Method and system for optimizing the operating temperature of a superconducting quantum processor

Abstract

A system for controlling the temperature of a quantum circuit comprises a housing having a housing wall made of a thermally conductive material, a substrate for holding the quantum circuit, at least one cooling fluid source, at least one port within the housing coupled to the at least one cooling fluid source, and a control unit coupled to the at least one cooling fluid source and configured to control or enable control of the supply of cooling fluid to a chamber. The system fills the housing with cooling fluid during use to cool the quantum circuit. Preferably, the at least one cooling fluid source is a source consisting of liquid 3 He, 4 He, or a mixture of the two. The present invention provides a method and system for optimizing the operating temperature of superconducting quantum circuits and processors and the environment in which they operate.

Description

Technical Field

[0001] The present invention relates to a method and system for thermalizing the surface of a solid-state quantum processor, and more particularly, to a method and system for achieving an optimal operating temperature for solid-state quantum devices, circuits, and processors. In a preferred embodiment, the methods and systems taught herein can provide adaptive control of the operating temperature of quantum circuits and processors to achieve optimal performance therefrom and improve quantum coherence. The present invention is particularly suitable for, but not limited to, quantum circuits operating in a superconducting state.

Background Art

[0002] Solid (superconducting, semiconductor) quantum circuits (QCs) are used to implement qubits (qubits that can be based on superconductors, semiconductor spins, or other solid-state platforms), and such circuits also include low-loss components used to interact with qubits (transmission lines, conductors, resonators) in various architectures. These solid circuits are planar circuits, typically composed of a substrate material (usually 0.1 - 1 mm thick, generally made of high-resistance silicon or sapphire), on which various circuit layers (usually one or more thin films of metal, dielectric, superconductor, etc.) are deposited and patterned using microfabrication techniques to form shapes. The surface area of the substrate can be up to several square centimeters.

[0003] In a more advanced implementation, multiple chips are used. For example, one chip is composed of a quantum bit layer, and another chip is "flip-chip mounted" on top to provide other circuit components (such as resonators, transmission lines, etc.), solving the problem of connectivity in large-scale circuits. These two (or more) "flip-chip mounted" chips are usually connected using metal or superconducting links (such as bump bonds, pads, clamps, wire bonds, etc. located around the chip or away from the quantum bits), passing signals from one to the other, with a small gap (vacuum) existing in between. This gap exists for practical purposes, as it is difficult to perfectly align the chips without a gap, and the quantum bits have electric fields that extend to a certain distance from the plane of the circuit / chip, and these electric fields must not couple with the introduced lossy dielectric material.

[0004] US-2021 / 076,530 discloses a device and method for facilitating the application of a thermalization material within the housing of a quantum computing device. The system includes a quantum computing device disposed within the housing. The system also includes a thermalization material disposed within the housing, which can be superfluid helium.

[0005] US-2013 / 258,595 acknowledges that heat transfer is a concern when scaling up a quantum computer. Some basic superconducting devices dissipate some energy during switching and may come into contact in proximity to the quantum bits. The present disclosure proposes highly conductive thermal vias used to transport hot electrons from the quantum bits to liquid 3He, which has relatively good bulk heat transport properties such as a relatively high thermal conductivity and heat capacity at millikelvin temperatures. It is recognized that there may be problems in obtaining heat from the thermal vias to the liquid helium due to the large Kapitza resistance between the solid and liquid helium. The present disclosure proposes that the Kapitza resistance can be minimized by using a porous open-cell metal "sponge" with a very large internal surface area per unit volume.

[0006] A primary objective in the art is to enhance the coherence of quantum circuits. Coherence time is the time that a quantum circuit can hold quantum information before losing it. (As will be discussed in more detail below) there are numerous causes of decoherence, which is the mechanism that causes the loss of coherence. Since the coherence time directly affects the fidelity of operation, the art aims to enhance coherence. High fidelity is a requirement for implementing fault-tolerant quantum error correction and is a prerequisite for general-purpose quantum computing. To maintain sufficient coherence, solid-state quantum circuits need to operate at low temperatures.

[0007] Many of the different causes of decoherence may be directly or indirectly related to excess energy present in the quantum circuit or its environment, and certain decoherence mechanisms constitute an external energy source that raises the temperature of the circuit or other degrees of freedom of its environment unless it is efficiently removed from the quantum circuit and its environment.

[0008] In the current context, a "quantum circuit" is defined as the complete chip or chip assembly as described. A quantum circuit typically comprises a substrate, dielectrics, metal layers, and superconducting layers, etc., and is patterned into a specific circuit topology to realize the desired functions using quantum physics. The aforementioned components can form a quantum circuit and it is possible to use the quantum circuit to perform quantum computing, quantum sensing, or define other quantum devices that operate based on the fundamental principles of quantum mechanics in other ways.

[0009] The terms "cooling" or "warming" may or may not include the cooling or warming of the quantum state of the device during operation and the thermal distribution of the quantum state. Further, the terms "cooling" or "warming" may or may not include the cooling or warming of the environment of the quantum circuit to which the quantum circuit is coupled, which means different physical subsystems (or degrees of freedom) present on the quantum circuit chip and other aspects of the cryogenic assembly that may have associated temperatures or temperature-dependent properties that affect the performance of the quantum circuit. Such subsystems are described in detail below.

[0010] a) Considerations regarding cooling of quantum circuits Typically, a quantum circuit is cooled within a dilution refrigerator (DR) to achieve a base temperature of about 10 mK, and 5 mK can be achieved with the best commercially available dilution refrigerators. However, in practical quantum circuit embodiments with a large number of signal lines reaching the base of the quantum circuit, temperatures far exceeding 10 mK are common and can reach 50 mK or 60 mK depending on the number of lines.

[0011] The dilution refrigerator operates to cool the phonon temperature of the lowest temperature stage. The coldest plate is usually a large copper plate, which can be plated with a material such as gold (Au) to improve thermal contact and prevent oxidation of the copper. Copper is used because it is an excellent thermal conductor even at very low temperatures, which means that heat generated at one point on the copper plate can be efficiently removed by the cooling mechanism of the dilution refrigerator to maintain a low temperature.

[0012] To cool a quantum circuit, it needs to be thermally fixed to the cold plate of the dilution refrigerator. The thermal anchor can usually be realized as follows. (i) The chip is placed directly on a metal base plate (copper is mainly used because of its excellent thermal properties) or on a printed circuit board (PCB) (specifically, a dielectric or metallized surface), or the chip is surrounded and a cavity (vacuum) is formed in the empty space below it. (ii) Subsequently, the circuit board (if present) is placed on the metal plate (base plate). (iii) The metal base plate forming part of the housing is attached to the cold plate of the dilution refrigerator (DR), either directly or via some additional metal brackets, depending on the configuration.

[0013] It is reasonably easy to achieve fairly good thermalization up to the point of the quantum circuit housing base plate to which the PCB / QC chip is attached. The main problem is the thermal link between the QC components on the chip and the metal base plate, i.e., the thermalization of the QC environment. The circuit layers (superconductors, dielectrics) are thin and have very low thermal conductivity. Furthermore, the thermal conductivity of the substrate (usually silicon, sapphire) becomes zero at the temperature at which the quantum circuit operates. Therefore, in order to cool the quantum circuit itself, materials with better thermal conductivity with respect to the quantum circuit material and low interfacial thermal resistance (Kapitza resistance) are required. Ideally, the empty space (usually vacuum) above (and in some cases below) the quantum circuit chip should be filled with some material that can remove heat better and thermalize the quantum circuit to the temperature of the metal housing.

[0014] Electromagnetic environment and QC housing At the same time, the material filling this empty space needs to be insulating so as not to short-circuit the signals, and the dielectric loss at microwave frequencies must be very low so as not to degrade the performance of the quantum circuit.

[0015] When a dielectric material is introduced into the volume occupied by the microwave electric field, the electric field mediates the coupling between the quantum circuit and two-level material defects, increasing losses, noise, and decoherence. To avoid this, it is common to remove the dielectric substrate material in the regions around the qubits and other high-coherence elements where the electric field is large and penetrates the substrate, on the chip that hosts the qubits themselves. Therefore, to improve coherence, it is desirable to surround the qubits and resonator circuits with vacuum (without substrate) as much as possible, which is well known in the art.

[0016] Quantum circuits are typically housed within a well-shielded environment formed by, for example, superconducting shields, magnetic shields, photon emission shields, etc. In practice, a large number (5 to >10) of individual metal components attached together in various ways are produced using fasteners. The thermal conductivity between the base plate and the dilution refrigerator (DR) cold plate depends on the number of different metal pieces and their interfaces. For this purpose, in order to prevent oxidation that reduces the thermal conductivity across the boundary, the contact between components is improved and the copper is often gold-plated. Since thermal conductivity is a function of the cross-sectional area and length of the thermal conductor, the thermal conductivity also depends on the shape of the components.

[0017] To ensure a good electromagnetic environment, the quantum circuit and the metal base plate are also typically covered with a base plate cover, and the quantum circuit and the PCB are completely surrounded by metal (usually copper). This metal enclosure should be placed so as not to get too close to the quantum circuit, otherwise the electromagnetic modes of the circuit may be distorted, increasing losses and decoherence. This means that the volume inside the enclosure above the quantum circuit is empty (vacuum), and unfortunately, heat can only be conducted by radiation, which is a very inefficient process.

[0018] Figure 1 illustrates a typical enclosure (left) and a flip-chip configuration (right) of a quantum circuit used in the art.

[0019] The heat (residual heat and generated heat) within the quantum circuit cannot be removed from the quantum circuit with the same high efficiency as would be possible if there could be an uninterrupted copper link between the surface layer of the quantum circuit and the cold plate. In fact, when the temperature of the cold plate is 10 mK, the effective temperature of the quantum circuit itself generally far exceeds 50 mK.

[0020] Since quantum circuits require the propagation of electrical signals and a properly designed electromagnetic environment, they cannot be constructed using only materials with very high thermal conductivity (such as copper). Dielectrics with very low thermal conductivity at millikelvin temperatures (vacuum is an ideal dielectric with zero thermal conductivity) are still necessary to realize quantum circuits and enable the controlled propagation of electrical signals. Furthermore, many signal / control lines in typical quantum circuits are made of superconducting materials with low electromagnetic losses, but have very low thermal conductivity compared to ordinary metals (such as copper).

[0021] As a result, the art faces the need to construct quantum circuits from materials with low thermal conductivity, and thermalization in actual implementations relies on heat conduction through many interfaces and materials with low thermal conductivity to the cold plate of a cryocooler.

[0022] Various attempts have been made to improve thermalization in various implementations, but such attempts have not significantly improved the situation so far due to fundamentally mutually exclusive constraints that, for good performance, quantum circuits need to be surrounded by low-dissipation dielectric materials with low thermal conductivity by definition to maintain high coherence and desired functions.

[0023] In large-scale quantum processing units (QPUs), the thermalization problem becomes even more pronounced as the size of the circuits (chips) that require thermalization increases and as a substantially larger number of control signals propagate across the chips, resulting in more heating.

[0024] Cooling the Physical Environment of Quantum Circuits As described above, mainly in the form of phonons, the method by which heat is removed from a quantum circuit, and the physical constraints on the operation of such a quantum circuit that limit phonon-mediated cooling from a quantum circuit chip at mK temperatures have been explained. The above description also shows substrates, oxide layers of superconductors, ordinary metals, elements in flip-chip arrangements, etc., which are many objects in the immediate vicinity of the quantum circuit. In other words, a quantum circuit is coupled to an environment with many degrees of freedom, and the performance of the quantum device degrades due to unwanted energy exchange with this environment. Therefore, it is important to remove extra or unwanted energy or excitations from the environment.

[0025] In actual quantum circuit embodiments, various physical subsystems and imperfections (defects) present in / on the chip (such as surface or bulk spin defects, quasiparticles, conduction electrons in signal wiring, material defects [usually two-level system "TLS" defects], and reservoirs of low-energy fluctuations that cause material-related noise and decoherence) are temperature-dependent, and it has been found that as the temperature decreases, the performance of the quantum device degrades and typically saturates at about 50 mK. This is because these subsystems are not sufficiently thermalized with respect to the base temperature of the dilution refrigerator, and a small heat load (such as due to stray radiation, material losses, signal propagation, etc.) causes significant overheating of the aforementioned subsystems with respect to the base temperature of the cryostat. This has been verified in many experiments on quantum circuits and superconducting resonators in the quantum regime, demonstrating that neither surface spins nor TLS reservoirs can be actually cooled below about 50 mK.

[0026] As an example, FIG. 2 shows a graph representing the measured electron spin resonance (ESR) peak intensity and the theoretically predicted electron spin resonance (ESR) peak intensity as a function of the temperature of two coupled surface spin transitions. This data was obtained from a quantum circuit mounted in a vacuum using typical techniques in the art, and thus thermalization is insufficient. Thermal saturation occurs below about 50 mK, deviating from the theoretically predicted results.

[0027] Many of the published research documents available regarding the temperature dependence of parameters related to quantum circuits need to be borne in mind as reports on research conducted more than five years ago. At that time, the materials and other technologies related to quantum circuits were not as developed as they are today. In particular, the coherence time of qubits was at least one order of magnitude worse than it is today. As a result, many of the previous studies did not necessarily investigate the characteristics relevant to state-of-the-art high-coherence circuits.

[0028] What is currently understood in the art is that as coherence increases, parameter fluctuations due to TLS (which is also related to noise) become more prominent. As a result, in the case of state-of-the-art qubits, based only on current knowledge regarding TLS, the concept of cooling to lower temperatures can even become less desirable.

[0029] Thermal dissipation within the system Even when the quantum circuit is passive and not operating, several different mechanisms, including the following, can contribute to the generation of heat within the quantum circuit that raises the temperature to well above the temperature of the cold plate. (i) Heat generated by electrical control signals dissipated from the circuit. Typical control signals are microwave pulses, constant microwave tones, low-frequency (DC) current signals. (ii) Heat from stray photons, thermal radiation from high-temperature stages within the cryostat, or thermal radiation from the output amplification chain. Recently, much effort has been devoted to designing the quantum circuit environment to suppress high-energy photons reaching the quantum circuit. Techniques include cryostat attenuation and filtering and optimization of absorption materials. (iii) Heat from cosmic particles or ionizing radiation absorbed by the quantum circuit or its substrate. (iv) Heat from stray phonons resulting from temperature rises in other locations within the cryostat, or heat resulting from other remote high-impact events such as (iii). (v) Heat due to ortho-para conversion of hydrogen in the material.

[0030] To thermally equilibrate a quantum circuit to a desired temperature and thereby improve performance, it is desirable to remove this excess heat as efficiently as possible.

[0031] Characteristic Temperature and Temperature Dependence The performance of a quantum circuit depends on the number of competing temperature-dependent mechanisms. For the following reasons, it is not obvious from the knowledge in the art that lowering the temperature is a solution to improving all of these performance metrics.

[0032] (i) Superconductor. Below a specific transition temperature (Tc), some metals lose their electrical resistance and repel magnetic fields. Due to the former property, electromagnetic losses are reduced, and due to the latter property, they exhibit excellent performance as a magnetic shield. The physical reason for superconductivity is that the conduction electrons in the metal form "pairs", and these (Cooper) pairs form a "condensate" that behaves as a single entity as a whole. At finite temperatures, Cooper pairs coexist with quasiparticles, which are broken Cooper pairs (single electrons).

[0033] (ii) Quasiparticles. These are properties of superconducting materials. Quasiparticles contribute to electromagnetic losses at high frequencies, cause parity fluctuations in quantum circuits, and their mechanism leads to noise and decoherence. Near the superconducting transition temperature (Tc), the number of quasiparticles reaches a maximum and decreases exponentially at T < Tc. In common superconductors (such as aluminum, niobium, niobium nitride, etc.) used for quantum circuits, the temperature of the quantum circuit is usually at least one-twentieth of the superconducting transition temperature, which means that the residual quasiparticle density is basically zero (<exp(-20) = 2e-9). However, it has been observed that the number of existing quasiparticles saturates at a much higher value below 100 mK.

[0034] This reason is a topic currently being discussed in the relevant technical field. The origin is thought to be a combination of the continuous replenishment of quasiparticles due to Cooper pair breaking events associated with high-energy effects (cosmic particles or ionizing radiation), and the very slow quasiparticle recombination time (when two quasiparticles form one Cooper pair) at the limit where the number of quasiparticles is small. Other sources of high energy that generate pair-breaking events are also possible, and in this situation, it may be desirable to further lower the temperature in order to understand how it affects the number of quasiparticles and improves phonon thermalization. Currently, the relevant technical field is trying to understand and eliminate this cause. It is theoretically possible to remove the ionizing radiation source next to the quantum circuit by using materials with extremely few radioactive isotopes. Shielding from high-energy cosmic rays can also be achieved by operating the quantum circuit deep underground, but this is unrealistic. Another approach that reduces, but does not completely eliminate, the effects of high-energy events and quasiparticles demonstrated in the relevant technical field is to create quasiparticle traps in the superconducting layer of the quantum circuit by designing the zone where quasiparticles are mainly trapped away from the quantum circuit, preventing their propagation to the associated quantum circuit elements.

[0035] Therefore, based on current knowledge, there is no reason to think that further cooling of the quantum circuit will reduce the number of residual quasiparticles.

[0036] (iii) Thermal distribution of residual qubits. Superconducting qubits typically operate using only two energy levels with typical separations (splittings) corresponding to frequencies in the range of 1 - 10 GHz or temperatures in the range of 50 - 400 mK. To ensure reliable control of the qubits, an undesired thermal (spontaneous) distribution at the upper level is not desired. This thermal distribution follows Boltzmann statistics, meaning that the lower the temperature of the qubit environment, the lower the thermal distribution. In experiments using superconducting qubits, a thermal distribution is typically expected to drop down to about T = 50 mK and saturates with an excess value of a few percent. This is a major problem as it limits the fidelity of qubit operation. In this situation, extensive filtering of the input signal line is required to reduce the amount of stray photons coupled to the device, and the electromagnetic environment needs to be well shielded from thermal photons. Therefore, it is beneficial to cool the quantum circuit and its environment where there can be many different sources of thermal photons. In this regard, in the art, it is desired to thermalize to the lowest possible temperature.

[0037] (iv) Flux noise. Magnetic impurities and surface magnetic moments give rise to magnetic (flux) noise, which also limits the coherence of the quantum circuit. It has been observed that the flux noise within the quantum circuit increases as the temperature decreases (usually until it saturates at 50 - 100 mK).

[0038] (v) Critical current fluctuations. These fluctuations are thought to arise from defects in the Josephson junction barrier. Little is known about the temperature dependence below 90 mK, but above this temperature, the critical current noise has been shown to be proportional to T 2 as shown.

[0039] (vi) Material defects in two-level systems (TLS). These are mainly thought to exist in the dielectrics surrounding the quantum computer, such as the substrate and oxide layers of the superconductor, although some special types of TLS may exist in the superconductor or the Josephson junction barrier itself. Briefly, TLS defects are described as atomic-scale defects that jump between two positions. Importantly, this defect has a charge, resulting in an electric dipole or quadrupole moment that can couple to the quantum circuit. This "jump" causes noise that degrades the performance of the quantum circuit. TLS also interact with each other. It is known in the art that as the temperature decreases, the noise and decoherence generated by TLS increase. Experimentally, it has been shown that in the region where TLS is dominant, the noise increases until it saturates at about 50 mK. This is the same temperature range in which other properties of the quantum circuit appear to saturate. TLS defects also cause parameter fluctuations, which are a major problem in the coordinated control of a large number of qubits within a quantum circuit.

[0040] Therefore, in this regard, seeking lower temperatures would go against the knowledge and understanding in the art. The art focuses on efforts to understand the physics and chemistry of TLS defects, identify their locations, and eliminate or inactivate the defects as much as possible. This may seem like a viable direction, but progress has been limited so far.

[0041] In the general understanding in the art, such TLS defects usually saturate at high temperatures. However, when the material is cooled, these additional degrees of freedom become available and can dominate the low-temperature properties.

[0042] Integrating all these mechanisms results in a contradiction regarding the optimal temperature for operation. The art has long settled on operating quantum circuits at an easily achievable temperature of about 50 mK (using the base temperature of a dilution refrigerator which is 10 mK). This can be easily achieved by attaching the quantum circuit to the mixing chamber plate of the dilution refrigerator, which constitutes the best compromise among the competing mechanisms described above. However, the need to improve the coherence of the quantum circuit remains unsolved.

[0043] Cooling of Electrical Circuits to Microkelvin Temperatures Using adiabatic nuclear demagnetization refrigeration (ANDR), temperatures lower than those of a typical dilution refrigerator (DR) (the highest achievable DR temperature is 5 mK to 10 mK or more) can be realized. By the latter technique, temperatures in the range below 100 μK can be reached. Importantly, in this temperature range, the problem of cooling the quantum circuit and its environment is even more severe than in the millikelvin temperature range. Using adiabatic nuclear demagnetization refrigeration, a remote nuclear stage (NS), which is usually also a copper plate, is thermally connected to a paramagnetic material (such as copper, PrNi5, etc.), and additional cooling is performed by the process of adiabatic nuclear demagnetization. The nuclear stage is connected to the mixing chamber plate of the dilution refrigerator via a thermal switch. A quantum circuit housing with a quantum circuit mounted inside is thermally equilibrated either directly to the nuclear stage or to a plate to which the nuclear stage is thermally connected.

[0044] As far as the attachment of the quantum circuit chip is concerned, there is no difference between the dilution refrigerator and the adiabatic nuclear demagnetization refrigerator, and both are attached to a housing on a copper base plate, but in this case the base plate is the nuclear stage.

[0045] The art has hitherto focused on the development of techniques for cooling electronic systems to cryogenic temperatures, aiming to make the electronic temperature within the device as low as possible. Whether these techniques can also cool TLSs and other subsystems related to quantum circuits is not clear in the art. Previous research has focused on the cooling of low-frequency electronic devices, i.e., for example, phonons, conduction electrons such as semiconductors, metals, or quantum Hall devices and two-dimensional electron gases, or single-charge devices including Coulomb blockade thermometers commonly used to determine temperature at temperatures below mK. The techniques hitherto applied in the art for cooling devices of the aforementioned type have little relation to quantum circuits, and it is not certain in the art that these techniques can cool subsystems related to quantum circuits.

[0046] To measure temperature below mK, two main techniques are used that effectively measure the electronic temperature, which is not the temperature of all subsystems within the device. Usually, these thermometers are placed somewhere on the cold plate of the cryostat. The two most common techniques are Coulomb blockade thermometry (CBT) and (current-sensing) resistance noise thermometry. In the following disclosure, the latter technique is used to measure the temperature of the cold plate at the nuclear stage.

[0047] Therefore, the guidance in the art regarding what the optimal operating temperature of a quantum circuit is, is unclear from the current knowledge in the art because there are competing mechanisms that can contribute differently for each quantum circuit, and it is unclear whether it is even possible to cool the various subsystems relevant for quantum circuits. Therefore, it has not been shown in the art that there is an overall advantage in aiming for temperatures lower than those currently easily achievable (T ~ 50 mK).

Prior Art Documents

Patent Documents

[0048]

Patent Document 1

[0049] Preferred embodiments of the present invention aim to provide a method and system for introducing a cold quantum fluid and immersing a quantum circuit in this fluid. By controlling the temperature of the quantum fluid, the temperature of the quantum circuit and its environment (in the form of many different physical subsystems having unique specific temperature dependencies that affect the performance of the quantum circuit) can also be controlled.

[0050] More specifically, the present invention provides a method and system for optimizing the operating temperature of superconducting quantum circuits and processors and the environment in which they operate. In preferred embodiments, the methods and systems taught herein provide adaptive control of the operating temperature of superconducting quantum processor circuits, ensuring optimal operation and improving coherence. [Means for Solving the Problems]

[0051] The following disclosure teaches a method and system that can more efficiently cool a quantum circuit in a taught environment, for example, using immersion in liquid 3 He. With preferred methods and systems, an operator (human or machine) of a quantum circuit can select an optimal or desired operating temperature of the surrounding fluid, which is determined by the application (thereby also changing the temperature of the quantum circuit and its environment), over a much wider range than would otherwise be possible, and can also optimize performance for all different coherence-limiting mechanisms at work. The methods and systems taught herein can also accommodate future developments in materials science. For example, TLS-induced decoherence can be significantly reduced, and the optimal operating temperature can be significantly lower than the temperatures currently in use.

[0052] As demonstrated in this specification, 3 He is a very efficient low-loss cooling medium, and methods and systems for implementing the immersion of quantum circuits operating in commercially available ultra-low temperature dilution refrigerators in liquid 3 He are taught. Preferred embodiments can significantly improve the thermalization of surface spins and TLS subsystems, which are the main causes of decoherence. As will be described in detail below, in the preferred embodiments taught in this specification, the coupling of the TLS bath with 3 He is significantly improved, thereby significantly improving the thermalization of the TLS and increasing the relaxation rate of the TLS bath by more than 1000 times. The inventors are not aware of any previous experiments or studies that have successfully cooled any or all of these physical subsystems to temperatures below 40 - 50 mK. Some studies have reported circuits operating at a nominal temperature of 10 mK, which is the base temperature confirmed by the thermometer on the cold plate of the dilution refrigerator, but in all of these studies, the temperature of the cold plate does not represent the temperature of the quantum circuit and its environment.

[0053] According to an aspect of the present invention, a system for controlling the temperature of a quantum circuit to an operating temperature of less than 100 mK is provided, the system comprising a housing having a housing wall made of a thermally conductive material, a mass of a porous medium made of a thermally conductive material disposed within the housing and thermally coupled to at least a portion of the housing wall, a substrate for holding the quantum circuit, at least one cooling fluid source, at least one port within the housing directly coupled to the at least one cooling fluid source, a control unit coupled to the at least one cooling fluid source for filling the housing with the cooling fluid to cool the quantum circuit and / or its environment and The control unit is configured to control the supply of the cooling fluid to the chamber to control the degree of cooling provided by the thermalizing fluid within the housing and thereby the amount of cooling provided to the quantum circuit.

[0054] As used herein, the term "cooling fluid" is used to denote a fluid that is a gas or a liquid capable of transferring heat, i.e., having a cooling effect.

[0055] Preferably, at least one cooling fluid source is 3 He, 4 He, or a source consisting of a mixture of these two. More preferably, at least one cooling fluid source is a liquid 3 He source.

[0056] Advantageously, the mass of the porous medium is a sintered material.

[0057] The mass of the porous medium is preferably separated from the quantum circuit to provide a certain amount of thermalizing fluid between the quantum circuit and the porous medium. In a preferred embodiment, the mass of the porous medium is positioned relative to the quantum circuit such that the distance at which the electromagnetic field enters the porous medium from the quantum circuit is small enough not to degrade the performance of the quantum circuit.

[0058] Preferably, a screening element is provided that is disposed between the mass of the porous material and the quantum circuit. The screening element is advantageously made of at least one of a conductive metal and a superconducting material. The screening element may comprise a layer of superconducting material disposed on a layer of metallic material.

[0059] In some preferred embodiments, the porous material comprises a textured or porous inner surface of the housing wall.

[0060] The porous material may comprise a sintered powder or particles of a thermally conductive material.

[0061] The system preferably comprises a capillary that couples a cooling fluid source to the housing, and during use, the capillary is continuously filled with the thermalizing fluid during operation of the system. The capillary can be a valve - less connection between the housing and the control unit.

[0062] A filter can be provided that comprises a housing of conductive material and has one end coupled to the inlet capillary and the other end coupled to the housing or to a capillary coupled to the housing. The housing provides a chamber filled with a sintered filter element, and the filter is operable to reduce or prevent high - frequency noise from entering the housing through the filled capillary and to improve the thermalization of the cooling fluid entering the housing.

[0063] The system can comprise a first cooling fluid source and a second cooling fluid source, the first source being 3 a source of He, and the second source being 4 a source of He, and the control unit is configured to operate or enable the operation of the first and second sources to supply the cooling fluid sequentially or simultaneously. In these implementations, the system can deposit layers of the cooling fluid on the quantum circuit, and these layers can actually take the form of a solid. By layering in this way, the coupling of the cooling liquid to the quantum circuit and different subsystems within its environment can be optimized.

[0064] The control unit is preferably operable to control the amount and / or pressure of the cooling fluid within the housing.

[0065] Advantageously, the control unit is configured to control the supply and pressure of the thermalizing fluid to create one or more layers of thermalizing material on the quantum circuit.

[0066] In some embodiments, the control unit is configured to template separate layers of solid thermalizing material on the surface of the quantum circuit, and the layers are made of the same or different thermalizing materials.

[0067] Advantageously, the control unit is operable to control the amount and / or pressure of the cooling fluid within the housing.

[0068] The system preferably comprises one or more sensors configured to measure at least one parameter of the quantum circuit.

[0069] The system may comprise at least one temperature sensor configured to obtain a measured value of the operating temperature of the quantum circuit, and the control unit is configured to control or enable control of the cooling fluid source based on the temperature measurement.

[0070] Advantageously, the control unit is operable to control the amount and / or pressure of the cooling fluid within the housing based on the measured parameters.

[0071] Preferably, one or more sensors are provided that are configured to measure one or more of noise, decoherence, the probability of thermal excitation of qubit states, phonons, quasiparticle density, loss, temperature-dependent superconducting properties.

[0072] One or more sensors may be provided that are configured to measure one or more of the relaxation or dephasing time of qubits, the gate fidelity of single or multiple qubits, the error rate of logical qubits, the algorithm fidelity, the quantum gate operation fidelity.

[0073] The control unit may be configured to control or enable control of the amount and / or pressure of the cooling fluid within the housing based on the measured or predicted power dissipation within the quantum circuit.

[0074] In some embodiments, the housing may be configured to hold multiple quantum circuits within multiple sub-housings, and the temperature within each sub-housing is controllable, preferably individually controllable.

[0075] Advantageously, at least a part of the inner wall of the housing is connected to a mass of porous thermally conductive material for the purpose of effecting thermalization of the liquid to the metal of the housing and thus effecting thermalization to the lowest temperature stage of the cryogenic refrigerator. When the liquid is sufficiently thermalized to the temperature of the refrigerator, it can provide cooling to the quantum circuit. The inner wall of the housing may be provided with a textured or porous inner surface comprising a thermally conductive sintered powder or particles. In some embodiments, the housing may be filled with a thermally conductive sintered powder or particles.

[0076] The control unit may be configured to control the temperature based on the determined performance of the quantum circuit or to enable the control of the temperature. This may be based on the determined coherence of the quantum circuit.

[0077] The control unit can be configured to control the amount and / or pressure of the cooling fluid within the housing based on the measured or anticipated power dissipation within the quantum circuit.

[0078] In some embodiments, the housing is configured to hold a plurality of quantum circuits within a plurality of sub-housings, and the temperature within each sub-housing is controllable.

[0079] The system may include an adsorption pump operable to adsorb an amount of cooling fluid for the purpose of transferring (gaseous) cooling fluid between the gas handling system and the filling line and the housing, thereby providing better and wider control of the amount and pressure of the cooling fluid within the housing. In a preferred implementation, the adsorption pump is used to achieve a filling line pressure significantly higher than the pressure on the low pressure side of the gas handling system that functions as a (gaseous) cooling fluid source and storage. In a preferred implementation, the low pressure side of the gas handling system is operated at a pressure lower than atmospheric pressure. In some implementations, it may be advantageous to operate the system with the pressure of the cooling fluid significantly higher than atmospheric pressure.

[0080] The system may include a ballast volume connected to the filling line at room temperature for the purpose of stabilizing the pressure of the liquid in the filling line and the housing, thereby stabilizing the physical and dielectric properties of the cooling fluid, such as improving the stability of the quantum circuit parameters. For example, when the filling line operates with continuous filling in a valve - less manner, it helps to protect the quantum circuit from fluctuations caused by temperature variations in different temperature stages of the refrigerator. In a preferred implementation, the volume of the ballast volume is much larger than the total volume of the filling line and the internal housing.

[0081] According to another aspect of the present invention, a housing comprising a housing wall made of a thermally conductive material, a mass of a porous medium made of a thermally conductive material disposed within the housing and thermally coupled to at least a portion of the housing wall, a substrate for holding a quantum circuit within the housing, at least one cooling fluid source, at least one port within the housing directly coupled to the cooling fluid source, In a system including a control unit coupled to at least one cooling fluid source, a method is provided for controlling the temperature of a quantum circuit to an operating temperature of less than 100 mK. The method includes filling the housing with a cooling fluid to cool the quantum circuit and / or its environment, and operating the control unit to control the supply of the cooling fluid to the chamber to control the amount of cooling provided to the quantum circuit and, thereby, the degree of cooling provided by the thermalized fluid within the housing, whereby the performance of the quantum circuit can be adjusted by said control.

[0082] Preferably, the method includes providing, as the cooling fluid, 3 He (helium with isotope number 3), 4 He (helium with isotope number 4), or a combination or mixture of the two. In some embodiments, the systems and methods taught herein have the effect of first creating a layer of a first cooling material on the surface of the circuit (substrate), for example, 4It is configured to add a certain amount of one cooling fluid, such as He. Subsequently, a second cooling fluid ( 3 such as He) is supplied into the chamber and has the effect of creating a layer of cooling compound on the surface of the circuit to be cooled. This layering technique can be used to control the coupling between the environment of the quantum circuit and the physical subsystem with respect to the cooling fluid, and as a result, the thermal properties of the cooling medium and the controlled cooling of the circuit can be optimized. In these embodiments, a plurality of thermal materials are provided in layers, but in other embodiments, the thermal materials can also be mixed into a single layer (or one of the layers of a multi-layer thermal control structure).

[0083] In practice, the purpose of this feature is to form one or more solid layers on the substrate (circuit) that optimize the thermal coupling. Usually, the layer is very thin, with a thickness on the order of one to several atoms. Preferably, the layer or each layer is a complete layer across the entire surface of the substrate (circuit), but in some cases, it is not excluded that the layer or at least one of its layers can be a partial layer, that is, it does not form a complete coating across the entire surface of the substrate (circuit).

[0084] The principle of these embodiments is to form a solid layer of a material or composition different from the bulk cooling material in the chamber on the substrate (circuit). In one practical embodiment, first 4 a thin layer of He is applied on the substrate, and then the chamber is filled with bulk 3 He. In other embodiments, one or more 3 He, 4 He, or a mixture of the two layers are applied before the chamber is filled with 4 He or 3 He.

[0085] More preferably, this method includes providing liquid 3 He as the cooling fluid.

[0086] This method advantageously controls the amount and / or pressure of the cooling fluid in the housing.

[0087] This method may include the step of measuring at least one parameter of a quantum circuit. This method may include, for example, measuring the operating temperature of the quantum circuit and controlling the supply of the cooling fluid based on the temperature measurement. It may also include the step of controlling the amount and / or pressure of the cooling fluid in the housing based on the measured parameter.

[0088] Advantageously, this method includes the step of sensing one or more of noise, decoherence, thermal excitation probability of qubit states, phonons, quasiparticle density, loss, temperature-dependent superconducting properties. Alternatively or instead, it may include the step of measuring one or more of the relaxation or phase shift time of qubits, the gate fidelity of single or multiple qubits, the error rate of logical qubits, the algorithm fidelity, the quantum gate operation fidelity.

[0089] This method may include the step of controlling the amount and / or pressure of the cooling fluid in the housing based on the measured or predicted power dissipation in the quantum circuit.

[0090] In some embodiments, this method includes the step of holding a plurality of quantum circuits in a plurality of sub-housings and individually controlling the temperature in each sub-housing.

[0091] Preferably, the housing wall has a textured or porous inner surface. The housing wall may have a textured or porous inner surface provided with a thermally conductive sintered powder or particles. The housing may be filled with a thermally conductive sintered powder or particles.

[0092] This method may include the step of controlling the temperature based on the determined performance of the quantum circuit, for example, based on the determined coherence of the quantum circuit.

[0093] Generally speaking, the teachings herein are for a liquid as a cooling medium in a technical solution for implementing an immersion cell suitable for a quantum circuit operating in a dilution refrigerator. 3It is preferable to use He (helium with isotope number 3). The results shown below relate to 3 He in a "normal" fluid (non-superfluid) state rather than in a superfluid state (below 0.9 mK at saturated vapor pressure). However, for 3 He in a superfluid state, cooling is also efficient, but the efficiency is considered to decrease.

[0094] In the methods and systems taught herein, in addition to cooling, 3 He is thought to be able to affect the circuit and its environment in various ways and may lead to an improvement in the coherence of the quantum circuit.

[0095] The teachings herein 3 demonstrate that He can be a very good cooling medium with low dielectric loss and teach a method of implementing the immersion of a quantum circuit operating in a commercially available cryogenic dilution refrigerator in liquid 3 He. The thermalization of the surface spin and TLS subsystems can be significantly improved. When attached to a dilution refrigerator, the quantum circuit and environmental temperature can be effectively controlled from 5 mK to above 50 mK, and when attached to a nuclear adiabatic demagnetization refrigerator stage with additional cooling capabilities, from below 1 mK to above 50 mK.

[0096] 3 Instead of 4 He, 3 He (helium with isotope number 4) is also beneficial and, as described herein, 3 can be used instead of

[0097] A preferred embodiment of the present invention aims to provide a method and system for adaptive cooling that can obtain the optimal temperature of a quantum circuit regardless of the optimal temperature. Such adaptive cooling may be either static or dynamic, in which one or more performance metrics related to the quantum circuit are optimized with respect to temperature. In the operation of a quantum circuit and in the main aspects of its specific applications, the optimal temperature may vary for each quantum circuit depending on the specific effects of various physical mechanisms that cause performance degradation. Even for different quantum circuits having the same application or function, the optimal temperature may still be different depending on the implementation method.

[0098] Suitable performance metrics include, but are not limited to, the following properties of directly measured physical systems, which can be used alone or in combination. - Noise due to charged material defects or paramagnetic impurities (charge noise or flux noise), - Decoherence, - Thermal excitation probability of qubit states, - Distribution density of thermally excited phonons, - Quasiparticle density, - Loss, - Temperature-dependent superconducting properties.

[0099] Other suitable performance metrics are parameters that can be inferred from the operation of the device, - Relaxation or phase shift time of qubits (an important fundamental metric), - Gate fidelity of single or multiple qubits (an important metric for quantum processors), - Error rate of logical qubits (composed of multiple physical qubits), - Fidelity of specific quantum gate operations, - Fidelity of specific algorithms executed on a quantum processing unit (QPU), or classes of algorithms and sub-algorithms, - Regarding minimizing the need to repeatedly recalibrate the QPU to achieve optimal performance, - The temporal stability of one or more device-specific parameters or performance metrics, - includes one or more of the sensitivity, stability, or signal-to-noise ratio of a quantum circuit operating as a quantum sensor (e.g., magnetometer, charge sensor, single photon detector, etc.).

[0100] Any combination of parameters, not limited to those listed, can also be used to evaluate the optimal temperature.

[0101] In some situations, it may be desirable to change the temperature of the quantum circuit during operation, 3 or to change the cooling power provided by the He cooling system. For example, when performing a less resource-intensive calculation in a quantum processing unit, only a part of the unit may be utilized, so less heat is dissipated. To maintain the optimal temperature of the circuit, an adaptive cooling system can be configured to reduce the cooling power. On the other hand, when performing a resource-intensive calculation using the entire quantum processing unit, more heat is dissipated, and to maintain the same low optimal operating temperature, the cooling power of the adaptive cooling system can be increased.

[0102] To implement such adaptive cooling, a feedback loop can be constructed, i.e., the relevant quantities are measured and the deviation from the optimal temperature is determined by an appropriate algorithm or by user evaluation. The algorithm or the user determines a new target temperature, which, as described above, is achieved by increasing or decreasing the heating power applied by a (resistive) heater to the cryostat cold plate thermally linked to the quantum circuit.

[0103] Even in a configuration where multiple quantum circuits are integrated within the same housing, the same housing and an adaptive cooling system can still be used. This example is a quantum processing unit and an individual parametric amplifier connected in series to the output (readout) microwave line of the quantum processing unit. This enables the amplifier to be placed as close as possible to the quantum processing unit in order to minimize signal loss between the quantum processing unit and the amplifier. With such an arrangement, the quantum processing unit is less affected by the additional heat dissipated by the amplifier. The microwave filter through which the (to-be-described) cooling medium flows can also provide a convenient means of separating two microwave environments that share the same cooling housing (such as by using a sintered metal powder mass in between).

[0104] In other implementations, the same adaptive cooling system and housing are made to form part of the dilution refrigerator itself, and the cell containing the cooling fluid and the quantum circuit is integrated with the mixing chamber of the dilution refrigerator.

[0105] Other aspects and features of the present invention will become apparent to those skilled in the art from the following teachings, as will be described later.

[0106] Embodiments of the present invention will be described by way of example only with reference to the accompanying drawings.

Brief Description of the Drawings

[0107]

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Embodiments for Carrying Out the Invention

[0108] The following teachings relate to methods and systems (devices) for providing additional cooling to quantum circuits (QCs) and quantum processing units (QPUs) and their environments in order to guarantee operation at low temperatures below about 50 mK, preferably on the order of 10 mK. The method and system also adaptively control the temperature of the quantum circuit or quantum processing unit, preferably to guarantee optimal, or near-optimal, or desired operation. The temperature to be controlled need not be the lowest temperature, but is determined by measuring one or more operating parameters of the quantum circuit or processor, and it is preferred to ensure that the one or more measured parameters are at an optimal or preferred level. Such adaptive control can be performed, for example, periodically at startup or continuously during operation of the circuit or processing unit.

[0109] A preferred embodiment utilizes a housing made of a high thermal conductivity material that is thermally connected to the base plate of the lowest temperature stage of the cryostat in which the embodiment is housed. 3 The housing filled (i.e., saturated) with a preferred cryogenic fluid, He, has a temperature transfer enhancement function and provides a large surface area between the conductive walls of the housing and the enclosed fluid to optimize heat transfer from the fluid to the housing and the cryostat. The quantum circuit or unit is held within the housing and is directly exposed to the low temperature environment via the cryogenic fluid. The system includes a control unit configured to control or enable control of the temperature of the system (housing and liquid) based on measured circuit, or processing unit parameters, or generated thermal energy, or based on an estimated operating temperature or heat generating operation. As a result, the quantum circuit can operate at a lower speed than previously achieved to optimize the function of the circuit. In addition, due to the adaptability of the system and method, even if the actual operating temperature of the quantum circuit normally increases due to the operation of the circuit as occurs in conventional systems, the system and method taught herein can guarantee that the actual operating temperature of the circuit is maintained at a temperature considered optimal or other preferred temperature.

[0110] The following description discloses only the preferred embodiments, and it should be understood that those skilled in the art can devise other embodiments by utilizing the teachings herein.

[0111] The main components of the described embodiments are considered to consist of the following three parts, namely, (1) Gas Handling System (GHS), (2) Control Signal System for Quantum Circuits, (3) Cells or housings for quantum circuits.

[0112] It will also be understood that the system includes a controller for controlling the temperature of a fluid, including, for example, heating a plate by a resistive heater.

[0113] The system is intended to immerse micro / nano-fabricated quantum devices, preferably in a quantum bath containing liquid 3 He, 4 He, or a mixture of the two. What is provided below is a qualitative and quantitative evaluation of each part or element of the setup.

[0114] A schematic diagram of the apparatus or system is illustrated in FIG. 3. The apparatus 100 includes a housing or chamber 110 preferably made of a highly thermally conductive material such as copper (or gold-plated copper) or lined internally with such a material. The inner wall 118 of the housing is preferably configured to have a surface area much larger than the area of the wall itself. In this example, as will be described in more detail below, a part of the inner wall is formed by sintering a thermally conductive particulate material. Increasing the effective surface area of the inner wall and adjusting the packing ratio of the sintered body optimize the heat transfer from the wall to the interior of the housing, specifically to the fluid within the chamber 110.

[0115] As a result of the acoustic mismatch between liquid He and the bulk metal, the thermal resistance at the solid metal / He interface becomes very high, and the thermalization of liquid He becomes insufficient. To reduce the thermal resistance at the interface, sintering can be used to increase the contact area between the fluid and the solid. By sintering, the 3 Another reason for the decrease in the thermal boundary resistance at the liquid 3 He / solid metal interface is due to its porous structure. When the packing fraction is optimized, the particles constituting the sintered body are bridged with each other, forming a long structure intertwined with long fluid channels. These sintered structures are

[0116] Inside the chamber 110, a quantum circuit or a processor unit 112 supported on a substrate 114 is arranged. The substrate 114 can be a PCB or a part of the housing wall or a directly formed part of other materials. This substrate preferably mediates cooling to a much lower temperature (10 mK or less) disclosed herein, a temperature lower than 50 mK, preferably close to the temperature of the cryogenic refrigerator used.

[0117] The device also, in a preferred embodiment, includes a fluid source 122 in the form of a liquid or a gas, 3 He, 4 He, or a mixture of these two. The fluid source is connected to a fluid control unit or valve 130 used to control the amount of fluid supplied to the chamber 110 via a pipe or other conduit 124.

[0118] Also provided is a sensor unit 140 suitably connected to the chamber 110, the quantum circuit 112, and any other elements of the apparatus via one or more sensor connectors 142. The sensor unit 140 may include one or more sensors designed to measure one or more parameters of the apparatus 100, including, for example, the temperature of the fluid in the chamber 110, the pressure of the fluid in the chamber 110, the operating temperature of the quantum circuit or quantum processing unit 112, the power usage of the quantum circuit or processing unit 112, etc., as described in further detail below. The unit 140 may utilize sensors known or apparent to those of skill in the art and will not be described in further detail herein.

[0119] The apparatus also typically includes a processing unit for controlling the system, which may be part of the fluid source 122, the sensor unit 140, or a separate unit. The processing system also typically includes a temperature control system.

[0120] The gas handling system, in this embodiment, comprises: 3 The gas handling system is used to store He gas at room temperature. 3 a gas transfer unit 130 configured to transfer He gas, the gas transfer unit 130 regulating the amount of gas transferred to the chamber and 3 Adjust the pressure of the He fluid and finally release it from the chamber. 3 The He fluid can be removed. The gas transfer unit is described in more detail below.

[0121] The apparatus also includes a control signal system, which will be described in more detail below and which may form part of cell 110. In this embodiment, it is used to carry microwave signals to the cell, return and amplify signals from the cell, and minimize interference from the external environment to the cell. The control signal system may include any number of input and output signal lines that can support either microwave signals in the range of typically 1 to 10 GHz or low-frequency signals from below 1 GHz to 0 Hz used for the control and readout of quantum circuits, and the specific requirements are determined by the specific implementation of the quantum circuit.

[0122] The control signal system is preferably designed to be compatible with measurements performed in an adiabatic nuclear demagnetization stage or a dilution refrigerator. The cell or chamber 110 contains the quantum device 112 and the cooling fluid (helium), provides electrical and mechanical shielding for the quantum device, connects the quantum device to the control signal system, and provides appropriate conditions for microwave measurements of the quantum device.

[0123] Typically, a dilution refrigerator is used to cool the quantum circuit, but there are also alternative means for achieving even lower temperatures. By attaching a nuclear demagnetization unit to the base plate of the dilution refrigerator, an additional cooling stage using the physical laws of adiabatic nuclear demagnetization is provided. As a result, another plate (nuclear stage, NS) similar to the cold plate of the dilution refrigerator (usually gold-plated copper) is generated, and a thermodynamic temperature below 100 microkelvin can be achieved. Techniques for cooling electronic devices to very low temperatures are known.

[0124] Gas handling system A gas handling system of a preferred embodiment is schematically illustrated in FIG. 4 and includes a high-pressure line or tube (thin black line) 200 and a low-pressure line (thick black line) 210. Outside the cryostat, the inner diameter of the low-pressure line 210 is preferably about 4.6 mm, and the inner diameter of the high-pressure line 200 is preferably about 1.4 mm. The selected material is 316 stainless steel, but other materials can also be selected. The wide-diameter line 210 is provided to minimize the fluid flow impedance when the fluid returns to the storage 220 (either through the cold trap 230 or the release valve), and the narrow-diameter line 200 is provided to minimize the dead volume of the gas in the gas handling system while countering a moderately low impedance to the fluid flow.

[0125] Inside the cryostat 240, the line 212 preferably has an inner diameter of about 0.14 mm and is made of a cupronickel capillary with a wall thickness preferably of about 0.18 mm or more to maintain pressure. This is 3 to minimize the dead volume of He and the heat flow between the cryostat plates.

[0126] As is apparent from FIG. 4, the gas handling system includes a room-temperature portion 224 and a portion inside the cryostat 240 indicated by the dashed line. The elements 50K, 4K, CP, MXC, and NS in FIG. 4 represent different temperature stages inside the cryostat 240, and the elements CP, MXC, and NS represent the cold plate (CP), the mixing chamber plate (MXC), and the nuclear stage plate (NS). The digital pressure gauge is used for accurate pressure measurement with a resolution of 1 millibar to accurately control the amount of gas transferred.

[0127] The heating of each plate inside the cryostat is achieved by soldering silver to a helix formed by winding a CuNi capillary approximately 10 times around a copper bobbin having an outer diameter of about 6.5 mm (1 / 4 inch), and preferably fixing the bobbin to the plate with brass screws. Since brass shrinks more than copper during cooling, the thermal contact between the bobbin and the plate is improved.

[0128] The capillary 214 connecting the cell 250 to the filter 260 is preferably dimensioned to keep the heat flow to the nuclear stage below 1 nW under the following operating conditions. - Mixing chamber temperature: T MC = 30 mK - Nuclear stage temperature: T NS = 1 mK - Capillary material: CuNi - Capillary inner diameter: ID = 0.14 mm - Capillary outer diameter: OD = 0.50 mm

[0129] Under these conditions, the length Lc of the capillary is 2.5 cm or more. In a preferred design, the length of the capillary is 50 cm. When filled with He at 0 bar 3 about 50 pW of power P is added to the nuclear stage (P capillary = 10 pW and P 3He = 40 pW). Thus, by using a thin capillary having the described characteristics, or a similar one, the disclosed cooling system can operate with a liquid cooling medium inside the cell and inside the capillary without the need to evacuate the capillary to reduce the heat load on the refrigeration system used. The gas handling system is designed to operate safely at operating pressures in the range from 0 bar to 60 bar or more.

[0130] The device is preferably configured, as disclosed above, such that when filled with a thermalizing material, the capillary that drops from room temperature to the lowest temperature stage of the cryogenic cooler does not cause a heat deficit between different temperature stages of the cryogenic cooler and does not impair the performance of the cryogenic cooler. For this purpose, the heat leakage between the continuous high-temperature stage and the low-temperature stage caused by the capillary and the internal heat medium is smaller than the cooling power of each temperature stage. Under this condition, when both the cell and the capillary are filled with the thermalizing liquid, the operation of the quantum circuit inside the cell becomes possible without the need to seal the cell after filling or remove the thermalizing agent from the inside of the capillary. This is achieved by using a capillary made of a material with low thermal conductivity (CuNi is used in a preferred implementation form), having a small cross-sectional area and a small inner diameter, and keeping the cross-sectional area of the heat medium inside the capillary sufficiently small.

[0131] As described above, thermalization at each plate inside the cryostat is achieved by soldering a CuNi capillary about 10 times around a copper bobbin having an outer diameter of about 6.5 mm (1 / 4 inch) in a spiral and preferably fixing the bobbin to the plate with brass screws.

[0132] The design of the filter 260 on the mixing chamber plate is aimed at preventing high-frequency noise from entering the cell 250 through the filling capillary and improving the thermalization of the cooling fluid entering the cell through the large surface area provided by the sintered body to the cryogenic cold plate of the refrigerator, as shown in FIG. 5. Without the filter, heat radiation can freely propagate from one end (room temperature) to the other end (inside the cell), impairing the operation of the quantum circuit. The filter 260 preferably comprises a copper body or housing 300, one end through which the capillary 216 to the CP plate passes, and the other end is closed by a copper lid 320 which has an opening for the passage of the capillary 214 to the cell. The lid 320 is hermetically fixed to the housing 300, for example, by a solder joint 330. The housing 300 provides a chamber filled with a filtering element, preferably a silver (Ag) sintered body 310. The sintered silver powder 310 preferably has a particle size of 1 micrometer or less and is compressed inside the housing 300 which preferably has a length of about 0.5 cm in this embodiment.

[0133] The filter 260 in the MXC temperature stage is used to heat the cooling fluid to the MXC temperature.

[0134] The microwave filter disclosed herein is not only useful as an input line for the cooling fluid to the cell, but also the same 3 It can also be used to separate cells sharing a He bath, thereby providing a high-frequency shield between the cells.

[0135] As shown again with reference to FIG. 4, the adsorption pump 271 is a sealed mass connected to the rest of the gas handling system via line 200 and preferably contains activated carbon m charcoal = 25 g as the adsorbent. The adsorption pump is inserted into the low-temperature environment 270 to adsorb a certain amount of the cooling medium (preferably 3 He) from the gas handling system and is preferably liquid 4It is cooled to a temperature of about 4K by insertion into He. The adsorbed cooling medium can be released from the adsorption pump and sent to other parts of the gas handling system by raising the temperature of the adsorption pump 271, preferably by removing it from the low-temperature environment 270. The body of the adsorption pump 271 is preferably made of austenitic stainless steel (316L) that maintains mechanical properties in liquid helium.

[0136] In order to prevent pressure fluctuations due to temperature fluctuations at different temperature stages inside the refrigerator, the 3 When operating He at high pressure, it is preferable to connect the ballast volume 280 at room temperature to the filling line. The ballast volume 280 preferably has a volume that is 10,000 times or more the internal volume of the cell and the filling line. In a preferred implementation, the ballast volume is 60,000 times or more the internal volume of the cell and the filling line, and the temperature of the gas contained in the ballast is regulated.

[0137] In some embodiments, multiple gas handling systems connected to the same cell are used to template separate layers of solid 3 He or 4 He on the surface of the quantum circuit. This can be a preferred solution when it is necessary to maintain the purity of 3 He. In another preferred implementation, a single gas handling system using two storage volumes 220, one with 3 He and one with 4 He, can be used. In another implementation, 4 since the absorption efficiency of 3 He is higher than that of 3 He, a single gas handling system with a single storage volume 220 filled with a mixture of 4 He and 4 He and a very small amount of 4 He can be used to pre-plate the quantum circuit with

[0138] Control signal system As shown with reference to FIG. 6, the quantum circuit control signal system up to the mixing chamber can be in a form known for dilution refrigerator systems. Coaxial cables are used to exchange microwave signals with the quantum circuit. Preferably, the coaxial cable is 0.86 mm CuNi - CuNi for the input line, 0.86 mm NbTi - NbTi for the output line up to the HEMT amplifier, and 0.86 mm CuNi - CuNi for the output line between the HEMT amplifier and the room temperature plate.

[0139] The quantum circuit control signal system can be composed of any number of input signal lines and output signal lines and can have different configurations depending on the application. The signal lines can be microwave lines that support signals in the GHz frequency range (usually 1 - 10 GHz), as in the implementation shown in FIG. 6, or low - frequency lines that support signals in the frequency range from 0 Hz to 1 GHz.

[0140] The input line between the IR filter (thermalized to the mixing chamber plate) and the cell is desirably interrupted by an additional 0 dB attenuator thermalized to the nuclear stage plate. This allows the central core of the coaxial cable to be thermalized before connecting to the cell and at the same time minimizes the microwave dissipation at the nuclear stage. The coaxial cable connecting the IR filter to the nuclear stage plate (via the cell or the attenuator on the plate) is sized to keep both the passive and active loads to the nuclear stage below 100 pW per line under the following operating conditions. - Mixing chamber temperature: T MC = 30 mK - Nuclear stage temperature: T NS = 1 mK - Material of the drive line: CuNi - PTFE - CuNi - Material of the output line: NbTi - PTFE - NbTi - Coaxial dimensions (outer diameter - PTFE outer diameter - core outer diameter): 0.86 mm - 0.66 mm - 0.20 mm - Maximum input power to the cell: - 82.4 dBm

[0141] Under these conditions, the length of the coaxial cable is preferably L for the CuNi drive line CuNi ≧8 cm, and L for the NbTi output line NbTi ≧0.7 mm. (Assuming that the dissipated power in the coaxial cable is evenly distributed between the nuclear stage plate and the mixing chamber), when Pcell = -82.4 dBm, for the active load condition P active ≦100 pW, the length L of the CuNi coaxial cable CuNi ≦115 cm (this includes the CuNi coaxial cable between the 0 dB attenuator and the cell). The dissipation in the NbTi coaxial cable is negligible compared to that in CuNi, so there is no substantial limit on the maximum length of the NbTi output line.

[0142] Cell The cell, or housing, is considered to consist of three main elements: a quantum circuit (sample) holder, an optional sample cover, and a lid. Each of these elements is formed of different parts with specific functions. The entire cell, specifically the three elements and their components, is shown in FIG. 7. Below, each of these elements, their parts, and their functions will be described.

[0143] In FIG. 7, the diagonal stripes represent (in this embodiment) a mass filled with liquid 3 He, the dotted region represents the sintered body, and the wavy region represents the microwave cavity filled with liquid 3 He.

[0144] The sample holder for holding the quantum circuit 410 includes a sample holder body 400, a silver sintered body 430, and a hermetic microwave feedthrough 460. Its functions are - To cool the liquid helium - To support and secure the quantum circuit (sample) - To form one side of the microwave cavity (where the quantum circuit is located) - Connecting a quantum circuit to a signal control system, - Completing parts of a leak - free container for liquid helium (in normal or superfluid state), - Providing a high - frequency shield to a mass inside a cell.

[0145] The body of the sample holder 400 is preferably made of oxygen - free high - conductivity (OFHC) copper with a residual resistance ratio (RRR) exceeding 100. The body 400 preferably has a stepped profile on the base 402 to accommodate an indium seal 470 that can hold at least 50 bar. The cell body 400 is directly thermally coupled to the lowest - temperature stage of the cryostat and cools all other components of the cell.

[0146] In the body 400, as shown in FIG. 7, holes are drilled to accommodate microwave feed - through connectors 460. These connectors 460 are sealed to prevent liquid 3 He or 4 He480 from leaking out of the cell. In a preferred implementation, the connectors are made of a glass dielectric and a metal body.

[0147] The silver - sintered heat exchanger 442 is pressed directly against the sample - holder body 400 to maximize the heat conduction of the cooling fluid to the body 400, and as a result, it is sufficiently thermally coupled to the cryostat base plate. The sinter 430 is made of silver powder with a typical particle size d 3 ≦1 micrometer and a packing fraction p≦50% (density≦5 g / cm grain ). In a preferred implementation, the sinter has a particle size of about 70 nm and is a silver sinter. The dimensions of the heat exchanger are based on the following operating conditions, namely, - Nuclear stage temperature: T NS = 400 microK, - Heat load dissipated from the quantum circuit to the liquid 3 He bath: P dissipated = 2 pW, and deltaT=T 3He - T sinterDimensioned to maintain ≦10 microK.

[0148] Under these conditions, the required surface area of the sintered body is A sinter ≧0.5 m 2 which corresponds to a sintered body of m sinter >0.25 g. In this implementation form, the total sintered surface area is A sinter >10 m 2 and is estimated to be.

[0149] The function of the sample cover 440 is - to form the opposite side of the microwave cavity, - to reduce the required volume of liquid inside the cell.

[0150] In an exemplary implementation form, the total sintered surface area was 24.1 m 2 In a preferred implementation form, the sintered material is placed in a sample housing sufficiently far from the quantum circuit chip so as not to cause additional loss or decoherence. For example, on the opposite side of the copper plate holding the sample, the sintered surface is separated from the sample and covers the mass below the sample through which no electrical signal propagates from the sample. Further details of this characteristic of the preferred implementation form, applicable to all embodiments disclosed herein and thereby contemplated, are given below in connection with FIG. 16.

[0151] The body of the sample cover 440 is preferably made of OFHC copper and is screwed to the sample holder body 400. The microwave cavity 450 is formed by the body of the sample holder 400 and the sample cover 440. This mass is also filled with bulk liquid helium 480. The cavity side of the sample cover is profiled to maximize the compatibility between the quantum circuit (sample) to be measured and the cavity.

[0152] The lid is composed of a lid body 420 and a filling line 490. Its function is - to complete the part of the leak - free container for liquid helium (in the normal or superfluid state), - Directly connected to the filling line of liquid helium, - Providing a high-frequency shield to the mass inside the cell.

[0153] The lid body 420 is preferably made of OFHC copper. The filling line 490 is preferably attached to the lid 490, whereby the quantum circuits can be prepared separately without removing the filling line 490 from the cell and can be attached to the sample holder body, for example, on a bench. The hermetic seal 470 for confining liquid helium is provided by a stepped indium seal. In some implementations, the filling line can also be attached to the sample holder body 400.

[0154] In a preferred embodiment, the cell is preferably designed to withstand a high pressure of the internal liquid coolant, preferably 60 bar or more.

[0155] Method of introducing the liquid cooling medium At T = 10 mK, the liquid 3 The viscosity of He is very high, and it takes a considerable amount of time to fill the cell through a small capillary. To fill the cell, the base temperature is preferably raised to about 200 mK (or higher), and then small "shots" of gas (condensed into liquid by the cooling stage in the cryostat) are introduced one by one from the gas handling system. By opening and closing the relevant valves of the gas handling system, a single "shot" is introduced, and at that point, the pressure of the gauge connected to the capillary volume is used to 3 Monitor the condensation of He. A pressure of 0.1 - 3 bar is applied, and then 3 As a result of the condensation of He, the gas handling system is sealed until the pressure in the capillary drops. When the pressure is low enough, a specific amount of 3Another "shot" is introduced until He is injected into the cell. The quantum circuit can be used as a "level meter" indicating the case where the liquid level is above the quantum circuit (see Fig. 8). In another implementation, it is assumed to have a second quantum circuit (e.g., a superconducting resonator) placed on top of the actual quantum circuit and functioning as a level meter. In another embodiment, a plurality of quantum circuits can be geometrically arranged at different heights and made to function as a level indicator. This procedure can be carried out by operating the gas handling system manually or by implementing a computer software control system that performs the same function.

[0156] Results 3 Evidence of the presence of liquid He Fig. 8 shows 3 the time variation of the resonance frequencies (measured using a vector network analyzer, VNA) of two superconducting resonators when He is introduced into the cell. Specifically, Fig. 8 (left side) shows 3 the frequency shift of the superconducting resonator when He is introduced into the cell. The two traces show two resonators having resonance frequencies of 5.85 GHz and 6.44 GHz, respectively.

[0157] When the liquid accumulates at the bottom of the cell and coats all the surfaces in the thin film layer, a small frequency shift is observed. A sharp increase in frequency is seen at t = 1400 minutes, which corresponds to the liquid level rising to cover the entire resonator. The relative total frequency shift from t = 0 to t = 1600 (i.e., the empty cell and the filled cell) 3 corresponds to the predicted frequency change due to the relative dielectric constant of He of 1.0426. The measured values agree within 2%. This is shown in the right panel of Fig. 8, where for the 5.85 GHz resonator, the measured frequency shifts for two cases (the round markers correspond to the filled cell and a film of about 4 nm thickness of 10 monolayers) are compared with the shifts predicted based on electrostatic simulations, indicating that the resonator can be used as a level meter.

[0158] Evidence of Cooling Surface Spin 3 The effect of He can be seen in the surface spins that exist within the device and are magnetically coupled to the resonator (note that TLS electrically causes resonator frequency noise and loss coupling). Figures 9A and 9B show the electron spin resonance (ESR) spectra obtained in situ within the resonator. The y-axis shows the additional loss when a magnetic field is applied, and the zero-field loss has been subtracted. The spectra have several features, and in this specification, particular focus is on the rightmost peak that arises from atomic hydrogen within the quantum circuit. This is associated with the leftmost of the three existing peaks and is hyperfine split with an energy of h*1.4 GHz, where h is Planck's constant. Thus, the relative intensities of these peaks function as a thermometer, and their intensity is given by the Boltzmann distribution between the two peaks. The peaks exist when the quantum circuit is in vacuum at both T = 50 mK and T = 1 mK of the cryostat base plate, and their intensities are similar. This means that, as previously seen in the prior art, the surface spins are not cooled beyond 50 mK. When 3 He is present in the cell and the cold plate is maintained at 40 mK, no qualitative difference is seen in the data compared to the data of the empty cell at 50 mK (see Figure 2). However, when the cold plate is cooled to 1 mK, the third peak completely disappears, meaning that these hydrogen surface spins have been cooled to a lower temperature. Thus, 3 He cools the surface spins very efficiently.

[0159] Evidence of Cooling of TLS Figure 10 shows the magnitude of the frequency noise measured with a superconducting resonator versus the temperature of the cryostat (NS stage).

[0160] Specifically, FIG. 10 shows the superconducting resonator frequency spectrum noise density normalized to the resonance frequency (6.44 GHz) at 0.1 Hz, with respect to the temperature of the cold plate of the nuclear demagnetization stage (NS) used to achieve temperatures well below 1 mK. The NS is attached to the base plate of the dilution refrigerator and provides one additional cooling step. The well-known dependence of noise on temperature can be seen, and the noise increases at a rate of T -1.5 as the temperature decreases. Then, it saturates and appears to decrease instead when the threshold of 30 - 40 mK is crossed. However, the inventors have discovered that this is not a decrease in the noise itself, but rather a transition of the system into the region of TLS saturation. The red data obtained at low power has a specific characteristic that the magnitude of the noise changes by about a factor of 3 over time. These are temporal fluctuations due to defects in the TLS material. At high microwave power (photon number N ~ 400 in the resonator), these TLS saturate. It takes about 6 days to reach from 1 mK to 300 mK.

[0161] The data (Sy) shown is the extracted magnitude of the power spectral density at 0.1 Hz, in the region of the frequency noise spectrum where 1 / f - type TLS noise is dominant. The y - axis is scaled to the resonator frequency (convention). This figure shows two data sets obtained at different power levels (photon number N) in the resonator. As the power increases, more TLS saturate. The noise follows the expected trend of increasing as the temperature decreases down to about 50 mK. Then, the noise dependence reverses and appears to decrease again below about 30 - 40 mK. This transition is related to the saturation of the TLS. At high temperatures, the system is in the moderately weak electric field region (N ~ N c ), and the noise is expected to be proportional to T -1-2μ , where μ is a positive number less than 1. This is shown by the dashed line using μ = 0.25 in FIG. 10. When the transition temperature drops below about 80 mK, the noise begins to decrease upon cooling. This region is discussed in more detail below.

[0162] The "low-power" dataset shown (photon number N~40 in the resonator) is less smooth than the "high-power" dataset. This is due to the temporal fluctuations of the TLSs, and during the measurement process (about 6 days), strongly coupled individual TLSs enter and exit resonance with the resonator and drift, temporarily increasing the noise. Thus, the fluctuations in the "low-power" data are considered to be additional to the general trend due to a large ensemble of weakly coupled TLSs. At high power, the strongly coupled TLSs saturate easily, and the remaining trend is that of the ensemble. This is expected to shift towards a higher noise level and the transition temperature to shift slightly lower, looking the same as the "high-power" data.

[0163] This can instead be verified by measuring the power dependence of the noise at a fixed temperature (Figure 11), where [Number] it can be observed that the noise decreases as the power (photon number N) increases, where A 0 is the magnitude of the noise at zero photons, and N c is the critical photon number for saturation, determined by the characteristics of the TLSs, their coupling, and the shape of the resonator. Since this measurement is performed on a very short time scale (10 hours) at a specific temperature, it is less susceptible to the effects of temporal fluctuations. The same trend is present at both the maximum value of the noise (T = 40 mK) and T = 1 mK. This means that based on the high-power data in Figure 10, it is possible to determine the general trend of the noise and avoid the problem of long-term temporal fluctuations of the TLSs.

[0164] Figure 11 shows the power dependence of the noise at three temperatures, indicating that the ratio with respect to the power (photon number n) follows the expected dependence by the TLSs at all of above the threshold temperature, near the threshold temperature, and well below the threshold temperature, indicating being close to the weak-field region of saturation. Quantum circuits typically operate within a limit N of about 1.

[0165] Note that the fact that the noise shows a clear tendency to decrease according to the same power law at about 1 mK implies that cooling is also efficient for the TLS subsystem. Therefore, 3 immersion in He - cools the surface spins (which cause flux noise), - cools the TLS, - the fact that the "high-power" noise follows the expected power law (linear on a log-log scale) all the way down to about 1 mK means that the noise can be used to confirm the thermalization of the TLS bath down to about 1 mK, - removes the extra heat from the quantum circuit generated by the dissipated control signals, - cools both the control lines inside the cell itself and the resistive interfaces for signal propagation introduced there to such an extent that the TLS and spin baths do not overheat, - at zero (nearly zero) saturation vapor pressure, 3 operating with He results in a stable 3 He liquid being obtained and the pressure fluctuations not causing problems ( 3 He has a pressure-dependent permittivity), but the noise increases, - 3 The dielectric loss tangent of He is very low and no significant additional losses occur that would affect the performance of the quantum circuit. The upper limit tanδ ~ 1e-5 is limited by the sensitivity of the device and is probably much lower than that, - By using a heater to adjust the temperature of the cold plate to the desired temperature, the desired or optimal operating temperature of the quantum circuit can be selected.

[0166] The quantum circuit is efficiently protected from stray thermal photons (from other temperature stages within the cryostat) by a dielectric seal (except for the signal line ports) or a hermetic enclosure without gaps. From the observed reduction of TLS noise, it has also been confirmed that there are no other heating sources that limit the temperature. That is, all other major heat sources are also effectively handled. 3He is expected to improve the heating of the input line (and the stray thermal radiation of the amplifier) and also provide attenuation of the phonon environment of the quantum circuit.

[0167] Also, 3 By He immersion, - The number of residual thermal photons of the qubit is further reduced, - It results in a decrease in quasiparticle density, - The effects of high-energy particle collision events are more efficiently mitigated, - Protect the quantum circuit from phonons that cause decoherence and excite quasiparticles, - A shield that absorbs cosmic particles before they reach the quantum circuit 3 He can be formed, - 3 He is also expected to have and obtain another important effect on the TLS cell as described later.

[0168] 3 Complete immersion in He is very advantageous Figure 12 shows how the noise behaves when the cell is filled with 3 He and when there is a small amount of He in the cell. Note that the data presented in Figure 12 is for a resonator (with a different frequency) different from the data presented in Figure 10. In the case of a small amount, 3 He first coats the entire surface of the cell with a thin layer (a few nanometers), and then, 3 as more He is added, it accumulates at the bottom of the cell. In the case of the data shown in Figure 12, it is estimated from the observed frequency shift that 4 nm of 3 He covers the device surface. 3 The thin film of He is expected to have a much worse cooling effect on the quantum circuit compared to the filled cell. This can also be seen in Figure 12, where the noise is constant below 100 mK. As shown in Figure 12, the situation is also very similar when the cell is in vacuum (an empty cell). Figure 12 is, ( 3 3 ​In the case of (absence of He) vacuum, saturation occurs at about 100 mK, and then the noise decreases at the predicted temperature ratio of μ = 0.5, which indicates that in the case of vacuum and thin films, the TLSs are not cooled below about 100 mK.

[0169] Increase in the energy relaxation rate of the TLS bath The TLS has an energy relaxation rate Γ 1 and a phase shift rate Γ 2 and can be characterized by these two rates. The noise in a quantum circuit is dominated by Γ 2 in the weak field region, but the loss is determined by Γ 1 . Saturation occurs in the strong field region, and the noise and loss depend on both quantities. This also holds for each individual TLS, and the average relaxation rate and phase shift rate of the TLS bath can also be considered. Below, Γ 1 and Γ 2 are referred to as these average quantities. In a normal dielectric with TLSs, Γ 1 is typically about 10 2 ~10 3 Hz. This is compared with the phase shift rate Γ 2 that dominates the noise. Usually, at about 100 mK, Γ 2 is about 10 7 , and thus it can be seen that Γ 2 >>Γ 1 . Γ 2 is proportional to the temperature as Γ 2 ~T 1+μ . Therefore, in vacuum, it is necessary to cool to about 10 microkelvin to reach the transition Γ 2 =Γ 1 . This cannot be achieved experimentally.

[0170] The data in Fig. 14 shows 3 another role of He, 3 and He increases Γ 1 by about 1000 times. Fig. 14 shows the saturation power, i.e., the power applied to the cell 3As He is added, the number of photons required to saturate a certain number of TLSs increases by a factor of about 1000, up to a certain quality factor of the resonator. The saturation power is given by the product Γ 1 Gamma 2 The noise (Figure 10) at high temperatures is proportional to 3 Since it is the same regardless of the presence or absence of He, Γ 2 teeth, 3 This shows that the introduction of He is not affected. 3 With He, Γ 2 = Γ 1 This could raise the transition temperature, , to much higher experimentally achievable temperatures of 10-100 mK, potentially allowing quantum circuits to operate in the regime where the TLS chamber is relaxed-limited. The observed regime of noise reduction on cooling is desirable as it has the effect of reducing the noise generated by the TLS chamber on the quantum circuit. This is seen in Figure 10 for temperatures below 50 mK.

[0171] As a result, it becomes desirable to further reduce the temperature of quantum circuits from the standpoint of TLS and noise.

[0172] Figure 14 shows the 3 The change in the quality factor and the average number of photons in the cavity with and without He is shown. As can be seen, 3 When He is present, 3 To reach the same Q as without He, we need to increase the photon number by a factor of about 1000.

[0173] The role of dielectrics 3 He interface Relaxation rate .GAMMA. for phonons in a TLS cell 1 teeth,

number

[0174] Comparing this formula with typical dielectrics used in quantum circuits, Γ 1 is about 10 2 ~10 3 Hz, and if all the material parameters are 3 Substituting the He parameters, Γ 1 is about 10 6 ~10 7 Hz or more. Without measuring γ an accurate estimation is not possible, and γ is not known in the art. However, the estimate is more than 10 times the value observed in FIG. 14. The inventors believe that the reason for this is that the coupling between the TLS (which is in the dielectric near the surface) 3 We found that this was due to the lack of completeness for He.

[0175] When the pressure in the chamber changes, 3 The properties of He change, its density and speed of sound change. When the pressure increases from 0 to 5 bar, these quantities change by about 30%. This is called the Γ 1 When the equation is applied, the sound speed is entered as a fifth power, and the bulk 3 If He is the main limiting factor for this additional TLS relaxation, large changes can be expected.

[0176] Now, referring to Fig. 15, when N is large, all Q i (N) The measurements are found to converge to almost the same curve, which is expected to affect phonon propagation. 3 This means that the bulk properties of He (density, speed of sound) do not have a significant effect. The effect is very small (increasing the pressure to 5 bar increases the saturation power by less than 20%, which is the opposite of what would be expected). This means that the limiting mechanism for energy relaxation is 3 It is suggested that the coupling is at the interface between He and the TLS medium (dielectric), and it is expected that this coupling can be increased by several orders of magnitude by engineering the interface. 3It is desirable to enhance the coupling with He, which means that during the operation of the quantum circuit, energy leakage is less likely to occur and damage its quantum state. As shown in Figure 10, the noise caused by the TLS bath also decreases, which means that by lowering the temperature and / or strengthening the coupling between the TLS bath and 3 He, the phase shift due to the frequency fluctuation of the superconducting quantum circuit can be suppressed.

[0177] 3 Regarding Figure 15 showing the effect of applying pressure to He, the left graph verifies that pressure is being applied. The measured frequency shift of the resonator is due to the 3 change in the dielectric constant of He, which is calculated from the Clausius-Mosorotti relation. The measured frequency shift is in very good agreement with the theoretical prediction. The right graph shows the effect (lack thereof) on the saturation power.

[0178] 3 With the goal of enhancing the coupling between He and the TLS bath, several approaches can be pursued individually or in combination. 1. Apply a pressure of up to 60 bar or more, depending on the GHS component used and the design of the immersion cell, with the aim of densifying the atoms near the surface / interface. This causes 3 the number of solid layers to increase until the entire bulk of He becomes solid. The location where this transition occurs and the number of layers formed depend on the temperature, but, without limitation, adaptive cooling can also be pursued to control the amount of solid layer based on some quantity measurement, such as loss in the strong field region. 2. Surface templating: Before completely filling the cell with 3 He, coat the surface in any order with 4 He and / or 3 a thin layer of He (ranging from less than one atomic layer to several nanometers). Due to the van der Waals interaction, 3 He atoms adsorb to the surface and change the device / liquid interface. This interaction results in a maximum number of solid layers on the surface3 He is formed and the number of layers depends on temperature and pressure. To achieve such templating, one 3 supplies He and the other 4 supplies He (of the type described herein). Two gas handling systems can be connected to the same immersion cell. In another embodiment, a single gas handling system with multiple gas storage volumes can be used. Next, either gas can be introduced into the cell in small amounts and in the desired order and condensed within the cell until the next layer is introduced. 3. 3 For introducing a layer or submonolayer of electron spins that mediate the dipole-dipole electron-nuclear coupling to the nuclear spin of He onto the surface. 4. For treating or coating the surface of the quantum circuit with a thin layer of dielectric for the purpose of changing the interface. 5. To increase the effective surface area of the quantum circuit containing TLS by roughening or perforating its surface.

[0179] Selection of the cooling fluid At mK temperatures, only two liquids are known to be suitable, namely, 3 He and 4 He, or a mixture of the two.

[0180] 4 He has a superfluid transition at 2.17 K at saturated vapor pressure, while 3 He has a superfluid transition at about 0.9 mK at saturated vapor pressure. The thermal conductivity of superfluid 4 He is low at low temperatures, the density of phonon excitations is negligibly small, and conduction by thermal counterflow between the normal and superfluid components, which is dominant near the superfluid transition, is also negligible. On the other hand, the thermal conductivity of liquid 3 He (and 4 He in 3 He dilute solutions) increases inversely with temperature. Limited results and theory indicate that the thermal conductivity in the superfluid state is not significantly impaired. Thus, 3 He (or 4 He in 3a dilute solution of He) is expected to be a more effective coolant than He at mK temperatures. However, this is not certain because cooling is not based solely on the liquid's thermal conductivity. It also depends strongly on the thermal conductivity (Kapitza resistance) through the boundary between the liquid being cooled and the substance. Little is known about such interfaces and the thermal coupling between the helium liquid and the components of the quantum circuit. In the case of quantum circuits, it is not known what the Kapitza resistance will be between the circuit and its environment and 4 He or 3 He. Not only has it not been studied in detail, but it is not even known for sure what makes up the surface of the quantum circuit. Quantum circuits have complex surface chemistries that are exposed to ambient conditions, which means that the ambient conditions are covered with layers of water and hydrocarbons, resulting in complex chemistries and unknown mixed surface species. This is an issue in the art of quantum circuits. In this art, it is not understood what the material properties of the TLS are or how the surface and interface behave microscopically at the relevant energy scales (<10 mK). Therefore, it is not possible to predict how 4 He or 3 He or 4 He will cool (or not cool) the quantum circuit and the physical subsystem coupled to it.

[0181] The systems and methods disclosed herein enable quantum circuits and processor units, and their environments, to be effectively cooled to significantly lower temperatures than previously achieved. Specifically, as described above, prior art systems attempted to cool circuits below 50 mK, but were unable to actually achieve this because they relied on cooling the substrate on which the quantum circuits were placed. During operation of the quantum circuits, cooling was inefficient and heat was generated, resulting in an actual operating temperature in the region above 50 mK. There was no demonstrated solution to further cool the quantum circuits and their environment, and in certain processes, it was understood that performance decreased at low temperatures, so achieving a temperature of about 50 mK was considered not a disadvantage but rather the best compromise that could be easily achieved.

[0182] Known systems are not suitable for cooling quantum circuits below this level because they cannot reduce the heat generated during operation or sufficiently cool various components of the environment.

[0183] The methods and systems taught herein can cool quantum circuits and their environments to significantly lower temperatures than previously achieved, specifically well below 50 mK, actually down to 10 mK or less, depending on the cryocooler used. In practice, this is achieved by creating the environment in which the quantum circuits are held with a very low-loss and low-temperature fluid for which He is preferred. Although the disclosed systems and methods can cool to temperatures well below 10 mK, the inventors believe that this does not necessarily result in optimal functioning of the quantum circuits for the reasons detailed above. However, depending on the use and purpose of the quantum circuits, the optimal temperature is often lower than the easily achievable approximately 50 mK set in the art. 3 The cooling characteristics of the environment are obtained by a housing made of a highly conductive metal for which copper is preferred that can be cooled to very low temperatures (10 mK or less). The housing provides maximum cooling to the fluid

[0184] by the fluid( 3It is preferably constructed to provide a cooling metal with a large surface area for He). The large surface area can be achieved by adding an internal surface or coating to the housing that can be described as textured or porous. In embodiments, this is done by a layer or block of sintered metal powder such as silver, although other materials including copper, gold, etc. can also be used. In other embodiments, the chamber of the housing in which the quantum circuit is held can be filled with sintered powder (again, for example, silver, copper, gold).

[0185] The advantage of such a structure is that the housing can be kept small, thus optimizing the performance of the system and, in particular, reducing the required amount of the 3 material, which is He.

[0186] The system and method are also configured to control the cooling of the quantum circuit in the housing by various means, including controlling the amount and / or pressure of the fluid coolant in the housing. The control can be determined from various factors, including measuring the actual temperature of the quantum circuit and measuring other temperature-dependent parameters such as the operating state of the quantum circuit. Controlled cooling makes it possible to provide a system and method that can achieve adaptive cooling of one or more quantum circuits to maintain the quantum circuit at optimal performance. This can be achieved by measuring one or more parameters, as disclosed herein, and also by measuring changes in the performance of the quantum circuit and changing the set temperature to optimize that performance, particularly improved coherence. Adaptive cooling can be applied at the start or during the operation of the operating state of the quantum circuit.

[0187] In particular, the described methods and systems for adaptive cooling can reach and maintain the optimal temperature of a quantum circuit, regardless of what that optimal temperature is. Such adaptive cooling can be static or dynamic, where the performance metrics associated with the quantum circuit are optimized with respect to temperature. The optimal temperature can vary for each quantum circuit, depending on the specific impact of various physical mechanisms that degrade the operation of the quantum circuit and the performance of important quantities related to its particular application. Even different quantum circuits with the same application or function can have different optimal temperatures, depending on the implementation method. Such performance metrics can be - noise (charge noise or flux noise) due to charged material defects or paramagnetic impurities, - coherence, - the thermal excitation probability of qubit states, - phonons, - quasiparticle density or parity switching events, - losses, - properties of the directly measured physical system, such as temperature-dependent superconducting properties.

[0188] Similarly, from the operation of the device, - the relaxation or dephasing time of qubits, - the gate fidelity of single or multiple qubits, - the error rate of logical qubits (composed of multiple physical qubits), - the fidelity of a specific algorithm executed on the quantum processing unit, or a class of algorithms or sub-algorithms, - the fidelity of a specific quantum gate operation, - related to minimizing the need to repeatedly recalibrate the quantum processing unit to achieve optimal performance, - performance metrics such as the sensitivity, stability, or signal-to-noise ratio of a quantum circuit operating as a quantum sensor (e.g., magnetometer, charge sensor, single-photon detector, etc.) can be inferred.

[0189] For the evaluation of the optimal temperature, it is also possible to use the listed parameter combinations.

[0190] Depending on the situation, it may be desirable to change the temperature of the quantum circuit during operation or 3 the cooling power provided by the He cooling system. For example, in a quantum processing unit, while executing a less resource-intensive calculation, only a part of the circuit may be utilized, so less heat is dissipated. Therefore, to maintain the optimal temperature of the circuit, 3 the reduced cooling power of the He adaptive cooling system may be required. For example, when using a complete quantum processing unit to execute a resource-intensive calculation, more heat may be dissipated, and to satisfy the same optimal operating temperature, 3 it may be necessary to increase the cooling power of the He cooling system.

[0191] To implement such adaptive cooling, a feedback loop can be used, the relevant quantities are measured, and the deviation from the optimal temperature is determined using the same algorithm. The algorithm determines a new target temperature, which is achieved, as described, by increasing or decreasing the heating of a resistor (the power supplied to the resistor) attached to the cryostat cold plate thermally linked to the quantum circuit.

[0192] As shown with reference to FIG. 13, this shows an embodiment of an apparatus for a unit comprising a plurality of quantum circuits. In this embodiment, the system 500 has the same characteristics as those taught herein and shown, for example, in FIG. 7, and the same cooling fluid, preferably a liquid 3It includes a housing using He, and a configuration in which a plurality of quantum circuits 563 and 573 are integrated within the same housing, specifically within a plurality of sub-housings 510 and 520. An example of such an arrangement is a quantum processing system comprising individual parametric amplifiers connected in series to the output (readout) microwave line of a quantum processing unit. This allows the amplifier (which needs to be placed as close as possible to the quantum processing unit in order to minimize signal loss between the quantum processing unit and the amplifier) to be placed closer to the quantum processing unit, reducing the impact on the quantum processing unit from additional heat dissipated by the amplifier. The microwave filter (described above) also provides a convenient way to separate two microwave environments 510 and 520 that share the same liquid-cooled housing (using a sintered mass in between), and the cooling fluid is supplied through a single capillary 105.

[0193] As shown with reference to FIG. 13, the sintered powder is schematically shown as a mass of sintered material 530 within the sub-housings 510 and 520 and at the joint 580 between the two sub-housings. The quantum circuits 563 and 573 are preferably arranged on respective cooling substrates such as the housing base 550 as already described, or on printed circuit boards (562 and 572) as shown in FIG. 13. This device also includes individual signal feed-through paths 560 and 570 where signal propagation lines (561 and 571) are connected to the printed circuit boards (562 and 572) and wire bonded (564 and 574) to the quantum circuits (563 and 573) for control and readout of the quantum circuits within each sub-housing, for example. These paths may also include feedback paths for individual sensors used for adaptive cooling of the quantum circuits and determination of the optimal operating temperature.

[0194] As shown with reference to FIG. 16, the mass of sintered material is preferably carefully arranged within the housing with respect to the quantum circuits.

[0195] In some embodiments, the sintered body is disposed at a position within the cell and thermally coupled to at least one housing wall or the lid of the housing, separated from the quantum circuit by a predetermined minimum distance. In other embodiments, the sintered body can be disposed within the volume of the housing, together with one or more screening materials disposed between the quantum circuit and the mass of the sintered body (an example is shown in FIG. 16). Each screen is attached directly or indirectly to the inner wall, base, or lid of the housing (in a preferred embodiment, one or more fasteners are used). The purpose of the screen is to protect the quantum circuit from the sintered body. When most of the electromagnetic field from the quantum circuit expands into the mass of the sintered body, losses and decoherence occur, and the performance of the quantum circuit deteriorates. Placing a screen between the sintered body and the quantum circuit can attenuate losses due to the sintered body or losses imposed by the sintered body in certain situations, allowing the screen to be placed closer to the quantum circuit than usual, resulting in a reduction in the volume of the cell that needs to be filled with the thermalization fluid.

[0196] In one example, the screen can be made of a low-loss good conductor such as copper. In other examples, the screen can also be made of a superconducting material such as aluminum, tin, or niobium, which has an even smaller electrical resistance. It is also envisioned that multiple screens made from both metallic and superconducting materials can be used.

[0197] As shown with reference to FIG. 16, a housing 600 of a type consistent with the above teachings has an internal chamber or volume 602 filled with a thermalization fluid, preferably a liquid 3 He and / or 4 He. Within the housing 600, in a preferred embodiment, on the side facing the quantum circuit 603, there is disposed a screen 605 composed of a solid copper body coated with a thin layer 606 (e.g., from 1 micrometer to 1 mm) of a superconducting material (such as Al, Nb, Sn, In, etc.), and the quantum circuit 603 is disposed within the region 604 of the housing.

[0198] In each of these implementations, it is advantageous for the sintered body 601 and the optional screening plates 605 / 606 to be placed sufficiently far from the quantum circuit 603, which is determined by the extent of the electromagnetic field radiated from the quantum circuit, and this extent depends on the implementation and design of the quantum circuit and usually varies from circuit to circuit. The sintered body 601 and the screening plates 605 / 606 are preferably placed at a distance from the quantum circuit such that the presence of the sintered body 601 and the screening 605 / 606 does not degrade the measured coherence or performance of the quantum circuit 603 as compared to a cell implemented without the sintered body and the screen. The amount of decoherence may vary from circuit to circuit, although not limited to, by other decoherence and noise mechanisms of the type described above.

[0199] An important preferred characteristic of the screen 605 / 605 is that it is arranged so as not to completely restrict the flow of liquid between the sintered body 601 and the quantum circuit 603. The liquid needs to be able to flow across the side of the screen 601 facing the quantum circuit 603.

[0200] In the various embodiments disclosed herein, the sintered body may be provided on one or more internal housing walls, a sub-housing within the main housing, a separate substrate such as a screen, etc. The relevant criterion is that the sintered body optimizes heat transfer to the thermalized fluid without interfering with the electromagnetic field of the circuit.

[0201] The cooling fluid is in liquid form, preferably liquid 3 He, 4 He, or a mixture of the two, as will be understood.

Claims

1. A system for controlling the temperature of a quantum circuit to an operating temperature of less than 100 mK, wherein the system is A housing with housing walls made of thermally conductive material, A mass of porous medium made of a thermally conductive material is placed inside the housing and thermally bonded to at least a portion of the housing wall, A substrate for holding quantum circuits, At least one cooling fluid source, At least one port in the housing that is directly coupled to the at least one cooling fluid source, A control unit coupled to the at least one cooling fluid source for filling the housing with cooling fluid to cool the quantum circuit and / or its environment. Includes, The aggregate of the porous medium is separated from the quantum circuit. During use, a cooling fluid is placed between the quantum circuit and the mass of porous medium within the housing. The control unit is configured to control the supply of cooling fluid to the chamber, thereby controlling the degree of cooling provided by the thermal fluid within the housing and the amount of cooling provided to the quantum circuit. The control unit is configured to control the amount of thermal fluid in order to adjust the performance of the quantum circuit.

2. The system according to claim 1, wherein the mass of porous medium is separated from the quantum circuit in order to provide a certain amount of thermal fluid between the quantum circuit and the porous medium, and the mass of porous medium is positioned at a distance from the quantum circuit such that the electromagnetic field entering the mass of porous medium from the quantum circuit is small enough not to degrade the performance of the quantum circuit.

3. The system comprises a screening element disposed between the block of porous medium and the quantum circuit, The aforementioned screening element is (i) at least one of conductive metallic materials and superconducting materials, and / or (ii) A layer of superconducting material placed on top of a layer of metallic material. Made from, The system according to claim 1 or 2.

4. The porous medium is (i) the textured or porous inner surface of the enclosure wall, and / or (ii) Thermally conductive sintered powder or particles The system according to claim 3, comprising:

5. The system according to claim 1, further comprising a capillary connecting the cooling fluid source to the housing, wherein the capillary is a valveless coupling between the housing and the control unit, the ballast volume is connected to a filling line at room temperature, and during use, the capillary is continuously filled with a thermal fluid while the system is operating.

6. The system according to claim 5, comprising a housing of a conductive material and a filter having one end coupled to an inlet capillary and the other end coupled to the capillary or capillary, wherein the housing provides a chamber filled with a sintered filter element, and the filter is operable to reduce or prevent high-frequency noise from entering the housing through the capillary and to improve the thermalization of the cooling fluid entering the housing.

7. The system comprises a first cooling fluid source and a second cooling fluid source, wherein the first cooling fluid source is ３ The source of He, and the second cooling fluid source, ４ The system according to claim 1, wherein He is a source, and the control unit is configured to control the operation of the first cooling fluid source and the second cooling fluid source in order to supply the cooling fluid sequentially or simultaneously.

8. The control unit is (i) To control the amount and / or pressure of the cooling fluid inside the housing, (ii) Control the supply and pressure of the thermal fluid to generate one or more thermal material layers on the quantum circuit, and / or (iii) To template separate layers of the same or different solid thermoforming material on the surface of the quantum circuit, The system according to claim 1, which is operable.

9. The system according to claim 1, comprising one or more sensors configured to obtain a measurement of the performance of the quantum circuit, wherein the control unit is configured to control the at least one cooling fluid source based on a measured amount by controlling the amount and / or pressure of the cooling fluid in the housing based on the measured parameters.

10. (i) one or more sensors configured to measure one or more of the following: noise, decoherence, thermal excitation probability of a qubit state, phonons, quasiparticle density, quasiparticle parity fluctuations, losses, thermal distribution of spin, temperature-dependent superconducting properties, and / or temperature-dependent properties of the quantum circuit, and / or (ii) One or more sensors configured to measure one or more of the following: qubit relaxation or phase shift time, gate fidelity of one or more qubits, error rate of logical qubits, algorithm fidelity, quantum gate operation fidelity, and temperature-dependent characteristics affecting the performance of a quantum computing circuit. The system according to claim 9, comprising:

11. The control unit is (i) Control the temperature of the cooling fluid based on the determined coherence of the quantum circuit, and / or (ii) Control the amount and / or pressure of the cooling fluid in the housing based on the measured or expected power dissipation within the quantum circuit. The system according to claim 1, which is capable of operating in this manner.

12. The system according to claim 1, wherein the housing is configured to hold a plurality of quantum circuits within a plurality of sub-housings, and the temperature within each sub-housing can be controlled collectively or individually.

13. A housing with housing walls made of temperature-conductive material, A mass of porous medium made of a thermally conductive material is placed inside the housing and thermally bonded to at least a portion of the housing wall, A substrate for holding a quantum circuit inside the aforementioned housing, At least one cooling fluid source, At least one port in the housing directly connected to the cooling fluid source, Includes a control unit coupled to at least one cooling fluid source, The aggregate of the porous medium is separated from the quantum circuit. In a system in which a cooling fluid is placed between the quantum circuit and the mass of porous medium within the housing during use, a method for controlling the temperature of the quantum circuit to an operating temperature of less than 100 mK, The method comprises the steps of filling the housing with a cooling fluid to cool the quantum circuit and / or its environment, and controlling the supply of the cooling fluid to the chamber to operate the control unit to control the degree of cooling provided by the thermal fluid in the housing, thereby the amount of cooling provided to the quantum circuit, the control enabling adjustment of the performance of the quantum circuit.

14. The system comprises a first cooling fluid source and a second cooling fluid source, the first cooling fluid source being ３ The source of He, and the second cooling fluid source, ４ The method is a source of He, and includes the step of the control unit operating the first cooling fluid source and the second cooling fluid source, or enabling such operation, in order to supply the cooling fluid sequentially or simultaneously. The method according to claim 13, further comprising the steps of measuring at least one parameter indicating the performance of the quantum circuit, and controlling at least one supply of cooling fluid based on the measured performance by controlling the amount, temperature, and / or pressure of the cooling fluid in the housing based on the measured parameter.

15. The method according to claim 13 or 14, comprising operating the control unit to control the supply and pressure of a thermoforming fluid to generate one or more layers of the same or different thermoforming material on the quantum circuit.

16. The method according to claim 13, further comprising the step of controlling the amount and / or pressure of the cooling fluid in the housing based on the measured or expected power dissipation in the quantum circuit.

17. The method according to claim 13, comprising the step of holding a plurality of quantum circuits in a plurality of sub-enclosures and controlling the temperature of the cooling fluid in each sub-enclosure collectively or individually.

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