The Google Quantum AI group is constructing quantum computer systems with superconducting microwave circuits, however very like a classical laptop the superconducting processor on the coronary heart of those computer systems is barely a part of the story. A whole expertise stack of peripheral {hardware} is required to make the quantum laptop work correctly. In lots of instances these components have to be customized, requiring intensive analysis and growth to succeed in the very best ranges of efficiency.

On this submit, we spotlight one facet of this supplemental {hardware}: our superconducting microwave amplifiers. In “Readout of a Quantum Processor with Excessive Dynamic Vary Josephson Parametric Amplifiers”, revealed in Utilized Physics Letters, we describe how we elevated the utmost output energy of our superconducting microwave amplifiers by an element of over 100x. We talk about how this work can pave the best way for the operation of bigger quantum processor chips with improved efficiency.

Why microwave amplifiers?

One of many challenges of working a superconducting quantum processor is measuring the state of a qubit with out disturbing its operation. Essentially, this comes right down to a microwave engineering downside, the place we’d like to have the ability to measure the vitality contained in the qubit resonator with out exposing it to noisy or lossy wiring. This may be completed by including a further microwave resonator to the system that’s coupled to the qubit, however removed from the qubit’s resonance frequency. The resonator acts as a filter that isolates the qubit from the management traces but additionally picks up a state-dependent frequency shift from the qubit. Identical to within the binary section shift keying (BPSK) encoding method, the digital state of the qubit (0 or 1) is translated right into a section for a probe tone (microwave sign) reflecting off of this auxiliary resonator. Measuring the section of this probe tone permits us to deduce the state of the qubit with out straight interfacing with the qubit itself.

Whereas this sounds easy, the qubit truly imposes a extreme cap on how a lot energy can be utilized for this probe tone. In regular operation, a qubit ought to be within the 0 state or the 1 state or some superposition of the 2. A measurement pulse ought to collapse the qubit into certainly one of these two states, however utilizing an excessive amount of energy can push it into a better excited state and corrupt the computation. A secure measurement energy is often round -125 dBm, which quantities to solely a handful of microwave photons interacting with the processor through the measurement. Sometimes, small indicators are measured utilizing microwave amplifiers, which improve the sign stage, but additionally add their very own noise. How a lot noise is suitable? If the measurement course of takes too lengthy, the qubit state can change on account of vitality loss within the circuit. Which means that these very small indicators have to be measured in only a few hundred nanoseconds with very excessive (>99%) constancy. We due to this fact can not afford to common the sign over an extended time to scale back the noise. Sadly, even one of the best semiconductor low-noise amplifiers are nonetheless nearly an element of 10 too noisy.

The answer is to design our personal customized amplifiers based mostly on the identical circuit parts because the qubits themselves. These amplifiers usually encompass Josephson junctions to offer a tunable inductance wired right into a superconducting resonant circuit. By establishing a resonant circuit out of those parts, you’ll be able to create a parametric amplifier the place amplification is achieved by modulating the tunable inductance at twice the frequency you need to amplify. Moreover, as a result of the entire wiring is fabricated from lossless superconductors, these units function close to the quantum restrict of added noise, the place the one noise within the sign is coming from amplification of the zero level quantum voltage fluctuations.

The one draw back to those units is that the Josephson junctions constrain the facility of the indicators we will measure. If the sign is just too giant, the drive present can strategy the junction crucial present and degrade the amplifier efficiency. Even when this restrict was enough to measure a single qubit, our aim was to extend effectivity by measuring as much as six qubits at a time utilizing the identical amplifier. Some teams get round this restrict by making touring wave amplifiers, the place the indicators are distributed throughout hundreds of junctions. This will increase the saturation energy, however the amplifiers get very difficult to provide and take up a number of house on the chip. Our aim was to create an amplifier that would deal with as a lot energy as a touring wave amplifier however with the identical easy and compact design we had been used to.

Outcomes

The crucial present of every Josephson junction limits our amplifier’s energy dealing with. Nonetheless, rising this crucial present additionally adjustments the inductance and, thus, the working frequency of the amplifier. To keep away from these constraints, we changed a customary 2-junction DC SQUID with a nonlinear tunable inductor made up of two RF-SQUID arrays in parallel, which we name a snake inductor. Every RF-SQUID consists of a Josephson junction and geometric inductances L1 and L2, and every array comprises 20 RF-SQUIDs. On this case, every junction of an ordinary DC SQUID is changed by certainly one of these RF-SQUID arrays. Whereas the crucial present of every RF-SQUID is far increased, we chain them collectively to maintain the inductance and working frequency the identical. Whereas this can be a comparatively modest improve in system complexity, it allows us to extend the facility dealing with of every amplifier by roughly an element of 100x. It is usually totally suitable with current designs that use impedance matching circuits to offer giant measurement bandwidth.

Circuit diagram of our superconducting microwave amplifier. A break up bias coil permits each DC and RF modulation of the snake inductor, whereas a shunt capacitor units the frequency vary. The stream of present is illustrated within the animation the place an utilized present (blue) on the bias line causes a circulating present (purple) within the snake. A tapered impedance transformer lowers the loaded Q of the system. For the reason that Q is outlined as frequency divided by bandwidth, reducing the Q with a continuing frequency will increase the bandwidth of the amplifier. Instance circuit parameters used for an actual system are Cs=6.0 pF, L1=2.6 pH, L2=8.0 pH, Lb=30 pH, M=50 pH, Z0 = 50 Ohms, and Zultimate = 18 ohms. The system operation is illustrated with a small sign (magenta) reflecting off the enter of the amplifier. When the massive pump tone (blue) is utilized to the bias port, it generates amplified variations of the sign (gold) and a secondary tone often called an loafer (additionally gold).

We measure this efficiency enchancment by measuring the saturation energy of the amplifier, or the purpose at which the achieve is compressed by 1 dB. We additionally measure this energy worth vs. frequency to see the way it scales with amplifier achieve and distance from the middle of the amplifier bandwidth. For the reason that amplifier achieve is symmetric about its heart frequency we measure this when it comes to absolute detuning, which is simply absolutely the worth of the distinction between the middle frequency of the amplifier and the probe tone frequency.

Enter and output saturation energy (1-dB achieve compression level), calibrated utilizing a superconducting quantum processor vs. absolute detuning from the amplifier heart frequency.

Conclusion and future instructions

The brand new microwave amplifiers signify an enormous step ahead for our qubit measurement system. They are going to permit us to measure extra qubits utilizing a single system, and allow strategies that require increased energy for every measurement tone. Nonetheless, there are nonetheless fairly a couple of areas we want to discover. For instance, we’re at the moment investigating the applying of snake inductors in amplifiers with superior impedance matching strategies, directional amplifiers, and non-reciprocal units like microwave circulators.

Acknowledgements

We want to thank the Quantum AI group for the infrastructure and help that enabled the creation and measurement of our microwave amplifier units. Due to our cohort of proficient Google Analysis Interns that contributed to the long run work talked about above: Andrea Iorio for creating algorithms that robotically tune amplifiers and supply a snapshot of the native parameter house, Ryan Kaufman for measuring a brand new class of amplifiers utilizing multi-pole impedance matching networks, and Randy Kwende for designing and testing a spread of parametric units based mostly on snake inductors. With their contributions, we’re gaining a greater understanding of our amplifiers and designing the following era of parametrically-driven units.