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What is Dilution refrigerator?

A refrigerator that uses a mixture of helium-3 and helium-4 to produce cryogenic temperatures of about 10 mK continuously. It is used to operate superconducting qubits and silicon spin qubits. The cooling power of its coldest stage is small, roughly ten to several tens of µW, so heat flowing in through the wiring is a challenge for scaling up.

Japanese name: 希釈冷凍機

Dilution refrigerator appears in 3 practice questions across 1 topic, including Quantum Computing Hardware.

Field: Quantum Computing Hardware

How it cools

Below about 0.87 K, a mixture of helium-3 and helium-4 separates into a layer rich in helium-3 and a layer of helium-4 with a little helium-3 dissolved in it. When helium-3 dissolves (is diluted) from the concentrated layer into the dilute layer, it absorbs heat, much as a liquid does when it evaporates. By continuously pumping helium-3 out of the dilute layer and returning it to the concentrated layer, this heat absorption keeps going and cools the stage to about 10 mK. For precooling, pulse-tube cryocoolers that cool to about 4 K are widely used.

Temperature stages and wiring

Inside the refrigerator, plates at different temperatures are stacked in several stages, such as about 50 K, about 4 K, around 1 K, about 100 mK and the coldest stage at about 10 mK. Coaxial control lines to the qubits are brought down through attenuators at each stage to reduce thermal noise from room temperature. Readout signals are amplified by cryogenic amplifiers and HEMT amplifiers at the 4 K stage before returning to room temperature. As a rough guide, the cooling power is about 1 W at the 4 K stage and about ten to several tens of µW near 20 mK at the coldest stage.

Challenges for scaling up

Even at the Carnot limit, pumping 1 µW of heat out of 10 mK takes about 30 mW of work, so handling heat becomes more expensive at colder stages. As qubits are added, platforms that need several lines per qubit see the number of cables and the heat load rise quickly, so frequency multiplexing, flexible multi-conductor wiring and cryo-CMOS control circuits at the 4 K stage are being developed. There are also efforts to build larger refrigerators and to link several refrigerators together.

Try it: questions about Dilution refrigerator

What is the main reason superconducting qubits are cooled to about 10–20 mK in a dilution refrigerator?

  1. ATo make the wiring and junctions superconducting and to make thermal excitation of the qubits and thermal noise sufficiently small
  2. BBecause cooling widens the band gap of silicon and raises the qubit frequency
  3. CBecause electron mobility rises at low temperature, making gate operations 1,000 times faster than at room temperature
Show answer and explanation

Answer: A. To make the wiring and junctions superconducting and to make thermal excitation of the qubits and thermal noise sufficiently small

The aluminum used in transmons becomes superconducting below about 1.2 K, eliminating resistive losses. In addition, the energy hf of a qubit at a frequency of about 5 GHz corresponds to a temperature of about 0.24 K, so unless the thermal energy kT is made much smaller than this, the qubit is thermally excited to |1⟩ and thermal noise enters through the wiring. Liquid helium temperature, about 4 K, is therefore not enough, and the qubits are cooled to about 10 mK with a dilution refrigerator that uses a mixture of helium-3 and helium-4. Qubit speed is not set by mobility, and superconducting qubits do not use the band gap of silicon.

FAQ

Why isn't liquid helium temperature (about 4 K) enough?

The energy hf of a 5 GHz qubit corresponds to a temperature of about 0.24 K, and at 4 K the thermal energy kT is about 17 times that, so the qubit would be thermally excited. To make thermal excitation negligible, it must be cooled well below 0.24 K, to a few tens of mK or less.

What are dilution refrigerators used for besides quantum computers?

They have long been used in physics research that requires cryogenic temperatures, such as studies of the properties of materials at low temperature, superconducting detectors for astronomical observation and detectors for dark matter searches. Progress in quantum computing research has driven the development of larger refrigerators with more wiring.

Dilution refrigerator in the explanations

Questions that mention Dilution refrigerator (3)

  1. What is the main reason superconducting qubits are cooled to about 10–20 mK in a dilution refrigerator?
  2. Which is closest to the minimum power required by the Carnot limit to pump 1 µW of heat out of a 10 mK stage and reject it at 300 K?
  3. Which is the most appropriate comparison of superconducting and trapped-ion platforms?

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Related terms

Qubit Transmon Thermal noise (Johnson noise) Mobility Band gap Ion trap Decoherence Josephson junction NISQ Post-quantum cryptography

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