by D. Scott Holmes, lead technologist, Booz Allen Hamilton, holmes_douglas@bah.com, and by Steven W. Van Sciver, emeritus professor, National High Magnetic Field Laboratory/FSU, svansciver@gmail.com

Quantum computing and large-scale digital cryogenic computing are under worldwide development. A survey of the applications and system requirements identifies needs for advances in cryogenic refrigeration systems.

Advances in quantum computing have been in the news due to the potential for extremely large speedups in solution times of some important applications such as decryption (code breaking), optimization or simulation of molecules and materials in which quantum-mechanical effects are important. Large-scale classical (digital) computers operating at cryogenic temperatures have generated less excitement yet are under development as potential control computers for quantum computers and for energy-efficient, high performance computing. Both quantum and digital cryogenic computers would benefit from modified or improved cryogenic refrigeration systems.

A survey of commercially available cryogenic refrigeration systems was recently published in the 2020 International Roadmap for Devices and Systems (IRDS) report on Cryogenic Electronics and Quantum Information Processing (CEQIP) [1]. Of interest to the cryogenics community is a plot of specific power versus cold temperature for cryogenic refrigeration, shown in Figure 1. The source data for this figure is available in the Excel file that accompanies the CEQIP report [1]. The plot shows that the cooling penalty grows rapidly as temperature decreases. A 20 mK operating temperature, necessary for some approaches to quantum computing, requires roughly one billion watts of input power per watt of cooling power. Approaches to dealing with such large cooling penalties include computing that is more energy efficient, computing that works at higher temperatures, or more efficient refrigeration. The following sections briefly cover major cryogenic computing approaches and their refrigeration requirements.. Delays in CMOS circuits decrease due to the lower interconnect resistances and lower RC time constants, which can decrease memory access times or allow increases in clock frequency. Decreases in leakage improve energy efficiency, especially for memory [3]. Studies indicate that cryo-CMOS computers operating in the liquid nitrogen temperature range might have advantages over more traditional systems [4]–[5]. Some CMOS circuits can even operate down to milli­kelvin (mK) temperatures for limited applications such as control of qubits for quantum computing [6]. While some semiconductor chips designed for room temperature operation do work at cryogenic temperatures, the greatest benefits are only possible with an optimized CMOS fabrication process. A challenge is that the benefits of process optimization rarely overcome the additional cost of both development and refrigeration.

Refrigeration needs for cryo-CMOS computing: Operating temperatures for large-scale cryo-CMOS computers are likely in the 50 to 150 K range. Although this is a temperature range readily accessible by commercial refrigeration systems, specific application requirements might benefit from development of specialized refrigeration systems.

Superconductor-based Computing (digital or neuromorphic)
Josephson junctions are 2-terminal superconductor devices that switch quickly (~1 ps), dissipate very little energy (~1 aJ), and produce quantized pulses of magnetic flux that can be used for digital logic. Combined with the ability to move signals on superconducting transmission lines ballistically at nearly the speed of light and with low loss, superconductor electronics is capable of high-speed signal processing. General-purpose digital computing might also be possible but would require larger and better memories than currently exist in the technology. Gaining an economic benefit based on energy efficiency would require large-scale applications.

Neuromorphic (brain-like) computing might be an even better application for superconductor electronics. The output pulses from Josephson junction circuits are similar in some ways to the spiking behavior of neurons in brains. Neurons in the human brain typically connect to thousands of other neurons. Replicating such interconnectedness using only superconductors is a challenge and has driven investigation of hybrid approaches using optical interconnects [7].

What are the prospects for increasing the operating temperature? Niobium, which has a critical temperature Tc ~ 9.2 K, is the superconductor most used for digital superconductor electronics. Somewhat higher operating temperatures might be possible using NbN or NbTiN (Tc ~ 15 K) if fabrication processes can be developed to make Josephson junctions meeting the requirement for critical current variation less than about 2%. The challenges to using high temperature superconductors (HTS) are even greater. Making large numbers of HTS junctions with uniform properties has proven difficult. Also, the increased thermal noise at higher temperatures requires larger switching energies, which in turn requires larger currents and smaller inductances, both of which are problematic.

Refrigeration needs for superconductor-based computing: Operating temperatures for large-scale digital superconductor computers are likely in the 2 to 5 K range. Commercial refrigeration systems have a gap between smaller, less efficient regenerative cycle based systems with cooling capacity of up to 2 W at 4.2 K and specific power of order 5000 W/W, and larger, more efficient recuperative cycle systems with cooling capacity of up to 10 kW at 4.4 K
and specific power as low as 250 W/W. Availability of systems with intermediate capacity around 10 W and specific power below 1000 W/W would allow scale-up in reasonable steps. Cooling with superfluid or supercritical helium might be needed to keep device temperature increases within acceptable limits.

Prospects include GM-JT systems that add a Joule-Thomson (JT) expansion cycle [8] to a Gifford-McMahon (GM) cryocooler. GM-JT systems might be able to increase cooling capacity and efficiency somewhat with some additional complexity and cost. A challenge is that the JT needle valve or expander operates at the cold end and can clog over time with frozen gasses or contaminants if not properly designed for long-term operation. Reverse turbo-Brayton cryocoolers [9] could provide both efficiency and reliability; however, they require development and will be expensive until the manufacturing process for the miniature turbines can be improved.

Quantum Computing
The hype around quantum computing stems from its potential to speed up some computations by factors of thousands to millions. A major challenge is that we are still figuring out how to build quantum computers. The range of approaches under development is still broad. For an introduction and survey of current status, see [1].

While quantum effects tend to become important at the scale of atoms, they also can affect the behavior of macroscopic systems such as superconducting circuits at extremely low temperatures, typically below 0.1 K. Semiconductor-based artificial atoms currently require similar temperatures but have prospects for operation in the 1 K range [11]. Trapped ion approaches use ions of elements such as Ca+ or Yb+ suspended in ultrahigh vacuum. Operating trapped ion systems at cryogenic temperatures helps to achieve the necessary vacuum conditions and reduces the anomalous electronic noise that is not presently understood . Operation at 50 to 100 K provides significant benefits; however, the 1 to 10 K range might prove necessary, especially for early systems. Photonic quantum computing approaches using superconducting nanowire single-photon detectors (SNSPDs) require temperatures in the 1 to 10 K range.

Refrigeration needs for quantum computing: Cryogenic refrigeration systems for trapped ion quantum computing might require components in contact with vacuum to be baked out to 100 to 300°C to achieve ultra-high vacuum. Scaling up quantum computing approaches requiring operation in the liquid helium temperature range (1 to 5 K) likely could also benefit from refrigeration systems with capacity around 10 W
near 4 K, as discussed in the section on superconductor-based computing.

Dilution refrigerators (DRs) add a still containing a mixture of 4He and 3He to the cold end of a refrigeration system capable of reaching the 4 K temperature range. DRs are commonly used to achieve operating temperatures below 100 mK. For scale-up, DRs with larger cooling capacity and better energy efficiency are needed. A straightforward approach might be to link a DR to a commercial cryogenic refrigerator with greater than 100 W cooling capacity at 4 K. A large DR under development by IBM is shown in Figure 2. Alternatively, if 500 mK is adequate for an application a pure 3He refrigerator can provide higher cooling power. However, one challenge for broad application of either approach is the scarcity and cost of 3He.

Magnetic refrigerators do not use 3He and have demonstrated ability to achieve temperatures below 100 mK [12]. A challenge is that the strong magnetic fields required could be problematic for quantum computing approaches that are sensitive to magnetic fields. Adiabatic demagnetization refrigeration (ADR) typically requires the magnet to be close to the cold end; however, cooling approaches such as active magnetic regenerative refrigeration (AMRR) [13] that use a magnetic fluid might be able to locate the magnet sufficiently far from the cooled circuits used for computing. Scaling up magnetic refrigeration to large refrigeration loads is a challenge.

Thermionic devices using normal-insulator-superconductor (NIS) junctions can provide cooling [14]–and have some similarities to thermoelectric coolers. Their temperature range is limited by the critical temperature of the superconductor so seem best suited as a last stage of cooling very close to the qubits.

Conclusion. Cryogenic computing is projected to need some improvements in cryogenic refrigeration systems in roughly 5 to 10 years. Considering the time necessary to develop commercial systems, such development should begin soon.

Acknowledgements
Holmes chairs the IRDS CEQIP International Focus Team and welcomes information about commercial cryogenic refrigeration systems not already in the database.

References
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