see figure 4). For cloud applications, readout fidelities in excess of 0.9 taken in less than 1 µs are highly desirable, both of which could only be attained using QLAs.
Figure 5. Bar graphs showing the average readout fidelity distributions (in percentages) for six IBM quantum processors measured over seven to eight days.
In figure 5, we show bar graphs representing the distribution (in percentages) of average readout fidelities measured for six different IBM quantum processors, available on the cloud, over a period of seven to eight days. For example, in the Yorktown 5-qubit processor all qubits (100%) have readout fidelities that are equal or larger than 0.95, whereas in the Poughkeepsie 20-qubit processor, the percentage is 80%. In the Rochester 53-qubit processor, the spread is larger mainly because there are more qubits and QLAs than the other systems. However, even in this relatively large system, most qubits (about 67%) have readout fidelities equal or above 0.9.
Figure 6. Readout fidelity variation measured over 7-8 days for six IBM Quantum systems. The blue squares and red Xs represent readout fidelities measured for qubits that have the least and largest variations, respectively. The green diamonds represent the average readout fidelity of all the qubits in the quantum processor.
In figure 6, we show the variation of the readout fidelity of qubits in the same six IBM quantum processors, as in figure 5, taken over the same period (7-8 days). It is important to point out here that automatic calibrations, including the readout fidelity, are run daily for these processors. Therefore, the data shown here include the effect of automatic adjustments to the working points of the QLAs to maintain good fidelities. In this figure, the blue squares and red Xs represent the measured fidelity data points for two qubits that achieve the least and largest variation in readout fidelity over time, respectively. The green diamonds in the same graphs represent the average fidelity of all the qubits in the respective quantum processor measured over time. Based on these results and data collected for longer periods of time (not shown), it is safe to say that the readout fidelities of these quantum processors are relatively stable over time, with an average variation of a few percent.
While the performance results of QLAs, shown in figures 5 and 6, are quite good at present, they exhibit some weaknesses that need to be enhanced in the next “large” processor generations deployed into the cloud, such as tighter distributions in the readout fidelities and better control over time. Moreover, since readout fidelity and speed affect, to a certain degree, the quantum volume of quantum processors, it is imperative to continue enhancing their performance together with that of the quantum chips and to further improve the synergy between the two systems.
Special thanks to Hasan Nayfeh who provided the IBM quantum measurement data used in this blog.
Quantum starts here