Traveling-Wave Parametric Amplifier Device for Quantum Computers

Abstract

The present disclosure relates to a TWPA device (1) for a quantum computer, which has a two-band dispersion relation and is configured to perform three-wave mixing. The TWPA device (1) comprises a chain of unit cells (φ), each comprising a non-linear inductance element (5) and a capacitor (6) connected to its ground (7). The unit cell (φ) further comprises a resonator circuit (8) and one of the periodically modulated input parameters. The two-band dispersion relation is composed of a lower frequency band and a higher frequency band, sandwiching a frequency gap. Further, the TWPA device (1) is configured to receive an amplified signal and a pump signal at the input (2). The pump signal is in the higher frequency band described above and has a frequency that is at least 2 / 3 of the cut-off frequency of the TWPA device (1) described above, or the pump signal described above is in the lower frequency band described above and its second harmonic has a frequency within the frequency gap described above.

Description

Technical Field

[0001] The present disclosure relates to a travelling-wave parametric amplifier (TWPA) device for a quantum computer. Further, the present disclosure relates to a method for amplifying an amplified signal.

Background Art

[0002] Generally, an amplifier is used to convert a small power signal into a large power signal. A specific type of amplifier called a travelling-wave parametric amplifier (TWPA) is used in several applications such as satellite communication, radio astronomy, and quantum bit readout of a quantum computer. The TWPA provides the advantage of amplifying a wideband signal frequency with little addition of noise, so that the signal-to-noise ratio can be improved at several signal frequencies. In a conventional parametric amplifier, a large microwave signal, usually called a pump, changes a certain parameter of the system and supplies energy for amplification.

[0003] The TWPA has a sharp cut-off frequency determined by the inductance and capacitance of the unit cell. Further, the TWPA typically comprises a number of unit cells connected in series. Different TWPAs can utilize either three-wave mixing, which depends on primary non-linearity, or four-wave mixing, which utilizes second-order non-linearity. Three-wave mixing offers the advantage that a smaller pump amplitude is required compared to four-wave mixing, and thus can in principle have a large dynamic range.

[0004] In a TWPA that utilizes three-wave mixing, there are two effects that can reduce the gain, namely phase mismatch and up-conversion. However, providing a TWPA that utilizes three-wave mixing while simultaneously minimizing up-conversion and phase mismatch is a challenge in the current art.

[0005] Accordingly, there is a need in the art for a traveling wave parametric amplifier (TWPA) that utilizes three-wave mixing while removing or at least reducing phase mismatch and up-conversion. More specifically, there is a need for a TWPA based on three-wave mixing that minimizes phase mismatch and up-conversion in order to achieve high gain.

[0006] While currently known solutions may function well in certain situations, it would be desirable to provide an improved TWPA utilizing three-wave mixing that meets the requirements for high gain while minimizing phase mismatch and up-conversion.

[0007] SUMMARY OF THE INVENTION Accordingly, an object of the present disclosure is to provide a TWPA device that alleviates, mitigates, or eliminates the deficiencies and drawbacks of currently known solutions.

[0008] This object is achieved by the TWPA device and method as defined in the appended claims.

[0009] The present disclosure is at least partially based on the insight that a TWPA device according to the present disclosure provides high gain in order to minimize phase mismatch and up-conversion. Accordingly, a TWPA device with improved reliability can be provided.

[0010] The present disclosure relates to a traveling wave parametric amplifier (TWPA) device for a quantum computer (based on superconducting qubits), the TWPA having a two-band dispersion relation and being configured to perform three-wave mixing in the aforementioned two-band dispersion relation. The TWPA device comprises a plurality of chained unit cells, each unit cell comprising a non-linear inductance element and a capacitor connected to its ground, where the aforementioned chained unit cells further comprise (i) a resonator circuit arranged in each of the plurality of unit cells described above, (ii) a periodically modulated input parameter, comprises one of them.

[0011] Furthermore, the two-band dispersion relationship is composed of / includes a lower frequency band and a higher frequency band, and there is a frequency gap between the higher frequency band and the lower frequency band described above. Furthermore, the TWPA device is configured to receive, at the input of the TWPA device described above, an amplification signal for amplification, and to receive, at the input described above, a pump signal for supplying energy to the amplification signal described above. The pump signal is in the higher frequency band described above and has a frequency that is at least 2 / 3 of the cut-off frequency of the TWPA device described above, or is in the lower frequency band described above and has a frequency whose second harmonic is within the frequency gap described above.

[0012] An advantage of the TWPA device of the present disclosure is to provide a high gain, which can be exponential. In other words, the TWPA based on three-wave mixing has a high gain that increases exponentially with the length of the TWPA. In other words, the TWPA device of the present disclosure minimizes phase mismatch and up-conversion simultaneously in order to achieve a high gain.

[0013] The TWPA device can be further configured to generate an idler signal, and the three-wave mixing described above is implemented by configuring the TWPA device described above to satisfy ω s < ω p , and ω i = ω p - ω s , where ω s is the frequency of the amplification signal described above, ω p is the frequency of the pump signal described above, and ω i is the frequency of the idler signal described above.

[0014] Therefore, with such a configuration of the TWPA device described above, three-wave mixing can be efficiently implemented.

[0015] The non-linear inductance element may be a single Josephson junction or a combination of at least two (i.e., a plurality of) Josephson junctions. Each Josephson junction can include a pair of superconducting elements coupled by a region / barrier that is less conductive than the superconducting element. In other embodiments, the non-linear inductance element may be a kinetic inductance element.

[0016] The advantage of using a Josephson junction as the non-linear inductance element is that the TWPA device becomes a superconducting TWPA device that minimizes losses.

[0017] The resonator circuit may be an LC oscillator. The LC oscillator includes an inductor element and a connected capacitor element. The LC oscillator can divide the original frequency band into two frequency bands (i.e., a higher band and a lower band). In other embodiments, the resonator circuit can be a transmission line resonator, a quarter-wavelength resonator, or any other suitable type of resonator circuit.

[0018] The input parameter can be at least one of inductance and capacitance.

[0019] Furthermore, the TWPA device is configured to receive an amplified signal having a frequency in the lower frequency band described above. Therefore, the pump signal is in the higher frequency band so as to prevent up-conversion within a certain band.

[0020] Furthermore, the TWPA device is configured to meet the following criteria. ω p +ω s >ω c and 2ω p -ω s >ω c , where ω s is the frequency of the amplified signal described above, ω pis the frequency of the pump signal described above, ω c is the cut-off frequency described above.

[0021] The TWPA device that satisfies the above criteria prevents up-conversion.

[0022] Furthermore, when each cell includes a resonator circuit in each of the plurality of unit cells described above (i.e., when following (i)), the dispersion relation of the two bands is

Equation

Equation

[0023] The two-band dispersion relation according to the above provides the advantage that it can be configured to bring the pump frequency closer to / associated with the cut-off frequency described above while maintaining phase matching.

[0024] The periodic modulation of the plurality of unit cells described above may include modulation that changes at least every other one of the plurality of unit cells in the chain of unit cells described above. In other words, the chain of unit cells described above can extend along a column, and every other unit cell can have a changed input parameter compared to the remaining unit cells along the column. In some aspects of the present disclosure, every third, fourth, or fifth unit cell can have a changed modulation. In one aspect, sub-cells of a unit cell can have different input parameters.

[0025] The advantage of this is that a two-band structure can be obtained without imposing a significant disadvantage on the hardware.

[0026] Furthermore, the TWPA device can be configured to comply with and satisfy a criterion of ω p > 2ω c / 3, where ω p is the frequency of the pump signal described above, and ω c is the cut-off frequency described above.

[0027] The advantage of such a configuration is that up-conversion can be suppressed for multiple signal frequencies while keeping the phase mismatch small.

[0028] It should be noted that the features of this specification can be combined in any way, even if not explicitly mentioned. For example, any variation of the pump signals described above (i.e., pump signals having a frequency that is at least 2 / 3 of the cut-off frequency of the TWPA device described above and in the higher frequency band described above, as well as pump signals having a frequency that is in the lower frequency band described above and whose second harmonic is within the frequency gap described above) can be combined with any chain of unit cell circuits (i.e., resonator circuits arranged in each of the plurality of unit cells described above and having periodically modulated input parameters).

[0029] Also, to achieve the exponential spatial increase in the amplitude of the amplified signal described above, a method for amplifying the amplified signal is provided. This method includes: · providing a TWPA device according to any aspect of this specification; · performing three-wave mixing in the TWPA device described above; · receiving an amplified signal for amplification at the input of the TWPA device described above; · receiving a pump signal for supplying energy to the amplified signal described above at the input described above; and · outputting the amplified amplified signal from the output of the TWPA device described above.

[0030] Thus, this method provides an efficient TWPA device capable of achieving exponential gain by minimizing upconversion and phase mismatch.

[0031] Hereinafter, a more detailed description of the present disclosure will be made non-limitingly with reference to the exemplary embodiments shown in the accompanying drawings.

Brief Description of the Drawings

[0032]

Figure 1

Figure 2A

Figure 2B

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7A

Figure 7B

Figure 8

Mode for Carrying Out the Invention

[0033] In the following detailed description, an embodiment of the present disclosure will be described. However, it should be understood that, unless specifically indicated, the features of different embodiments are interchangeable between embodiments and can be combined in different ways. In the following description, although a number of specific details are set forth in order to provide a more complete understanding of the present disclosure provided, it will be apparent to those skilled in the art that embodiments of the present disclosure can be practiced without these details. In other instances, detailed descriptions of well-known structures or functions are not provided so as not to obscure the present disclosure.

[0034] In the description of the examples of the following embodiments, the same reference numerals refer to the same or similar components.

[0035] FIG. 1 shows an objective view of a TWPA device 1 for a quantum computer. The TWPA device 1 can be used, for example, for quantum bit readout. The TWPA device shown in FIG. 1 includes an input 2, an output 3, and a transmission line 4 therebetween. The TWPA device 1 is configured to receive a pump signal and an amplification signal at the input 2 described above, and for this amplification signal to propagate along the transmission line to the output 3 described above, where the amplification signal described above is amplified at this output 3. The "TWPA device" means an amplification device that utilizes an amplification principle based on the non-linear interaction between an amplification signal and a strong co-propagating wave (pump signal), and the signal amplitude will increase spatially under the phase matching condition. In the quantum mechanism, the TWPA can generate squeezing of signals and entanglement of photons. The "pump signal" means an alternating current signal that supplies the energy necessary to amplify the amplification signal. Further, the output 3 of the TWPA device 1 described above can output the pump signal, the amplification signal of the amplifier, and an idler signal described above. The "idler signal" means a signal having a frequency equal to the difference in frequency between the pump signal and the amplification signal.

[0036] The TWPA device 1 according to the present disclosure includes a two-band dispersion relation, and in this two-band dispersion relation, it is configured to perform three-wave mixing.

[0037] FIGS. 2A-2B show that in the enlarged portions A and B of the transmission line 4 described above, the TWPA device 1 includes a plurality of chained unit cells φ, and each unit cell φ includes a non-linear inductance element 5 and a capacitor 6 connected to its ground 7. "Chained" means that the unit cells φ are connected so as to extend along the length L1 of the TWPA device described above. Further, the chained unit cells φ (i) resonator circuits 8 arranged in each of the plurality of unit cells φ described above, (ii) periodically modulated input parameters, and further includes one of them.

[0038] FIG. 2A is an enlarged portion A showing an enlarged part of the above-described transmission line 4, indicating that the chained unit cells φ include the resonator circuit 8. The resonator circuit 8 can be an LC oscillator as clarified in FIG. 2A.

[0039] FIG. 2B is an enlarged portion B depicting an enlarged part of the above-described transmission line 4, indicating that the chained unit cells φ have periodically modulated input parameters. The input parameters can be at least one of inductance and capacitance. Thus, as shown in the enlarged portion B of FIG. 2B, each unit cell φ includes two sub-cells φ', φ''. Thus, the non-linear inductance elements 5 of each sub-cell φ', φ'' can have different inductances. Therefore, the other sub-cells φ', φ'' within each unit cell φ can have different input parameters. In one aspect, the periodic modulation of the plurality of the above-described unit cells φ includes the changing modulation of at least every other unit cell φ in the chain of the above-described unit cells φ.

[0040] Furthermore, the two-band dispersion relation of the above-described TWPA device 1 is composed of a lower frequency band and a higher frequency band, and there is a frequency gap between the lower frequency band and the higher frequency band. The TWPA device 1 is further configured to receive an amplified signal for amplification at input 2 of the above-described TWPA device 1 and to receive a pump signal for supplying energy to the above-described amplified signal at the above-described input 2. The pump signal is in the above-described higher frequency band and has a frequency that is at least 2 / 3 of the cut-off frequency of the above-described TWPA device 1, or alternatively, the above-described pump signal has a frequency in the above-described lower frequency band and its second harmonic is within the above-described frequency gap.

[0041] The expression "performing three-wave mixing" means that the TWPA device 1 induces the lowest-order third-order non-linearity of energy (this is, for example, X in an optical crystal) (2)It can be meant to adopt (similar to non-linearity). Such non-linearity is related to the breaking of time-reversal symmetry, which can be introduced by applying a direct current bias or a magnetic flux bias. As a result, amplification to the amplified signal described above occurs by the down-conversion process, which can provide efficient amplification within a large bandwidth even in a weak dispersion medium even if the pump intensity of the pump signal described above is relatively small. The three-wave mixing of the TWPA device revealed in FIGS. 1A to 1B is ω s <ω p and ω i =ω p -ω s can be implemented by configuring the TWPA device described above so as to satisfy, where ω s is the frequency of the amplified signal described above, ω p is the frequency of the pump signal described above, and ω i is the frequency of the idler signal.

[0042] The non-linear inductance element 5 may be a single Josephson junction or a combination of at least two Josephson junctions.

[0043] FIG. 3 schematically shows that the nonlinear inductance element 5 of the TWPA device 1 according to the present disclosure can be a Josephson junction 5a, a current-biased junction, a rf superconducting quantum interference device (rf-SQUID) biased with magnetic flux, or a superconducting nonlinear asymmetric inductive element (SNAIL) biased with magnetic flux. When the nonlinear inductance element is a Josephson junction, the above-described nonlinear inductance element can be biased with a direct current that induces a certain shift in the phase difference across each unit cell. Further, when the nonlinear inductance element is an rf-SQUID or a flux-biased SNAIL, the above-described nonlinear inductance element 5 can be biased with a direct magnetic field that induces a certain shift in the phase difference across each unit cell φ.

[0044] FIG. 4 shows a graph clarifying the simulation of the performance of the TWAP device for different frequencies of the amplified signal and the pump signal disclosed herein. FIGS. 5 to 7B show the simulation of the dispersion relation of the two-band structure according to the aspects of this specification. The purpose of the simulations clarified in FIGS. 4 to 7B is to further explain the present disclosure introduced herein, together with its advantages. It should be noted that the simulations are based on aspects for disclosure purposes, but are not limited to those aspects and may be varied within the scope of the present disclosure.

[0045] FIG. 4 shows the region where there is / is no up-conversion of the pump signal, the amplified signal, and the idler signal. Up-conversion is not performed in the region indicated by r1, and the horizontal dashed line r2 is Ω thIndicates. In the regions of r3 and r4 (defined between r1 and r5), upconversion of either the amplified signal or the idler signal is possible. In region r5, both the amplified signal and the idler are upconverted, but the pump signal is not upconverted. Region r6, which is region 6, indicates the region where all three signals are upconverted. Therefore, for the pump signal, the condition ω p > ω0 (where ω0 represents the resonance frequency of the TWPA device 1) ensures that its second harmonic exceeds the aforementioned cut-off frequency ω c = 2ω0. For the signal / idler, the condition that the upconverted signal at zero detuning exceeds the cut-off, ω p + ω p / 2 > 2ω0 establishes the minimum boundary. This results in the more stringent constraint ω p > ω th = 4ω0 / 3. When the pump frequency of the aforementioned pump signal is greater than the aforementioned threshold, the detuned signal and the idler are not upconverted within the band defined by the formula [Number] and [Number] which is.

[0046] Therefore, Figure 4 demonstrates that no upconversion occurs by adjusting the aforementioned pump signal to be in the aforementioned higher frequency band and having a frequency that is at least 2 / 3 of the cut-off frequency of the aforementioned TWPA device 1.

[0047] Figure 5 shows a graph revealing the dispersion relation of the TWPA device 1 with a resonator circuit 8 (as clarified in Fig. 2A) for each unit cell φ. Thus, Figure 5 shows the two-band dispersion relation of the aforementioned TWPA device 1, which is composed of / includes a lower frequency band f1 and a higher frequency band f2, and has a frequency gap between its higher frequency band and lower frequency band, f1 and f2. The dashed line 1 reveals the dispersion relation when no resonator circuit is added, and the circles c0, c0’ reveal the sweet spots of the pump signal and the amplified signal, where upconversion is impossible but the phases of both are perfectly aligned. Furthermore, this dispersion relation presents the aforementioned frequency gap at the resonance frequency of the resonator circuit 8. As mentioned above, the circles c0, c0’ indicate the positions of the phase alignment points on the line 2, which is a straight line within the region without upconversion. Thereby, it is guaranteed that the phase misalignment is zero for the amplified signal at a frequency that is half of the pump frequency, and the phase misalignment is small for the frequencies of other amplified signals. Thus, in one aspect of the present disclosure according to the disclosure of Figure 5, the sweet spot that provides exponential gain while preventing upconversion requires that the pump frequency of the pump signal is within the higher band f2 (preferably c0’), and the signal frequency of the amplified signal is within the lower band f1 (preferably c0). Thus, the TWPA device 1 can be configured to follow ω p >2ω c / 3, where ω p is the frequency of the aforementioned pump signal, and ω c is the aforementioned cut-off frequency.

[0048] However, as mentioned in this specification, in one aspect, the pump frequency of the pump signal can be within the aforementioned lower frequency band f1, and its second harmonic is within the aforementioned frequency gap.

[0049] The two-band dispersion relation as shown in Fig. 5 can be defined in the aspect where each cell φ includes the resonator circuit 8 in each of the plurality of unit cells φ described above.

Number

[0050] Furthermore, when the plurality of unit cells φ described above include an input parameter that is periodically modulated, the dispersion relation described above is

Number

[0051] The coupling coefficient is

Number

[0052] Figure 6 shows the dispersion relation of the TWPA device including the input parameters periodically modulated at ω2 = 1.25ω1. This dispersion relation includes two bands, f01 and f02, separated by a gap. Line 4 indicates the dispersion relation without modulation, and circles c00, c00’ indicate the positions of the phase matching points that together form a straight line, line 5, within the frequency region without up-conversion. Thereby, the phase mismatch is zero for the amplified signal at a frequency that is half of the pump frequency, and it is guaranteed that the phase mismatch is small for the frequencies of other amplified signals. The positions of the pump signal and the amplified signal at degeneracy are indicated by circles, where c00 reveals the amplified signal and c00’ reveals the pump signal. The gain in this setting is qualitatively similar to the mode of the TWPA device 1 with the resonator circuit 8 (revealed in Figure 5) and provides an exponential gain.

[0053] In an aspect of the present disclosure, the aforementioned pump signal has a frequency within the lower frequency band described above, and its second harmonic is within the aforementioned frequency gap. The pump signal can be arranged, for example, such that wp is 1.5 / 2 in the graph of Figure 6. As a result, the up-converted pump frequency is within the aforementioned gap (between f01 and f02), thus preventing up-conversion.

[0054] Figure 7A shows the gain coefficient for the signal at zero detuning of the TWPA device 1 according to an aspect of the present disclosure, with ω r = 1.5, ω0, ν = 0.95, ε1 = 0.06. When the pump is arranged within the lower band, the gain coefficient is the same as that without an oscillator (the curve in the lower left corner of Figure 7A). In one aspect, when the pump is arranged within the higher band at the sweet spot ω p = 1.77ω0, a sharp high-amplification peak appears. The peak width is 0.048ω0.

[0055] Figure 7B shows the gain coefficient of the TWPA device 1 according to an aspect of the present disclosure for the pump signal at the optimal phase matching point ω p = 1.77ω0 and the pump intensity ε2 = 0.06, with respect to ω rIt is shown as a detuning function with ξ = 1.5 and ν = 0.95. The corresponding bandwidth is ω s - ω p / 2 = 0.23ω p According to the disclosure of FIG. 7B, when the pump intensity ε1 = 0.06 is applied, the amplified signal has a frequency in the range of 4.6 to 7.4 GHz, preferably 6 GHz. Then, the pump signal can have a frequency of about 12 GHz (ω p = 2ω s ). Therefore, when the aforementioned pump frequency is about 12 GHz and the aforementioned amplified signal is about 6 GHz, the cut-off frequency becomes about 14 GHz, and an exponential gain according to the aspects of the present disclosure is provided. However, it should be noted that the above is for illustrative purposes only and does not limit the present disclosure.

[0056] Therefore, FIGS. 7A to 7B show that, according to the present disclosure, a pure exponential increase in the amplified signal of the TWPA device 1 of the present specification with minimal additional noise in a wide band is made possible.

[0057] FIG. 8 schematically shows, in flowchart form, a method 100 for amplifying the amplified signal to achieve an exponential spatial increase in the amplitude of the amplified signal. Method 100 includes · providing a TWPA device 1 according to any aspect of the present specification (e.g., as disclosed in FIGS. 1 to 2B) (101), · performing three-wave mixing in the TWPA device 1 (102), · receiving an amplified signal for amplification at the input 2 of the TWPA device (103), · receiving a pump signal at the input 2 to supply energy to the amplified signal (104), · outputting the amplified amplified signal from the output of the TWPA device 1 (105), and includes.

Claims

1. A traveling wave parametric amplifier, TWPA, device (1) for a quantum computer, wherein the TWPA has a two-band dispersion relation, and the TWPA device (1) is configured to perform three-wave mixing with the two-band dispersion relation, and the TWPA device (1) A plurality of linked unit cells (φ), each unit cell (φ) includes a nonlinear inductance element (5) and a capacitor (6) connected to its ground (7), and the linked unit cells (φ) Each of the aforementioned plurality of unit cells (φ) has a resonator circuit (8) arranged in it, Periodically modulated input parameters, It comprises multiple chained unit cells (φ), further including one of the following: The dispersion relation of the two bands includes a lower frequency band and a higher frequency band, with a frequency gap between the higher frequency band and the lower frequency band. The aforementioned TWPA device (1) At the input (2) of the TWPA device (1), an amplification signal for amplification is received. The input (2) receives a pump signal in order to supply energy to the amplified signal. It is further configured in this way, The pump signal is in a higher frequency band and has a frequency that is at least 2 / 3 of the cutoff frequency of the TWPA device (1), The pump signal is in a lower frequency band than the one described above, and its second harmonic has a frequency within the frequency gap. TWPA device (1).

2. Further configured to generate an idler signal, ω ｓ <ω ｐ and ω ｉ = ω ｐ -ω ｓ The three-wave mixing is performed by configuring the TWPA device to satisfy the following conditions, where ω ｓ ω is the frequency of the amplified signal, ｐ ω is the frequency of the pump signal, ｉ The TWPA device according to claim 1, wherein the frequency of the idler signal is [the specified frequency].

3. The TWPA device according to claim 1, wherein the nonlinear inductance element (5) is a single Josephson junction or a combination of at least two Josephson junctions.

4. The TWPA device according to claim 1, wherein the resonator circuit (8) is an LC oscillator.

5. The TWPA device according to claim 1, wherein the input parameter is at least one of inductance and capacitance.

6. The TWPA device (1) according to claim 1, wherein the TWPA device (1) is configured to receive an amplified signal having a frequency in a lower frequency band.

7. When each cell (φ) is provided with the resonator circuit (8) for each of the plurality of unit cells (φ), the dispersion relation of the two bands is, [Math 1] Defined by, When the plurality of unit cells (φ) include periodically modulated input parameters, the dispersion relation is, [Math 2] Defined by, where ω ＋ represents the higher frequency band than the above, ω － represents the lower frequency band than the above, κ represents the value of the wave multiplied by the unit cell length within the range of 0 to π, ω ０ represents the resonance frequency of the TWPA, ω ｒ represents the resonance frequency of the resonator circuit, ν represents the coupling coefficient where ν < 1, each of the unit cells includes first and second sub-cells, ω １ represents the resonance frequency (φ’) of each first sub-cell, ω ２ represents the resonance frequency (φ’’) of each second sub-cell. The TWPA device (1) according to claim 1.

8. The TWPA device (1) according to claim 1, wherein the periodic modulation of the plurality of unit cells (φ) includes changing modulation of at least every other unit cell (φ) of the plurality of unit cells (φ) in a chain of unit cells (φ).

9. The aforementioned TWPA device (1) ω ｐ +ω ｓ >ω ｃ and 2*ω ｐ -ω ｓ >ω ｃ It is configured to satisfy the criteria, ω ｓ ω is the frequency of the amplified signal, ｐ ω is the frequency of the pump signal, ｃ The TWPA device (1) according to claim 1, wherein the cutoff frequency is .

10. A method (100) for amplifying the amplified signal in order to achieve an exponential spatial increase in the amplitude of the amplified signal, To provide a TWPA device (1) according to any one of claims 1 to 9 (101), The TWPA device (1) performs three-wave mixing (102), The input (2) of the TWPA device receives an amplification signal for amplification (103), In order to supply energy to the amplified signal, the input (2) receives a pump signal (104), The TWPA device (1) outputs an amplified signal (105), A method (100) including the following.

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