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 just a part of the story. An total expertise stack of peripheral {hardware} is required to make the quantum laptop work correctly. In many instances these elements should be customized, requiring in depth analysis and improvement to succeed in the very best ranges of efficiency.
In this publish, we spotlight one facet of this supplemental {hardware}: our superconducting microwave amplifiers. In “Readout of a Quantum Processor with High Dynamic Range Josephson Parametric Amplifiers”, revealed in Applied 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 the challenges of working a superconducting quantum processor is measuring the state of a qubit with out disturbing its operation. Fundamentally, this comes all the way down to a microwave engineering downside, the place we want to have the ability to measure the power 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 traces but additionally picks up a state-dependent frequency shift from the qubit. Just like within the binary section shift keying (BPSK) encoding approach, 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 immediately interfacing with the qubit itself.
While 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 the next excited state and corrupt the computation. A protected measurement energy is often round -125 dBm, which quantities to solely a handful of microwave photons interacting with the processor in the course of the measurement. Typically, small indicators are measured utilizing microwave amplifiers, which enhance the sign stage, but additionally add their very own noise. How a lot noise is appropriate? If the measurement course of takes too lengthy, the qubit state can change as a consequence of power loss within the circuit. This implies that these very small indicators should be measured in only a few hundred nanoseconds with very excessive (>99%) constancy. We subsequently can not afford to common the sign over an extended time to cut back the noise. Unfortunately, even one of the best semiconductor low-noise amplifiers are nonetheless virtually an element of 10 too noisy.
The answer is to design our personal customized amplifiers based mostly on the identical circuit components because the qubits themselves. These amplifiers sometimes include Josephson junctions to supply a tunable inductance wired right into a superconducting resonant circuit. By developing a resonant circuit out of those components, you possibly can create a parametric amplifier the place amplification is achieved by modulating the tunable inductance at twice the frequency you need to amplify. Additionally, as a result of all the wiring is fabricated 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 ability of the indicators we are able to measure. If the sign is simply too massive, the drive present can method the junction important present and degrade the amplifier efficiency. Even if this restrict was ample to measure a single qubit, our purpose 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 traveling wave amplifiers, the place the indicators are distributed throughout 1000’s of junctions. This will increase the saturation energy, however the amplifiers get very sophisticated to supply and take up a variety of area on the chip. Our purpose 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.
Results
The important present of every Josephson junction limits our amplifier’s energy dealing with. However, growing this important 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. Each RF-SQUID consists of a Josephson junction and geometric inductances L1 and L2, and every array comprises 20 RF-SQUIDs. In this case, every junction of an ordinary DC SQUID is changed by certainly one of these RF-SQUID arrays. While the important present of every RF-SQUID is far greater, we chain them collectively to maintain the inductance and working frequency the identical. While this can be a comparatively modest enhance in machine complexity, it permits us to extend the ability dealing with of every amplifier by roughly an element of 100x. It can be totally suitable with current designs that use impedance matching circuits to supply massive measurement bandwidth.
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| 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 move of present is illustrated within the animation the place an utilized present (blue) on the bias line causes a circulating present (crimson) within the snake. A tapered impedance transformer lowers the loaded Q of the machine. Since the Q is outlined as frequency divided by bandwidth, reducing the Q with a continuing frequency will increase the bandwidth of the amplifier. Example circuit parameters used for an actual machine 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 machine 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 generally known as 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. Since the amplifier achieve is symmetric about its heart frequency we measure this by way of 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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| Input 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 new microwave amplifiers symbolize a giant step ahead for our qubit measurement system. They will permit us to measure extra qubits utilizing a single machine, and allow methods that require greater energy for every measurement tone. However, there are nonetheless fairly a couple of areas we wish to discover. For instance, we’re presently investigating the appliance of snake inductors in amplifiers with superior impedance matching methods, directional amplifiers, and non-reciprocal gadgets like microwave circulators.
Acknowledgements
We wish to thank the Quantum AI group for the infrastructure and assist that enabled the creation and measurement of our microwave amplifier gadgets. Thanks to our cohort of gifted Google Research Interns that contributed to the longer term work talked about above: Andrea Iorio for creating algorithms that routinely tune amplifiers and supply a snapshot of the native parameter area, 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 based mostly on snake inductors. With their contributions, we’re gaining a greater understanding of our amplifiers and designing the subsequent era of parametrically-driven gadgets.