The Google Quantum AI staff is constructing quantum computer systems with superconducting microwave circuits, however very like a classical pc 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 pc work correctly. In lots of circumstances these components should be customized, requiring in depth analysis and growth to succeed in the best ranges of efficiency.
On this put up, 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”, printed 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 focus on how this work can pave the way in which 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 drawback, the place we want 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 achieved 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 strains but additionally picks up a state-dependent frequency shift from the qubit. Similar to within the binary part shift keying (BPSK) encoding method, the digital state of the qubit (0 or 1) is translated right into a part for a probe tone (microwave sign) reflecting off of this auxiliary resonator. Measuring the part of this probe tone permits us to deduce the state of the qubit with out instantly interfacing with the qubit itself.
Whereas this sounds easy, the qubit really imposes a extreme cap on how a lot energy can be utilized for this probe tone. In regular operation, a qubit must 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 protected measurement energy is usually round -125 dBm, which quantities to solely a handful of microwave photons interacting with the processor in the course of the measurement. Usually, small alerts are measured utilizing microwave amplifiers, which enhance 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 attributable to vitality loss within the circuit. Which means these very small alerts should be measured in only a few hundred nanoseconds with very excessive (>99%) constancy. We due to this fact can’t afford to common the sign over an extended time to scale back the noise. Sadly, even the most effective semiconductor low-noise amplifiers are nonetheless nearly an element of 10 too noisy.
The answer is to design our personal customized amplifiers primarily based on the identical circuit parts because the qubits themselves. These amplifiers sometimes include Josephson junctions to offer a tunable inductance wired right into a superconducting resonant circuit. By setting up a resonant circuit out of those parts, you possibly can create a parametric amplifier the place amplification is achieved by modulating the tunable inductance at twice the frequency you wish to amplify. Moreover, as a result of the entire wiring is manufactured from lossless superconductors, these gadgets 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 gadgets is that the Josephson junctions constrain the facility of the alerts we are able to measure. If the sign is just too giant, the drive present can method the junction essential present and degrade the amplifier efficiency. Even when this restrict was adequate 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 alerts are distributed throughout hundreds of junctions. This will increase the saturation energy, however the amplifiers get very difficult to supply and take up a variety 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 have been used to.
Outcomes
The essential present of every Josephson junction limits our amplifier’s energy dealing with. Nonetheless, growing this essential present additionally adjustments the inductance and, thus, the working frequency of the amplifier. To keep away from these constraints, we changed a normal 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 incorporates 20 RF-SQUIDs. On this case, every junction of a typical DC SQUID is changed by certainly one of these RF-SQUID arrays. Whereas the essential present of every RF-SQUID is way larger, we chain them collectively to maintain the inductance and working frequency the identical. Whereas it is a comparatively modest enhance in gadget 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 present designs that use impedance matching circuits to offer giant measurement bandwidth.
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| Circuit diagram of our superconducting microwave amplifier. A cut up bias coil permits each DC and RF modulation of the snake inductor, whereas a shunt capacitor units the frequency vary. The circulate of present is illustrated within the animation the place an utilized present (blue) on the bias line causes a circulating present (pink) within the snake. A tapered impedance transformer lowers the loaded Q of the gadget. Because the Q is outlined as frequency divided by bandwidth, reducing the Q with a relentless frequency will increase the bandwidth of the amplifier. Instance circuit parameters used for an actual gadget are Cs=6.0 pF, L1=2.6 pH, L2=8.0 pH, Lb=30 pH, M=50 pH, Z0 = 50 Ohms, and Zlast = 18 ohms. The gadget operation is illustrated with a small sign (magenta) reflecting off the enter of the amplifier. When the big 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 acquire is compressed by 1 dB. We additionally measure this energy worth vs. frequency to see the way it scales with amplifier acquire and distance from the middle of the amplifier bandwidth. Because the amplifier acquire is symmetric about its middle 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.
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| Enter and output saturation energy (1-dB acquire compression level), calibrated utilizing a superconducting quantum processor vs. absolute detuning from the amplifier middle frequency. |
Conclusion and future instructions
The brand new microwave amplifiers signify a giant step ahead for our qubit measurement system. They’ll permit us to measure extra qubits utilizing a single gadget, and allow strategies that require larger energy for every measurement tone. Nonetheless, there are nonetheless fairly just a few areas we wish to discover. For instance, we’re at present investigating the appliance of snake inductors in amplifiers with superior impedance matching strategies, directional amplifiers, and non-reciprocal gadgets like microwave circulators.
Acknowledgements
We wish to thank the Quantum AI staff for the infrastructure and assist that enabled the creation and measurement of our microwave amplifier gadgets. Because of our cohort of proficient Google Analysis Interns that contributed to the long run work talked about above: Andrea Iorio for creating algorithms that routinely 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 gadgets primarily based on snake inductors. With their contributions, we’re gaining a greater understanding of our amplifiers and designing the following technology of parametrically-driven gadgets.
