EP4669943A1 - QUANTUM COMPUTATION SYSTEM WITH LOWER TEMPERATURE SENSOR AND TEMPERATURE MEASURING METHOD - Google Patents

QUANTUM COMPUTATION SYSTEM WITH LOWER TEMPERATURE SENSOR AND TEMPERATURE MEASURING METHOD

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Publication number
EP4669943A1
EP4669943A1 EP24712774.9A EP24712774A EP4669943A1 EP 4669943 A1 EP4669943 A1 EP 4669943A1 EP 24712774 A EP24712774 A EP 24712774A EP 4669943 A1 EP4669943 A1 EP 4669943A1
Authority
EP
European Patent Office
Prior art keywords
material sample
superconductor material
current
voltage
temperature
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
EP24712774.9A
Other languages
German (de)
French (fr)
Inventor
Thomas Swift
Fabio OLIVIERI
Grayson NOAH
Miguel Fernando Gonzalez-Zalba
Alberto GÓMEZ SAIZ
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
UCL Business Ltd
Quantum Motion Technologies Ltd
Original Assignee
UCL Business Ltd
Quantum Motion Technologies Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by UCL Business Ltd, Quantum Motion Technologies Ltd filed Critical UCL Business Ltd
Publication of EP4669943A1 publication Critical patent/EP4669943A1/en
Pending legal-status Critical Current

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Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01K—MEASURING TEMPERATURE; MEASURING QUANTITY OF HEAT; THERMALLY-SENSITIVE ELEMENTS NOT OTHERWISE PROVIDED FOR
    • G01K7/00—Measuring temperature based on the use of electric or magnetic elements directly sensitive to heat ; Power supply therefor, e.g. using thermoelectric elements
    • G01K7/006—Measuring temperature based on the use of electric or magnetic elements directly sensitive to heat ; Power supply therefor, e.g. using thermoelectric elements using superconductive elements
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01K—MEASURING TEMPERATURE; MEASURING QUANTITY OF HEAT; THERMALLY-SENSITIVE ELEMENTS NOT OTHERWISE PROVIDED FOR
    • G01K1/00—Details of thermometers not specially adapted for particular types of thermometer
    • G01K1/02—Means for indicating or recording specially adapted for thermometers
    • G01K1/026—Means for indicating or recording specially adapted for thermometers arrangements for monitoring a plurality of temperatures, e.g. by multiplexing
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01K—MEASURING TEMPERATURE; MEASURING QUANTITY OF HEAT; THERMALLY-SENSITIVE ELEMENTS NOT OTHERWISE PROVIDED FOR
    • G01K13/00—Thermometers specially adapted for specific purposes
    • G01K13/006—Thermometers specially adapted for specific purposes for cryogenic purposes
    • G01K13/008—Thermometers specially adapted for specific purposes for cryogenic purposes using microstructures, e.g. made of silicon
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G06N10/40—Physical realisations or architectures of quantum processors or components for manipulating qubits, e.g. qubit coupling or qubit control

Definitions

  • This invention relates to a cryogenic temperature sensor and a method of measuring the temperature of a superconductor material sample.
  • the sensor and method are particularly suitable for quantum computing and other cryogenic electronics applications.
  • cryogenic temperature measurement techniques such as Coulomb blockade thermometry have not been successfully adapted to provide rapid, real-time and direct measurements of the temperature of quantum processors, and they require complex electronics for their implementation. More particularly, standard Coulomb blockade thermometry requires providing a large number of tunnel junction in series, which requires a complex electronic structure for its implementation, and relies on direct current measurements, which limit its speed. While radiofrequency Coulomb blockade thermometry techniques have been developed, they rely on complex off-chip electronics such as cryoamps and directional couplers, which make them unsuitable for directly measuring the temperature of parts of the chip. This invention aims to provide a way of measuring the temperature of components of a quantum processor that overcomes these limitations.
  • a first aspect of the invention provides a cryogenic temperature sensor comprising: a superconductor material sample; a current source configured to pass a current through the superconductor material sample; a voltage sensor configured to sense a voltage across the superconductor material sample; and a control unit configured to: control the current source to time-vary the current through the superconductor material sample while the voltage sensor senses the voltage across the superconductor material sample; detect a change in the sensed voltage; and compute the temperature of the superconductor material sample based on the value of the current at the time of the detected change in the sensed voltage.
  • This temperature sensor exploits the temperature dependence of the critical current of the superconductor material sample, l c , which is the greatest current that the sample can carry while remaining in the superconducting (i.e. zero resistance) state. It should be noted that the value of l c is specific to the particular sample and is sensitive to its shape and dimensions. While the superconductor material sample is in the superconducting state, changes in the current will not affect the voltage measured across it since its resistance remains zero (and accordingly, there will be no potential difference across the sample). However, once the current, I, reaches l c , the superconductor material sample undergoes a step-change in its resistance from zero to a finite, non-zero value.
  • the detected change in voltage therefore signifies that the time-varying current has exceeded the critical current above which the superconductor material sample has a non-zero resistance and, as the temperature-dependence of the value of the critical current l c can be known, the temperature of the sample can be computed based on the value of current at which the change in voltage occurred.
  • computing the temperature may comprise comparing the value that the current had at the time of the detected change in voltage to calibration data representing measurements of the critical current as a function of the temperature of the superconductor material sample, thereby inferring the temperature of the superconductor material sample.
  • the temperature sensor defined above requires only relatively simple electronics for its implementation and can be constructed entirely “on-chip” as part of the chip comprising a quantum processor (and indeed, in some preferred embodiments, the components are arranged on a quantum computing chip - though it will be appreciated that some or all of the components, for example the control unit, may be off-chip).
  • the temperature sensor can therefore be positioned very close to components of the processor whose temperature is of interest and thus achieves significantly more accurate temperature measurements than current techniques with a much less complex construction. It also enables rapid, real-time monitoring of the temperature since the critical current can be repeatedly measured and output at a high frequency.
  • cryogenic here has its conventional meaning, i.e. temperatures less than 120 K, though it will be appreciated that embodiments of the cryogenic temperature sensor of the invention are not necessarily capable of measuring temperatures across the entire cryogenic temperature range up to 120 K. For example, some embodiments of the invention may be suitable for sensing temperatures of up to 1.2 K, which is a suitable range for many quantum computing applications.
  • the current source may, in preferred embodiments, comprise a current digital-to- analogue converter (IDAC).
  • IDAC current digital-to- analogue converter
  • An IDAC can be controlled to produce a time-varying current of a desired profile based on a digital input, so can be conveniently controlled by a digital control unit to provide the required time-varying current.
  • the voltage sensor comprises an amplifier configured to amplify the voltage across the superconductor material sample.
  • the amplifier could be a negative feedback transimpedance amplifier in which the superconductor material sample is arranged as the negative feedback resistor.
  • an amplifier e.g. one in a negative feedback transimpedance amplifier configuration, in particular an operational amplifier in such a configuration
  • the voltage sensor further comprises a comparator circuit (most preferably a Schmitt trigger) configured to receive as input the amplified voltage and output a digital signal whose value changes in response to the change in voltage that occurs when the time-varying current exceeds the critical current, wherein the control unit detects the change in voltage based on a change in the digital signal.
  • a comparator circuit most preferably a Schmitt trigger
  • this voltage comparator changes its binary output value in response to changes in the input voltage of a sufficient magnitude.
  • a digital (e.g. binary) output is useful as the critical current (and hence the temperature) can be inferred from the value of the current at the time of the change in the digital signal.
  • the current source and the voltage sensor each comprise a respective pair of electrodes in electrical communication with the superconductor material sample, wherein the current through the superconductor material sample passes between the electrodes of the current source and the sensed voltage is sensed between the electrodes of the voltage sensor; wherein the electrodes of the voltage sensor are arranged between the electrodes of the current source.
  • This configuration can be described as a “four-point” measurement setup and is advantageous because the part of the circuit across which the voltage is measured (i.e. between the positions of the two electrodes of the voltage sensor) does not include the electrodes of the current sensor, as a result of which the voltage measured does not include any voltage dropped across the points at which the current sensor’s electrodes contact the circuit.
  • the cryogenic temperature sensor further comprises a magnetic field sensor arranged to measure the strength of the magnetic field at the location of the superconductor material sample, wherein the computation of the temperature is further based on the strength of the magnetic field.
  • the critical current typically varies in dependence on the strength of the magnetic field experienced by the superconductor material sample, and in many quantum computing applications the magnetic field in which the quantum processor will be varied over time. Taking the magnetic field strength into account for the computation of temperature therefore enhances the accuracy of the temperature measurements.
  • the superconductor material sample is preferably made of titanium nitride. This material has been found to be particularly suitable as samples of this material are easily manufactured and it has been found that its critical current exhibits a good sensitivity to temperature in the temperature ranges of interest to quantum computing applications, in particular in the range of about 0.1 -1.2 K. However, other superconductor materials may be used.
  • the superconductor material sample is formed as a film, preferably having a thickness in the range of 0.1-100 nanometres (nm), more preferably 1- 20 nm.
  • a film can easily be manufactured on semiconductor structures of the kind on which current quantum computing chips are based, for example by known deposition techniques.
  • the film may have a length, in the direction along which the current is passed through the superconductor material sample, in the range of 0.1-100 micrometres (pm), preferably 10-50 pm; and/or a width, in the direction transverse to the direction along which the current is passed superconductor material sample, of 0.01-100 pm, preferably 0.36-2 pm.
  • the cross-sectional area of the film along the direction in which the current travels is low so that, when the critical current is exceeded and the sample acquires a non-zero resistance, the resistance of the sample is large and the change in voltage is correspondingly large.
  • the value of the critical current increases with increasing cross-sectional area, and it is easier to control the value of the current in the region of the critical current if the critical current is not too small. The dimensions above have been found to achieve an optimum balance between these competing considerations.
  • control unit may be configured to increase, while the voltage sensor is sensing the voltage across the superconductor material sample, the current from below the critical current to above the critical current.
  • the critical current l c at which the superconductor material sample acquires a finite resistance in the presence of an increasing current (which approaches l c from below) is not the same (and is greater than) the current at which the sample resumes its superconducting behaviour as the current decreases.
  • the sample therefore exhibits a hysteresis: starting from low current, it stops superconducting once the current reaches l c , but only resumes superconducting when the current is lowered below a threshold (the “retrapping current”) that is significantly less than lc.
  • the cryogenic temperature sensor may further comprise a magnetic field source configured to generate a magnetic field at the location of the superconductor material sample, wherein the control unit is configured to control the generated magnetic field based on a target temperature value.
  • the generated magnetic field may be controlled such that the sensitivity of the critical current to changes in temperature has a maximum value at the target temperature value.
  • the critical current, and its sensitivity to changes in temperature depend on the magnetic field to which the superconductor material sample is subjected. It is therefore advantageous that that the magnetic field can be controlled to a value that maximises the sensitivity of the critical current for future measurements.
  • the control unit may be configured to control a magnetic field generator (e.g. a solenoid) that is separate to the cryogenic temperature sensor and arranged to control the magnetic field at the location of the superconductor material sample (and possibly the magnetic across the quantum computing chip whose temperature is being sensed).
  • a magnetic field generator e.g. a solenoid
  • Such a magnetic field generator could be provided as part of a quantum computing system in which the cryogenic temperature sensor and the chip are comprised.
  • the invention also provides a quantum computing system comprising: a quantum computing chip on which there is arranged a quantum processor; and the cryogenic temperature sensor defined above.
  • the current source, the voltage sensor and the superconductor material sample are arranged on the quantum computing chip for measuring the temperature of the quantum processor.
  • the control unit may also be arranged on the chip, through this does not have to be the case.
  • This provides a quantum computing chip with an “on-chip” temperature sensor.
  • the temperature sensor may be arranged on the chip close to a component whose temperature is of interest (e.g. the quantum processor), thereby providing accurate measurements of the temperature of that component.
  • the quantum computing system may comprise a plurality of the cryogenic temperature sensors, the current source, voltage sensor, and superconductor material sample of each of the plurality of cryogenic temperature sensors being arranged for measurement of the temperature of a different respective region of the quantum computing chip.
  • This allows a thermal ‘image’ of the chip to be produced, with each temperature sensor providing a measurement of the temperature of the chip at its respective location.
  • At least some of the plurality of temperature sensors could be configured to measure different temperature ranges - this could be achieved for example by providing different temperature sensors in which the superconductor material sample has different dimensions and/or is formed of a different superconductor material sample. This increases the range of temperatures that can be measured.
  • at least some of the temperature sensors configured to measure different temperature ranges may be arranged to measure the temperature of the same location on the chip.
  • the invention also provides a cryogenic system comprising: a cryogenic enclosure configured to generate cryogenic conditions in an interior space thereof; and the cryogenic temperature sensor defined above, wherein the cryogenic temperature sensor is disposed in the interior space of the cryogenic enclosure.
  • the cryogenic enclosure could be any apparatus configured to generate cryogenic conditions in the interior space, for example a cryostat.
  • a second aspect of the invention provides a method of measuring the temperature of a superconductor material sample, the method comprising: passing a timevarying current through the superconductor material sample while sensing a voltage across the superconductor material sample; detecting a change in the sensed voltage; and computing the temperature of the superconductor material sample based on the value of the current at the time of the detected change in the sensed voltage.
  • the superconductor material sample is arranged on a quantum computing chip comprising a quantum processor.
  • a quantum computing chip comprising a quantum processor.
  • Figure 1 shows the behaviour of a superconductor material sample carrying a varying current
  • Figure 2 shows measurements of the critical current and retrapping current of a superconductor material sample as a function of temperature
  • Figure 3 shows the measurements of the critical current shown in Figure 2 plotted over a theoretical model of the critical current as a function of temperature
  • Figure 4 shows measurements of the critical current of a superconductor material sample as a function of the magnetic field experienced by the superconductor material sample plotted together with a theoretical model of the critical current as a function of the magnetic field;
  • Figure 5(a) shows a theoretical phase diagram for a type-l superconductor material
  • Figure 5(b) shows the empirically measured phase diagram for a sample of the same superconductor material
  • Figure 6(a) shows the theoretical critical current of a superconductor material sample as a function of temperature for different values of magnetic field
  • Figure 6(b) shows the sensitivity of the critical current to temperature for each of the theoretical curves shown in Figure 6(a)
  • Figure 6(c) shows the change in voltage across the superconductor material sample corresponding to the critical current values shown in Figure 6(a)
  • Figure 6(d) shows the sensitivity of voltage to temperature for each of the theoretical curves shown in Figure 6(d);
  • FIG. 7 shows schematically an example of a cryogenic temperature sensor in accordance with an embodiment of the invention.
  • Figure 8 shows the arrangement of the superconductor material sample in the temperature sensor of Figure 7.
  • the critical current, l c of a superconductor material sample is the greatest current the sample can carry while remaining in the superconducting (i.e. zero resistance) state.
  • the critical current can be found by sensing the voltage across the sample while passing an increasing current, I, through it. Initially, as the current is swept upwards from zero, there will be no voltage across the sample as its resistance in the superconducting state is zero, and the voltage remains zero for I ⁇ I c . Once the value of I reaches l c , the superconductor material sample acquires a finite resistance and a step-change in the voltage across the sample will be observed.
  • Figure 1 is a graph showing the voltage, in millivolts (mV), sensed across a superconductor material sample as a function of the current, in microamps (pA), through it.
  • the line 101 annotated with solid arrows shows the voltage as the current is increased in magnitude from zero.
  • the critical current in this sample is about 1.2 pA (indicated by 103), at which point the voltage sharply increases from 0 mV to about 2.2 mV (or -2.2 mV, in the case of a negative current as shown on the left-hand side of the graph).
  • the superconductor material sample does not instantly return to the superconducting state when the current falls below l c .
  • the resistance of the sample (and hence the sensed voltage) gradually falls (as indicated by the line 102 annotated with dashed arrows) as the current decreases, until the current reaches the “retrapping current” value, which in this example is about 0.7 pA.
  • the retrapping current is more difficult to observe than the critical current because it exhibits a more gradual change in resistance than the step-change associated with the critical current.
  • the critical current of a superconductor material sample is dependent on its temperature.
  • the inventors have realised that, by observing the current at which a sharp change in voltage across a superconductor material sample occurs (indicating that the critical current has been reached, causing a transition from the superconducting state to a non- superconducting state with non-zero resistance), the temperature of the sample can be inferred. This is the principle on which the temperature sensor of the present invention operates.
  • Equation (1) The dependence of critical current on temperature can be fitted to a physically motivated equation based on the Bardeen formula.
  • the original Bardeen formula is of the form: Equation (1)
  • T is the temperature
  • T c is the critical temperature of the sample (i.e. the maximum temperature at which the sample can exhibit superconductivity in the absence of any current)
  • l c (T) is the critical current as a function of temperature
  • Equation 1 is based on the Bardeen-Cooper-Schrieffer (BCS) theory, a microscopic theory that models superconductivity based on condensation of Cooper pairs and is valid at all temperatures.
  • BCS Bardeen-Cooper-Schrieffer
  • Equation 1 assumes the sample is a thin wire, whereas in preferred embodiments of the present invention, a sample in the form of a thin film is preferred.
  • the formula may be adapted to the case of a thin film by replacing the power 3/2 in equation 1 with a parameter i to be determined based on measurements of the sample in question: Equation (2)
  • the superconductor material sample on which these measurements were performed was a film of titanium nitride (TiN) with a length (in the direction along which the current was passed) of 50 pm and a width (in the direction transverse to that along which the current was passed) of 0.36 pm.
  • TiN titanium nitride
  • Figure 3 shows a function in the form of equation 2 fitted to the critical current measurements 302 shown in Figure 2 (plotted as the dashed curve 301 extending from the top-left to the bottom-right of the graph).
  • This empirical fitting of equation 2 to the critical current values measured for the sample enable the sample to be used in a temperature sensor since, given a measurement of l c (T) (obtained by passing an increasing current through the sample while monitoring the voltage across it and recording the value of current at which the step change in voltage occurs), the temperature can be computed by solving equation 2 for T.
  • the sensitivity derived from the empirical fit shown in Figure 3 is plotted on that graph (as the dashed line 303 extending from the bottom-left to the top-right of the graph).
  • 7 c (0) and R depend on the dimensions of the superconductor material sample, which can be selected at the time of fabricating the sample.
  • the critical current l c of a superconductor material sample is dependent on the strength of magnetic field, B, applied to it.
  • B the strength of magnetic field
  • the critical current follows a Kim-Type formula: Equation (5)
  • Figure 4 shows measurements of the critical current (normalised to the critical current at zero magnetic field) as a function of B and a fit of equation 6 (plotted as a dashed line) to these measurements.
  • the critical temperature T c is also magnetic-field dependent and follows the equation: Equation (6)
  • Figure 5(a) is a phase diagram showing the boundary between the superconducting and non-superconducting states of a type I superconductor as a function of temperature and magnetic field (in the absence of any current). In the region 501 , the sample is superconducting, and in the region 502, it is non- superconducting (and therefore has a non-zero resistance).
  • Figure 5(b) is a graph showing measurements of the resistance of a sample of this type I superconductor material plotted as a function of temperature and magnetic field.
  • the data points plotted as circles represent the measurements taken and the tone area of the graph (set out on the scale on the right-hand side) represents the measured resistance, normalised to the greatest resistance measured (which was observed at values of temperature and magnetic field well outside the superconducting region).
  • the curve 503 shows the theoretical boundary between the superconducting and non-superconducting states represented in Figure 5(a). At values of temperature and magnetic field well within the theoretical superconducting region, the resistance measured was always about zero, and in the region of the theoretical boundary, the resistance was found to increase rapidly (but not instantaneously) to the maximum value with increasing temperature and magnetic field.
  • Figures 6(a) and 6(c) respectively show theoretical plots of critical current and the change in voltage at the critical current (which is the critical current multiplied by the resistance of the sample in the non-superconducting state) as a function of temperature for different values of magnetic field based on equations 2, 5 and 6.
  • the computation of temperature based on the sensed change in voltage can be performed based on a calibration of critical current to temperature and magnetic field as represented in Figures 6(a) and 6(c) - either with theoretical curves, as shown here, or more preferably, curves fitted to empirical measurements of the particular superconductor material sample incorporated in the temperature sensor.
  • the sensitivity of the temperature sensor may be maximised by application of a suitable magnetic field to the superconductor material sample.
  • a temperature sensor incorporating the sample on which the functions plotted in Figures 6(a)- 6(d) are based can thus achieve excellent sensitivity across the temperature range of 0.1 -1.2 K.
  • FIG. 7 is a circuit diagram showing schematically an example of a cryogenic temperature sensor in accordance with an embodiment of the invention.
  • the temperature sensor include a current source 700, which in this case is a 6-bit digital to analogue convertor that is configured to output a current ISNS, which in operation is varied over time by a control unit (not shown) configured to control the current source.
  • a control unit (not shown) configured to control the current source.
  • the time variation of the current is such that the current always approaches the critical current from below (therefore ensuring that the observed voltage change corresponds to the critical current rather than the retrapping current) - this could be achieved for example by varying the current in a cyclical “sawtooth” pattern, in each cycle of which the current increases continuously before falling back to zero in a step change.
  • the current ISNS is input to a voltage generation circuit 710, where it passes through a superconductor material sample 711.
  • the voltage generation circuit 710 includes an amplifier 712, which is in a negative feedback transimpedance amplifier configuration with the superconductor material sample arranged as the negative feedback resistor (being connected to the negative input terminal and the output terminal of the amplifier 712).
  • the amplifier 721 is an operational amplifier.
  • a constant reference voltage V RE F is input to the positive terminal of the amplifier 712.
  • the voltage sensed at the negative terminal of the amplifier 712 is equal to the voltage VTSNS at the output terminal of the amplifier 712.
  • VTSNS VREF
  • the critical current of the superconductor material sample 711 is exceeded, its resistance becomes non-zero and a voltage ISNSRSNS is dropped across it.
  • the output voltage VTSNS therefore changes by ISNSRSNS when the current through the superconductor material sample 711 is increased, from below, to the critical current.
  • the output voltage VTSNS is input into a voltage comparator circuit 720, which in this example comprises a Schmitt trigger 721.
  • the purpose of this circuit is to detect changes in the output voltage and output a digital signal indicating these changes.
  • the Schmitt trigger 721 in this example outputs a binary signal (0 or 1).
  • the value of the output is switched when either (i) the voltage VTSNS increases above an upper threshold (in which case the output is switched to 0) or decreases below a lower threshold, which is below the upper threshold (in which case the output is switched to 1).
  • the thresholds are selected such that changes in the voltage on the order of the voltage change expected as the critical current is exceeded result in a switch in the output value.
  • the output of the comparator circuit 720 is therefore a binary signal that indicates whether the superconductor material sample 711 is in the superconducting state or the non-superconducting state.
  • the output of the voltage comparator 720 is output to the control unit, which computes the temperature of the superconductor material sample 711 based on the value of the current at the time a change in the digital signal from 1 to 0 (indicating a transition from the superconducting state to the non-superconducting state) is detected. As described previously, this computation can be based on calibration data such as functions fitted to empirical measurements of the critical current of the sample 711 at different temperatures (and optionally also different magnetic field strengths).
  • Figure 8 shows schematically an example of how the superconductor material sample 711 in the temperature sensor may be arranged.
  • the superconductor material sample 711 is formed as a thin film arranged on a shallow trench isolation (STI) layer 803 on a silicon wafer 804.
  • STI shallow trench isolation
  • the dimensions of this film are thickness (in direction z) in the range of 1-20 nanometres (nm); length (in the direction x, along which current flows in use) in the range 0.1-100 micrometres (pm), more preferably 10-50 pm; and width (in the direction perpendicular to x and z) in the range 0.01-100 pm, more preferably 0.36-2 pm.
  • a contact layer 801 is arranged over the superconductor material sample 711 (optionally with intermediate layers 802 between them).
  • the current ISNS passes through the sample 711 between two current electrodes 811 , 812.
  • Arranged between the current electrodes 811 , 812 are two voltage electrodes 821 , 822.
  • One voltage electrode 821 is electrically connected to the negative terminal of the amplifier 712 and the other electrode 822 connects to the output of the amplifier 712 where the output voltage VTSNS is output.
  • This arrangement is a “four-point” measurement configuration, in which the electrodes that sense the voltage are separate from, and arranged between, those that convey the current through the sample. This arrangement improves the accuracy of sensing the voltage across the sample 711 as it ensures that any voltage dropped across the points of contact between the current electrodes 811 , 812 and the sample is not sensed.
  • the temperature sensor just described may be incorporated in a quantum computing chip, on which it is arranged together with a quantum processor.
  • the temperature sensor may be part of a cryogenic system in which it is disposed inside an interior space of a cryogenic enclosure (e.g. a cryostat) configured to generate cryogenic conditions in the interior space.
  • a cryogenic enclosure e.g. a cryostat
  • a cryogenic temperature sensor comprising: a superconductor material sample; a current source configured to pass a current through the superconductor material sample; a voltage sensor configured to sense a voltage across the superconductor material sample; and a control unit configured to: control the current source to time-vary the current through the superconductor material sample while the voltage sensor senses the voltage across the superconductor material sample; detect a change in the sensed voltage; and compute the temperature of the superconductor material sample based on the value of the current at the time of the detected change in the sensed voltage.
  • cryogenic temperature sensor of any preceding clause, wherein the voltage sensor comprises an amplifier configured to amplify the voltage across the superconductor material sample.
  • cryogenic temperature sensor of clause 2 wherein the voltage sensor further comprises a comparator circuit, preferably a Schmitt trigger, configured to receive as input the amplified voltage and output a digital signal whose value changes in response to the change in voltage that occurs when the time-varying current exceeds the critical current, wherein the control unit detects the change in voltage based on a change in the digital signal.
  • a comparator circuit preferably a Schmitt trigger
  • cryogenic temperature sensor of any preceding clause, further comprising a magnetic field sensor arranged to measure the strength of the magnetic field at the location of the superconductor material sample, wherein the computation of the temperature is further based on the strength of the magnetic field.
  • cryogenic temperature sensor of any preceding clause, wherein the superconductor material sample is formed as a film, preferably having a thickness in the range of 0.1-100 nanometres (nm), more preferably 1-20 nm.
  • Clause 7. The cryogenic temperature sensor of clause 6, wherein: the film has a length, in the direction along which the current is passed through the superconductor material sample, in the range of 0.1-100 micrometres (pm), preferably 10-50 pm; and/or a width, in the direction transverse to the direction along which the current is passed superconductor material sample, of 0.01-100 pm, preferably 0.36-2 pm.
  • cryogenic temperature sensor of any preceding clause, wherein the current source and the voltage sensor each comprise a respective pair of electrodes in electrical communication with the superconductor material sample, wherein the current through the superconductor material sample passes between the electrodes of the current source and the sensed voltage is sensed between the electrodes of the voltage sensor; wherein the electrodes of the voltage sensor are arranged between the electrodes of the current source.
  • control unit configured to increase, while the voltage sensor is sensing the voltage across the superconductor material sample, the current from below the critical current to above the critical current.
  • a quantum computing system comprising: a quantum computing chip on which there is arranged a quantum processor; and the cryogenic temperature sensor of any preceding clause.
  • Clause 12 The quantum computing system of clause 11 , wherein the current source, the voltage sensor and the superconductor material sample are arranged on the quantum computing chip for measuring the temperature of the quantum processor.
  • Clause 13 The quantum computing system of clause 12, comprising a plurality of the cryogenic temperature sensors, the current source, voltage sensor, and superconductor material sample of each of the plurality of cryogenic temperature sensors being arranged for measurement of the temperature of a different respective region of the quantum computing chip.

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Abstract

This specification describes a cryogenic temperature sensor is comprising: a superconductor material sample; a current source configured to pass a current through the superconductor material sample; and a voltage sensor configured to sense a voltage across the superconductor material sample. The temperature sensor further comprises a control unit configured to: control the current source to time-vary the current through the superconductor material sample while the voltage sensor senses the voltage across the superconductor material sample; detect a change in the sensed voltage; and compute the temperature of the superconductor material sample based on the value of the current at the time of the detected change in the sensed voltage.

Description

QUANTUM COMPUTING SYSTEM COMPRISING A CRYOGENIC TEMPERATURE SENSOR AND TEMPERATUR MEASURING METHOD
This invention relates to a cryogenic temperature sensor and a method of measuring the temperature of a superconductor material sample. The sensor and method are particularly suitable for quantum computing and other cryogenic electronics applications.
BACKGROUND
The provision of a stable cryogenic environment is key to the successful operation of current quantum processors. At temperatures greater than a few degrees Kelvin (K), the effects on which quantum processors rely for their operation, including the preservation of stable quantum states on quantum bits (qubits) for storage of information, rapidly diminish. To control the temperature of cryogenic environments for quantum computing applications, it is important to be able to accurately sense the temperature of these environments and doing so requires a temperature sensor capable of measuring temperatures close to absolute zero.
Most techniques currently used for measuring the temperature of quantum computing systems rely on “off-chip” temperature sensors - i.e. temperature sensors implemented as hardware that is physically separate to the quantum processor and arranged alongside the processor inside the cryogenic enclosure in which the processor is mounted. A drawback of this approach is that, as a consequence of the temperature sensor being physically separate from the processor, it does not directly measure the temperature of the processor itself. This is significant as localised heating of the processor by dissipation of power in its electronic components can cause the temperature of parts of the processor to deviate significantly from that of the surrounding parts of the cryogenic environment. Current techniques are therefore limited in their ability to accurately measure the temperature of the quantum processor. In addition, known cryogenic temperature measurement techniques such as Coulomb blockade thermometry have not been successfully adapted to provide rapid, real-time and direct measurements of the temperature of quantum processors, and they require complex electronics for their implementation. More particularly, standard Coulomb blockade thermometry requires providing a large number of tunnel junction in series, which requires a complex electronic structure for its implementation, and relies on direct current measurements, which limit its speed. While radiofrequency Coulomb blockade thermometry techniques have been developed, they rely on complex off-chip electronics such as cryoamps and directional couplers, which make them unsuitable for directly measuring the temperature of parts of the chip. This invention aims to provide a way of measuring the temperature of components of a quantum processor that overcomes these limitations.
SUMMARY OF THE INVENTION
A first aspect of the invention provides a cryogenic temperature sensor comprising: a superconductor material sample; a current source configured to pass a current through the superconductor material sample; a voltage sensor configured to sense a voltage across the superconductor material sample; and a control unit configured to: control the current source to time-vary the current through the superconductor material sample while the voltage sensor senses the voltage across the superconductor material sample; detect a change in the sensed voltage; and compute the temperature of the superconductor material sample based on the value of the current at the time of the detected change in the sensed voltage.
This temperature sensor exploits the temperature dependence of the critical current of the superconductor material sample, lc, which is the greatest current that the sample can carry while remaining in the superconducting (i.e. zero resistance) state. It should be noted that the value of lc is specific to the particular sample and is sensitive to its shape and dimensions. While the superconductor material sample is in the superconducting state, changes in the current will not affect the voltage measured across it since its resistance remains zero (and accordingly, there will be no potential difference across the sample). However, once the current, I, reaches lc, the superconductor material sample undergoes a step-change in its resistance from zero to a finite, non-zero value. A sharp change in the voltage across the sample proportional to the current and the sample’s resistance will then be observed. The detected change in voltage therefore signifies that the time-varying current has exceeded the critical current above which the superconductor material sample has a non-zero resistance and, as the temperature-dependence of the value of the critical current lc can be known, the temperature of the sample can be computed based on the value of current at which the change in voltage occurred. For example, computing the temperature may comprise comparing the value that the current had at the time of the detected change in voltage to calibration data representing measurements of the critical current as a function of the temperature of the superconductor material sample, thereby inferring the temperature of the superconductor material sample. A detailed explanation of the critical current, its temperature dependence and examples of methods of computing the temperature based on it will be given below.
As we will illustrate with reference to the examples below, the temperature sensor defined above requires only relatively simple electronics for its implementation and can be constructed entirely “on-chip” as part of the chip comprising a quantum processor (and indeed, in some preferred embodiments, the components are arranged on a quantum computing chip - though it will be appreciated that some or all of the components, for example the control unit, may be off-chip). The temperature sensor can therefore be positioned very close to components of the processor whose temperature is of interest and thus achieves significantly more accurate temperature measurements than current techniques with a much less complex construction. It also enables rapid, real-time monitoring of the temperature since the critical current can be repeatedly measured and output at a high frequency.
The term “cryogenic” here has its conventional meaning, i.e. temperatures less than 120 K, though it will be appreciated that embodiments of the cryogenic temperature sensor of the invention are not necessarily capable of measuring temperatures across the entire cryogenic temperature range up to 120 K. For example, some embodiments of the invention may be suitable for sensing temperatures of up to 1.2 K, which is a suitable range for many quantum computing applications.
The current source may, in preferred embodiments, comprise a current digital-to- analogue converter (IDAC). An IDAC can be controlled to produce a time-varying current of a desired profile based on a digital input, so can be conveniently controlled by a digital control unit to provide the required time-varying current.
In preferred embodiments, the voltage sensor comprises an amplifier configured to amplify the voltage across the superconductor material sample. This is beneficial as in many implementations, the voltage change detected as the current reaches lc will be small (e.g. on the order of 100 pV), so detection of the voltage change is improved by amplifying its magnitude. For example, the amplifier could be a negative feedback transimpedance amplifier in which the superconductor material sample is arranged as the negative feedback resistor. Furthermore, an amplifier (e.g. one in a negative feedback transimpedance amplifier configuration, in particular an operational amplifier in such a configuration) can produce a voltage output, which is convenient for monitoring the behaviour of the superconductor material sample. In addition, in particularly preferred embodiments, the voltage sensor further comprises a comparator circuit (most preferably a Schmitt trigger) configured to receive as input the amplified voltage and output a digital signal whose value changes in response to the change in voltage that occurs when the time-varying current exceeds the critical current, wherein the control unit detects the change in voltage based on a change in the digital signal. In the example of a Schmitt trigger, this voltage comparator changes its binary output value in response to changes in the input voltage of a sufficient magnitude. The provision of a digital (e.g. binary) output is useful as the critical current (and hence the temperature) can be inferred from the value of the current at the time of the change in the digital signal.
Preferably, the current source and the voltage sensor each comprise a respective pair of electrodes in electrical communication with the superconductor material sample, wherein the current through the superconductor material sample passes between the electrodes of the current source and the sensed voltage is sensed between the electrodes of the voltage sensor; wherein the electrodes of the voltage sensor are arranged between the electrodes of the current source. This configuration can be described as a “four-point” measurement setup and is advantageous because the part of the circuit across which the voltage is measured (i.e. between the positions of the two electrodes of the voltage sensor) does not include the electrodes of the current sensor, as a result of which the voltage measured does not include any voltage dropped across the points at which the current sensor’s electrodes contact the circuit.
Preferably the cryogenic temperature sensor further comprises a magnetic field sensor arranged to measure the strength of the magnetic field at the location of the superconductor material sample, wherein the computation of the temperature is further based on the strength of the magnetic field. The critical current typically varies in dependence on the strength of the magnetic field experienced by the superconductor material sample, and in many quantum computing applications the magnetic field in which the quantum processor will be varied over time. Taking the magnetic field strength into account for the computation of temperature therefore enhances the accuracy of the temperature measurements.
The superconductor material sample is preferably made of titanium nitride. This material has been found to be particularly suitable as samples of this material are easily manufactured and it has been found that its critical current exhibits a good sensitivity to temperature in the temperature ranges of interest to quantum computing applications, in particular in the range of about 0.1 -1.2 K. However, other superconductor materials may be used.
Preferably the superconductor material sample is formed as a film, preferably having a thickness in the range of 0.1-100 nanometres (nm), more preferably 1- 20 nm. Such a film can easily be manufactured on semiconductor structures of the kind on which current quantum computing chips are based, for example by known deposition techniques. Advantageously, the film may have a length, in the direction along which the current is passed through the superconductor material sample, in the range of 0.1-100 micrometres (pm), preferably 10-50 pm; and/or a width, in the direction transverse to the direction along which the current is passed superconductor material sample, of 0.01-100 pm, preferably 0.36-2 pm. It is desirable that the cross-sectional area of the film along the direction in which the current travels is low so that, when the critical current is exceeded and the sample acquires a non-zero resistance, the resistance of the sample is large and the change in voltage is correspondingly large. However, the value of the critical current increases with increasing cross-sectional area, and it is easier to control the value of the current in the region of the critical current if the critical current is not too small. The dimensions above have been found to achieve an optimum balance between these competing considerations.
Advantageously, the control unit may be configured to increase, while the voltage sensor is sensing the voltage across the superconductor material sample, the current from below the critical current to above the critical current. Typically, the critical current lc at which the superconductor material sample acquires a finite resistance in the presence of an increasing current (which approaches lc from below) is not the same (and is greater than) the current at which the sample resumes its superconducting behaviour as the current decreases. The sample therefore exhibits a hysteresis: starting from low current, it stops superconducting once the current reaches lc, but only resumes superconducting when the current is lowered below a threshold (the “retrapping current”) that is significantly less than lc. This is due in part to the fact that the sample experiences resistive heating by the current once the current has exceeded lc. The transition from superconducting to non-superconducting behaviour (which occurs when an increasing current crosses lc from below) exhibits a much sharper change in resistance than the lower threshold at which the sample returns to the superconducting state as the current decreases, so the increasing-current transition can be more reliably and accurately detected. Computing the temperature based on this transition therefore provides more accurate and reliable temperature measurements.
The cryogenic temperature sensor may further comprise a magnetic field source configured to generate a magnetic field at the location of the superconductor material sample, wherein the control unit is configured to control the generated magnetic field based on a target temperature value. In particular, the generated magnetic field may be controlled such that the sensitivity of the critical current to changes in temperature has a maximum value at the target temperature value. The critical current, and its sensitivity to changes in temperature, depend on the magnetic field to which the superconductor material sample is subjected. It is therefore advantageous that that the magnetic field can be controlled to a value that maximises the sensitivity of the critical current for future measurements. As we will show with reference to the examples below, the value of the critical current and its sensitivity to changes in temperature can be calibrated, and calibration data of this kind can be used to determine the magnetic field required to maximise the temperature-sensitivity of the critical current at the target temperature. As an alternative to the provision of a magnetic field source as part of the cryogenic temperature sensor, the control unit may be configured to control a magnetic field generator (e.g. a solenoid) that is separate to the cryogenic temperature sensor and arranged to control the magnetic field at the location of the superconductor material sample (and possibly the magnetic across the quantum computing chip whose temperature is being sensed). Such a magnetic field generator could be provided as part of a quantum computing system in which the cryogenic temperature sensor and the chip are comprised.
The invention also provides a quantum computing system comprising: a quantum computing chip on which there is arranged a quantum processor; and the cryogenic temperature sensor defined above. Preferably the current source, the voltage sensor and the superconductor material sample are arranged on the quantum computing chip for measuring the temperature of the quantum processor. It will be appreciated that the control unit may also be arranged on the chip, through this does not have to be the case. This provides a quantum computing chip with an “on-chip” temperature sensor. The temperature sensor may be arranged on the chip close to a component whose temperature is of interest (e.g. the quantum processor), thereby providing accurate measurements of the temperature of that component. The quantum computing system may comprise a plurality of the cryogenic temperature sensors, the current source, voltage sensor, and superconductor material sample of each of the plurality of cryogenic temperature sensors being arranged for measurement of the temperature of a different respective region of the quantum computing chip. This allows a thermal ‘image’ of the chip to be produced, with each temperature sensor providing a measurement of the temperature of the chip at its respective location. At least some of the plurality of temperature sensors could be configured to measure different temperature ranges - this could be achieved for example by providing different temperature sensors in which the superconductor material sample has different dimensions and/or is formed of a different superconductor material sample. This increases the range of temperatures that can be measured. In this case, at least some of the temperature sensors configured to measure different temperature ranges may be arranged to measure the temperature of the same location on the chip.
The invention also provides a cryogenic system comprising: a cryogenic enclosure configured to generate cryogenic conditions in an interior space thereof; and the cryogenic temperature sensor defined above, wherein the cryogenic temperature sensor is disposed in the interior space of the cryogenic enclosure. The cryogenic enclosure could be any apparatus configured to generate cryogenic conditions in the interior space, for example a cryostat.
A second aspect of the invention provides a method of measuring the temperature of a superconductor material sample, the method comprising: passing a timevarying current through the superconductor material sample while sensing a voltage across the superconductor material sample; detecting a change in the sensed voltage; and computing the temperature of the superconductor material sample based on the value of the current at the time of the detected change in the sensed voltage. This method achieves the advantages of the temperature sensor of the first aspect of the invention discussed above.
In this method, preferably the superconductor material sample is arranged on a quantum computing chip comprising a quantum processor. This again represents an “on-chip” arrangement in which measurements of the temperature of the superconductor material sample provide accurate measurements of the temperature in the vicinity of components near the sample. BRIEF DESCRIPTION OF THE DRAWINGS
Figure 1 shows the behaviour of a superconductor material sample carrying a varying current;
Figure 2 shows measurements of the critical current and retrapping current of a superconductor material sample as a function of temperature;
Figure 3 shows the measurements of the critical current shown in Figure 2 plotted over a theoretical model of the critical current as a function of temperature;
Figure 4 shows measurements of the critical current of a superconductor material sample as a function of the magnetic field experienced by the superconductor material sample plotted together with a theoretical model of the critical current as a function of the magnetic field;
Figure 5(a) shows a theoretical phase diagram for a type-l superconductor material, and Figure 5(b) shows the empirically measured phase diagram for a sample of the same superconductor material;
Figure 6(a) shows the theoretical critical current of a superconductor material sample as a function of temperature for different values of magnetic field; Figure 6(b) shows the sensitivity of the critical current to temperature for each of the theoretical curves shown in Figure 6(a); Figure 6(c) shows the change in voltage across the superconductor material sample corresponding to the critical current values shown in Figure 6(a); and Figure 6(d) shows the sensitivity of voltage to temperature for each of the theoretical curves shown in Figure 6(d);
Figure 7 shows schematically an example of a cryogenic temperature sensor in accordance with an embodiment of the invention; and
Figure 8 shows the arrangement of the superconductor material sample in the temperature sensor of Figure 7. DETAILED DESCRIPTION
With reference to Figures 1 -5(b), we will now explain in detail the theory underlying the temperature sensor of the present invention.
The critical current, lc, of a superconductor material sample is the greatest current the sample can carry while remaining in the superconducting (i.e. zero resistance) state. The critical current can be found by sensing the voltage across the sample while passing an increasing current, I, through it. Initially, as the current is swept upwards from zero, there will be no voltage across the sample as its resistance in the superconducting state is zero, and the voltage remains zero for I < Ic. Once the value of I reaches lc, the superconductor material sample acquires a finite resistance and a step-change in the voltage across the sample will be observed.
Figure 1 is a graph showing the voltage, in millivolts (mV), sensed across a superconductor material sample as a function of the current, in microamps (pA), through it. The line 101 annotated with solid arrows shows the voltage as the current is increased in magnitude from zero. The critical current in this sample is about 1.2 pA (indicated by 103), at which point the voltage sharply increases from 0 mV to about 2.2 mV (or -2.2 mV, in the case of a negative current as shown on the left-hand side of the graph). It should be noted that, as the magnitude of the current decreases from above the critical current, the superconductor material sample does not instantly return to the superconducting state when the current falls below lc. The resistance of the sample (and hence the sensed voltage) gradually falls (as indicated by the line 102 annotated with dashed arrows) as the current decreases, until the current reaches the “retrapping current” value, which in this example is about 0.7 pA. When the current falls below this value, the sample returns to the superconducting state. The retrapping current is more difficult to observe than the critical current because it exhibits a more gradual change in resistance than the step-change associated with the critical current.
The critical current of a superconductor material sample is dependent on its temperature. In producing the present invention, the inventors have realised that, by observing the current at which a sharp change in voltage across a superconductor material sample occurs (indicating that the critical current has been reached, causing a transition from the superconducting state to a non- superconducting state with non-zero resistance), the temperature of the sample can be inferred. This is the principle on which the temperature sensor of the present invention operates.
The dependence of critical current on temperature can be fitted to a physically motivated equation based on the Bardeen formula. The original Bardeen formula is of the form: Equation (1)
Where T is the temperature; Tc is the critical temperature of the sample (i.e. the maximum temperature at which the sample can exhibit superconductivity in the absence of any current); lc(T) is the critical current as a function of temperature; and lc(0) is the critical current at T = 0 K.
Equation 1 is based on the Bardeen-Cooper-Schrieffer (BCS) theory, a microscopic theory that models superconductivity based on condensation of Cooper pairs and is valid at all temperatures. However, equation 1 assumes the sample is a thin wire, whereas in preferred embodiments of the present invention, a sample in the form of a thin film is preferred. The formula may be adapted to the case of a thin film by replacing the power 3/2 in equation 1 with a parameter i to be determined based on measurements of the sample in question: Equation (2)
Measurements of the critical current (plotted as circles 201) and retrapping current (plotted as diamonds 202) of a superconductor material sample in the form of a thin film are shown in Figure 2. Here, the temperature is normalised to the value of Tc for the sample and the current is normalised to lc(T=0). It can be seen that the critical current is always greater than the retrapping current, but that both fall to zero as T approaches Tc (above which temperature the sample can no longer exhibit superconductivity). The superconductor material sample on which these measurements were performed was a film of titanium nitride (TiN) with a length (in the direction along which the current was passed) of 50 pm and a width (in the direction transverse to that along which the current was passed) of 0.36 pm.
Figure 3 shows a function in the form of equation 2 fitted to the critical current measurements 302 shown in Figure 2 (plotted as the dashed curve 301 extending from the top-left to the bottom-right of the graph). Here, the best fit was obtained with the parameters i = 0.63; Tc = 1.18 K and lc(T=0) = 1.37 pA. This empirical fitting of equation 2 to the critical current values measured for the sample enable the sample to be used in a temperature sensor since, given a measurement of lc(T) (obtained by passing an increasing current through the sample while monitoring the voltage across it and recording the value of current at which the step change in voltage occurs), the temperature can be computed by solving equation 2 for T.
The sensitivity of the temperature sensor just described (i.e. the rate of change of its critical current with respect to temperature) is given by:
The sensitivity derived from the empirical fit shown in Figure 3 is plotted on that graph (as the dashed line 303 extending from the bottom-left to the top-right of the graph). The sensitivity increases with temperature up to T=TC.
In a temperature sensor based on the principles described above, what will be sensed is the voltage across the superconductor material sample. The sensed voltage, Vsense, at the critical current (at which the voltage goes from zero to a finite value) will be the product the critical current, lc(T), and the resistance, R, of the sample at the time it stops superconducting. The sensitivity of the voltage change sensed at the critical current transition, Vsense, to temperature (i.e. its rate of change with respect to temperature) is given by: Equation (4)
7c(0) and R depend on the dimensions of the superconductor material sample, which can be selected at the time of fabricating the sample.
As well as being dependent on temperature, the critical current lc of a superconductor material sample is dependent on the strength of magnetic field, B, applied to it. For a magnetic field applied in a plane perpendicular to a superconductor material sample in the form of a thin film, the critical current follows a Kim-Type formula: Equation (5)
Figure 4 shows measurements of the critical current (normalised to the critical current at zero magnetic field) as a function of B and a fit of equation 6 (plotted as a dashed line) to these measurements.
The critical temperature Tc is also magnetic-field dependent and follows the equation: Equation (6)
Whether a superconductor material sample is in the superconducting state therefore depends on its temperature, the magnetic field and the current that it is carrying. Figure 5(a) is a phase diagram showing the boundary between the superconducting and non-superconducting states of a type I superconductor as a function of temperature and magnetic field (in the absence of any current). In the region 501 , the sample is superconducting, and in the region 502, it is non- superconducting (and therefore has a non-zero resistance). Figure 5(b) is a graph showing measurements of the resistance of a sample of this type I superconductor material plotted as a function of temperature and magnetic field. The data points plotted as circles represent the measurements taken and the tone area of the graph (set out on the scale on the right-hand side) represents the measured resistance, normalised to the greatest resistance measured (which was observed at values of temperature and magnetic field well outside the superconducting region). The curve 503 shows the theoretical boundary between the superconducting and non-superconducting states represented in Figure 5(a). At values of temperature and magnetic field well within the theoretical superconducting region, the resistance measured was always about zero, and in the region of the theoretical boundary, the resistance was found to increase rapidly (but not instantaneously) to the maximum value with increasing temperature and magnetic field.
Figures 6(a) and 6(c) respectively show theoretical plots of critical current and the change in voltage at the critical current (which is the critical current multiplied by the resistance of the sample in the non-superconducting state) as a function of temperature for different values of magnetic field based on equations 2, 5 and 6. In some embodiments of cryogenic temperature sensors in accordance with the present invention, the computation of temperature based on the sensed change in voltage can be performed based on a calibration of critical current to temperature and magnetic field as represented in Figures 6(a) and 6(c) - either with theoretical curves, as shown here, or more preferably, curves fitted to empirical measurements of the particular superconductor material sample incorporated in the temperature sensor.
The sensitivity to temperature of the critical current and corresponding voltage change formulae plotted in Figures 6(a) and 6(c) are shown in Figures 6(b) and 6(d) respectively. The expressions for these sensitivity curves are derived from the critical current and voltage curves by inserting the magnetic field-dependent formula for critical temperature TC(B) (equation 6) into the sensitivity formulae for critical current, lc, (equation 3) and voltage change sensed at the critical current, Vsense, (equation 4), which gives: Equation (7) V ' and .. /rix Equation (8)
It can be seen in Figures 6(b) and 6(d) that, at any given temperature, the sensitivity of the critical current and voltage change to temperature is different for different strengths of magnetic field. Therefore, in some embodiments, the sensitivity of the temperature sensor may be maximised by application of a suitable magnetic field to the superconductor material sample. A temperature sensor incorporating the sample on which the functions plotted in Figures 6(a)- 6(d) are based can thus achieve excellent sensitivity across the temperature range of 0.1 -1.2 K.
Figure 7 is a circuit diagram showing schematically an example of a cryogenic temperature sensor in accordance with an embodiment of the invention. The temperature sensor include a current source 700, which in this case is a 6-bit digital to analogue convertor that is configured to output a current ISNS, which in operation is varied over time by a control unit (not shown) configured to control the current source. Preferably the time variation of the current is such that the current always approaches the critical current from below (therefore ensuring that the observed voltage change corresponds to the critical current rather than the retrapping current) - this could be achieved for example by varying the current in a cyclical “sawtooth” pattern, in each cycle of which the current increases continuously before falling back to zero in a step change.
The current ISNS is input to a voltage generation circuit 710, where it passes through a superconductor material sample 711. The voltage generation circuit 710 includes an amplifier 712, which is in a negative feedback transimpedance amplifier configuration with the superconductor material sample arranged as the negative feedback resistor (being connected to the negative input terminal and the output terminal of the amplifier 712). In this example the amplifier 721 is an operational amplifier. A constant reference voltage VREF is input to the positive terminal of the amplifier 712. As outlined above, when the superconductor material sample is in its superconducting state, it has zero resistance and therefore no voltage is dropped across it. Consequently, when in the superconducting state, the voltage sensed at the negative terminal of the amplifier 712 is equal to the voltage VTSNS at the output terminal of the amplifier 712. The amplifier controls the voltage VTSNS at its output terminal such that the voltage at the negative terminal is equal to VREF, SO when the sample 711 is superconducting, VTSNS = VREF. However, when the critical current of the superconductor material sample 711 is exceeded, its resistance becomes non-zero and a voltage ISNSRSNS is dropped across it. The amplifier must then adjust the output voltage VTSNS to compensate for this voltage drop, and VTSNS then becomes VTSNS = VREF - ISNS SNS. The output voltage VTSNS therefore changes by ISNSRSNS when the current through the superconductor material sample 711 is increased, from below, to the critical current.
The output voltage VTSNS is input into a voltage comparator circuit 720, which in this example comprises a Schmitt trigger 721. The purpose of this circuit is to detect changes in the output voltage and output a digital signal indicating these changes. The Schmitt trigger 721 in this example outputs a binary signal (0 or 1). The value of the output is switched when either (i) the voltage VTSNS increases above an upper threshold (in which case the output is switched to 0) or decreases below a lower threshold, which is below the upper threshold (in which case the output is switched to 1). The thresholds are selected such that changes in the voltage on the order of the voltage change expected as the critical current is exceeded result in a switch in the output value. The output of the comparator circuit 720 is therefore a binary signal that indicates whether the superconductor material sample 711 is in the superconducting state or the non-superconducting state.
The output of the voltage comparator 720 is output to the control unit, which computes the temperature of the superconductor material sample 711 based on the value of the current at the time a change in the digital signal from 1 to 0 (indicating a transition from the superconducting state to the non-superconducting state) is detected. As described previously, this computation can be based on calibration data such as functions fitted to empirical measurements of the critical current of the sample 711 at different temperatures (and optionally also different magnetic field strengths).
Figure 8 shows schematically an example of how the superconductor material sample 711 in the temperature sensor may be arranged. In this example, the superconductor material sample 711 is formed as a thin film arranged on a shallow trench isolation (STI) layer 803 on a silicon wafer 804. Preferably the dimensions of this film are thickness (in direction z) in the range of 1-20 nanometres (nm); length (in the direction x, along which current flows in use) in the range 0.1-100 micrometres (pm), more preferably 10-50 pm; and width (in the direction perpendicular to x and z) in the range 0.01-100 pm, more preferably 0.36-2 pm.
A contact layer 801 is arranged over the superconductor material sample 711 (optionally with intermediate layers 802 between them). The current ISNS passes through the sample 711 between two current electrodes 811 , 812. Arranged between the current electrodes 811 , 812 are two voltage electrodes 821 , 822. One voltage electrode 821 is electrically connected to the negative terminal of the amplifier 712 and the other electrode 822 connects to the output of the amplifier 712 where the output voltage VTSNS is output. This arrangement is a “four-point” measurement configuration, in which the electrodes that sense the voltage are separate from, and arranged between, those that convey the current through the sample. This arrangement improves the accuracy of sensing the voltage across the sample 711 as it ensures that any voltage dropped across the points of contact between the current electrodes 811 , 812 and the sample is not sensed.
The temperature sensor just described may be incorporated in a quantum computing chip, on which it is arranged together with a quantum processor. The temperature sensor may be part of a cryogenic system in which it is disposed inside an interior space of a cryogenic enclosure (e.g. a cryostat) configured to generate cryogenic conditions in the interior space.
The invention may be further understood by reference to the following clauses. Clause 1 . A cryogenic temperature sensor comprising: a superconductor material sample; a current source configured to pass a current through the superconductor material sample; a voltage sensor configured to sense a voltage across the superconductor material sample; and a control unit configured to: control the current source to time-vary the current through the superconductor material sample while the voltage sensor senses the voltage across the superconductor material sample; detect a change in the sensed voltage; and compute the temperature of the superconductor material sample based on the value of the current at the time of the detected change in the sensed voltage.
Clause 2. The cryogenic temperature sensor of any preceding clause, wherein the voltage sensor comprises an amplifier configured to amplify the voltage across the superconductor material sample.
Clause 3. The cryogenic temperature sensor of clause 2, wherein the voltage sensor further comprises a comparator circuit, preferably a Schmitt trigger, configured to receive as input the amplified voltage and output a digital signal whose value changes in response to the change in voltage that occurs when the time-varying current exceeds the critical current, wherein the control unit detects the change in voltage based on a change in the digital signal.
Clause 4. The cryogenic temperature sensor of any preceding clause, further comprising a magnetic field sensor arranged to measure the strength of the magnetic field at the location of the superconductor material sample, wherein the computation of the temperature is further based on the strength of the magnetic field.
Clause 5. The cryogenic temperature sensor of any preceding clause, wherein the superconductor material sample is made of titanium nitride.
Clause 6. The cryogenic temperature sensor of any preceding clause, wherein the superconductor material sample is formed as a film, preferably having a thickness in the range of 0.1-100 nanometres (nm), more preferably 1-20 nm. Clause 7. The cryogenic temperature sensor of clause 6, wherein: the film has a length, in the direction along which the current is passed through the superconductor material sample, in the range of 0.1-100 micrometres (pm), preferably 10-50 pm; and/or a width, in the direction transverse to the direction along which the current is passed superconductor material sample, of 0.01-100 pm, preferably 0.36-2 pm.
Clause 8. The cryogenic temperature sensor of any preceding clause, wherein the current source and the voltage sensor each comprise a respective pair of electrodes in electrical communication with the superconductor material sample, wherein the current through the superconductor material sample passes between the electrodes of the current source and the sensed voltage is sensed between the electrodes of the voltage sensor; wherein the electrodes of the voltage sensor are arranged between the electrodes of the current source.
Clause 9. The cryogenic temperature sensor of any preceding clause, wherein the control unit is configured to increase, while the voltage sensor is sensing the voltage across the superconductor material sample, the current from below the critical current to above the critical current.
Clause 10. The cryogenic sensor of any preceding clause, further comprising a magnetic field source configured to generate a magnetic field at the location of the superconductor material sample, where in the control unit is configured to control the generated magnetic field based on a target temperature value.
Clause 11. A quantum computing system comprising: a quantum computing chip on which there is arranged a quantum processor; and the cryogenic temperature sensor of any preceding clause.
Clause 12. The quantum computing system of clause 11 , wherein the current source, the voltage sensor and the superconductor material sample are arranged on the quantum computing chip for measuring the temperature of the quantum processor. Clause 13. The quantum computing system of clause 12, comprising a plurality of the cryogenic temperature sensors, the current source, voltage sensor, and superconductor material sample of each of the plurality of cryogenic temperature sensors being arranged for measurement of the temperature of a different respective region of the quantum computing chip.
Clause 14. A method of measuring the temperature of a superconductor material sample, the method comprising: passing a time-varying current through the superconductor material sample while sensing a voltage across the superconductor material sample; detecting a change in the sensed voltage; and computing the temperature of the superconductor material sample based on the value of the current at the time of the detected change in the sensed voltage.
Clause 15. The method of clause 14, wherein the superconductor material sample is arranged on a quantum computing chip comprising a quantum processor.

Claims

1 . A quantum computing system comprising: a quantum computing chip on which there is arranged a quantum processor; and a cryogenic temperature sensor comprising: a superconductor material sample; a current source configured to pass a current through the superconductor material sample; a voltage sensor configured to sense a voltage across the superconductor material sample; and a control unit configured to: control the current source to time-vary the current through the superconductor material sample while the voltage sensor senses the voltage across the superconductor material sample; detect a change in the sensed voltage ; and compute the temperature of the superconductor material sample based on the value of the current at the time of the detected change in the sensed voltage; wherein the superconductor material sample is arranged on the quantum computing chip for measuring the temperature of the quantum processor.
2. The quantum computing system of any preceding claim, wherein the voltage sensor comprises an amplifier configured to amplify the voltage across the superconductor material sample.
3. The quantum computing system of claim 2, wherein the voltage sensor further comprises a comparator circuit, preferably a Schmitt trigger, configured to receive as input the amplified voltage and output a digital signal whose value changes in response to the change in voltage that occurs when the time-varying current exceeds the critical current, wherein the control unit detects the change in voltage based on a change in the digital signal.
4. The quantum computing system of any preceding claim, further comprising a magnetic field sensor arranged to measure the strength of the magnetic field at the location of the superconductor material sample, wherein the computation of the temperature is further based on the strength of the magnetic field.
5. The quantum computing system of any preceding claim, wherein the superconductor material sample is made of titanium nitride.
6. The quantum computing system of any preceding claim, wherein the superconductor material sample is formed as a film, preferably having a thickness in the range of 0.1-100 nanometres (nm), more preferably 1-20 nm.
7. The quantum computing system of claim 6, wherein: the film has a length, in the direction along which the current is passed through the superconductor material sample, in the range of 0.1-100 micrometres (pm), preferably 10-50 pm; and/or a width, in the direction transverse to the direction along which the current is passed superconductor material sample, of 0.01-100 pm, preferably 0.36-2 pm.
8. The quantum computing system of any preceding claim, wherein the current source and the voltage sensor each comprise a respective pair of electrodes in electrical communication with the superconductor material sample, wherein the current through the superconductor material sample passes between the electrodes of the current source and the sensed voltage is sensed between the electrodes of the voltage sensor; wherein the electrodes of the voltage sensor are arranged between the electrodes of the current source.
9. The quantum computing system of any preceding claim, wherein the control unit is configured to increase, while the voltage sensor is sensing the voltage across the superconductor material sample, the current from below the critical current to above the critical current.
10. The quantum computing system of any preceding claim, further comprising a magnetic field source configured to generate a magnetic field at the location of the superconductor material sample, where in the control unit is configured to control the generated magnetic field based on a target temperature value.
11. The quantum computing system of any preceding claim, wherein the current source and the voltage sensor are arranged on the quantum computing chip for measuring the temperature of the quantum processor.
12. The quantum computing system of any preceding claim, comprising a plurality of the cryogenic temperature sensors, the current source, voltage sensor, and superconductor material sample of each of the plurality of cryogenic temperature sensors being arranged for measurement of the temperature of a different respective region of the quantum computing chip.
13. A method of measuring the temperature of a superconductor material sample, wherein the superconductor material sample is arranged on a quantum computing chip comprising a quantum processor, the method comprising: passing a time-varying current through the superconductor material sample while sensing a voltage across the superconductor material sample; detecting a change in the sensed voltage; and computing the temperature of the superconductor material sample based on the value of the current at the time of the detected change in the sensed voltage.
EP24712774.9A 2023-02-20 2024-02-19 QUANTUM COMPUTATION SYSTEM WITH LOWER TEMPERATURE SENSOR AND TEMPERATURE MEASURING METHOD Pending EP4669943A1 (en)

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PCT/EP2024/054203 WO2024175553A1 (en) 2023-02-20 2024-02-19 Quantum computing system comprising a cryogenic temperature sensor and temperatur measuring method

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NL8800556A (en) * 1988-03-07 1989-10-02 Philips Nv DEVICE CONTAINING A TEMPERATURE SENSOR.
US10481174B2 (en) * 2015-03-11 2019-11-19 Yeda Research And Development Co. Ltd. Superconducting scanning sensor for nanometer scale temperature imaging
US20220328747A1 (en) * 2021-03-31 2022-10-13 Microsoft Technology Licensing, Llc Temperature sensing of regions within a superconducting integrated circuit using in-situ resonators

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