Quantum device and quantum computer

Abstract

A quantum device 10 includes: a data quantum bit 11; a readout resonator 12 coupled to the data quantum bit 11; a readout waveguide 13 coupled to the readout resonator 12; and a nonlinear filter 14 interposed between the readout resonator 12 and the readout waveguide 13. The nonlinear filter 14 has different transmission characteristics depending on the amplitude of a readout pulse input to the readout waveguide 13.

Description

Quantum Devices and Quantum Computers

[0001] The present invention relates to quantum devices and quantum computers.

[0002] Quantum computers use elements called qubits to process information, demonstrating computational capabilities beyond those of existing computers. However, qubits are more susceptible to noise than the classical bits used in existing computers. Therefore, a technique called error-tolerant quantum computing must be used to realize a general-purpose quantum computer. In error-tolerant quantum computing, the states of some qubits are read between each calculation step to detect calculation errors caused by noise. Figure 1 shows a schematic diagram of error-tolerant quantum computing. In this example, six qubits, qubits 1 to 6, are implemented, and the states of qubits 2, 4, and 6 are read between calculation steps 1 and 2. To put such error-tolerant quantum computing into practical use, it is necessary to read the qubit states quickly and accurately.

[0003] In superconducting qubits (hereinafter, unless otherwise specified, superconducting qubits will be simply referred to as "qubits"), which are one of the most popular implementations of qubits, high-speed and high-precision readout has been achieved by a method called distributed readout (see, for example, Non-Patent Document 1). Distributed readout utilizes the fact that a microwave resonator called a "readout resonator" is coupled to the qubit, and its resonant frequency changes depending on the state of the qubit. Strengthening the coupling between the qubit and the readout resonator increases the change in the resonant frequency. This enables high-speed and high-precision readout. However, this increases the qubit's sensitivity to thermal noise in the readout resonator, which shortens the time the qubit can retain information.

[0004] Conventionally, the main challenge in achieving high-speed and high-precision quantum bit readout has been the reduction in energy relaxation time due to quantum bit energy leakage through the readout resonator. To solve this problem, a linear filter called a Purcell filter was developed (see, for example, Non-Patent Documents 2 to 8). Furthermore, it has been demonstrated that the use of a non-linear filter called a Josephson quantum filter can also suppress energy leakage into the quantum bit control waveguide (see, for example, Non-Patent Documents 9 to 11).

[0005] T. Walter et al., "Rapid high-fidelity single-shot dispersive readout of superconducting qubits" Physical Review Applied 7 (May 26, 2017), p. 054020.M. D. Reed et al., “Fast reset and suppressing spontaneous emission of a superconducting qubit”, Applied Physics Letters 96, 203110 (2010).E. Jeffrey et al., “Fast accurate state measurement with superconducting qubits”, Physical Review Letters 112, 190504 (2014).E. A. Sete et al., “Quantum theory of a bandpass Purcell filter for qubit readout”, Physical Review A 92, 012325 (2015).N. T. Bronn et al., “Broadband filters for abatement of spontaneous emission in circuit quantum electrodynamics”, Applied Physics Letters 107, 172601 (2015).N. T. Bronn et al., “Reducing spontaneous emission in circuit quantum electrodynamics by a combined readout / filter technique”, IEEE Transactions on Applied Superconductivity 25, 1700410 (2015).L. C. G. Govia et al., “Enhanced qubit readout using locally generated squeezing and inbuilt Purcell-decay suppression”, New Journal of Physics 19, 023044 (2017).Y. Sunada et al., “Fast readout and reset of a superconducting qubit coupled to a resonator with an intrinsic Purcell filter”, Physical Review Applied 17, 044016 (2022).K. Koshino et al., “Protection of a Qubit via Subradiance: A Josephson Quantum Filter”, Physical Review Applied 13, 014051 (2020).S. Kono et al., “Breaking the trade-off between fast control and long lifetime of a superconducting qubit”, Nature Communications 11, 3683 (2020).I. Iakoupov et al., “Saturable Purcell filter for circuit quantum electrodynamics”, Physical Review Research 5, 013148 (2023).J.-H. Yeh et al., “Microwave attenuators for use with quantum devices below 100 mK”, Journal of Applied Physics 121, 224501 (2017).F. Yan et al., “Distinguishing Coherent and Thermal Photon Noise in a Circuit Quantum Electrodynamical System”, Physical Review Letters 120, 260504 (2018).Z.Wang et al., “Cavity attenuators for superconducting qubits”, Physical Review Applied 11, 014031 (2019).A. Blais et al., “Circuit quantum electrodynamics”, Reviews of Modern Physics 93, 025005 (2021).

[0006] The information held by a quantum bit is lost through two processes: energy relaxation and phase relaxation. Energy relaxation is the process by which a quantum bit transitions from a state |e> in which it has energy to a state |g> in which it does not. On the other hand, phase relaxation is the process by which the phase information of the quantum mechanical superposition of |e> and |g> is lost. The typical times at which energy relaxation and phase relaxation occur are called the energy relaxation time (hereinafter referred to as "T1") and the phase relaxation time (hereinafter referred to as "T2"), respectively.

[0007] The development of the above-mentioned prior art has made it possible to make the energy relaxation time T1 sufficiently long relative to the time required to read out a quantum bit. As a result, the time that a quantum bit can retain information is now more strongly limited by the phase relaxation time T2 than by T1. For this reason, improving T2 has become an issue in recent years.

[0008] The present invention has been made in view of these problems, and its purpose is to provide a technique that can lengthen the phase relaxation time while shortening the readout time of a quantum bit.

[0009] In order to achieve the above object, a quantum device according to one aspect of the present invention includes a data qubit, a readout resonator coupled to the data qubit, and a nonlinear filter inserted between the readout resonator and a readout waveguide, wherein the nonlinear filter has transmission characteristics that vary depending on the amplitude of a readout pulse input to the readout waveguide.

[0010] In one embodiment of the quantum device, the nonlinear filter is highly transparent to small amplitude input signals and less transparent to large amplitude signals.

[0011] In one embodiment of the quantum device, the linewidth of the coupling between the readout resonator and the readout waveguide via a nonlinear filter is defined as κ ｅｆｆ , the dispersion shift of the readout resonator due to the data qubit is χ, the nonlinear filter has a dispersion shift of κ when there is no data qubit readout. ｅｆｆ >>χ, κ during reading ｅｆｆ = χ.

[0012] In one embodiment of the quantum device, the nonlinear filter is constructed using superconducting qubits.

[0013] In one embodiment of the quantum device, the center frequency of the nonlinear filter is set to ω ｆ , the resonant frequency of the readout resonator is ω ｒ , the non-harmonic degree of the nonlinear filter is α ｆ When the coupling strength between the readout resonator and the nonlinear filter is g and the linewidth of the coupling between the nonlinear filter and the readout waveguide is κ, the nonlinear filter satisfies the following condition: Meet the following.

[0014] In one embodiment of the quantum device, the superconducting qubit is composed of a transmon coupled in parallel with a Josephson junction and a capacitor.

[0015] In one embodiment of the quantum device, the nonlinear filter and the readout waveguide are capacitively coupled.

[0016] In one embodiment of the quantum device, the nonlinear filter and the readout waveguide are inductively coupled.

[0017] Another aspect of the present invention is a quantum computer, which includes any one of the quantum devices described above.

[0018] Any combination of the above components, and any transformation of the present invention into an apparatus, method, system, recording medium, computer program, etc., are also valid aspects of the present invention.

[0019] According to the present invention, it is possible to lengthen the phase relaxation time while shortening the readout time of the quantum bit.

[0020] 12 is a schematic diagram illustrating error-tolerant quantum computing. It is a schematic diagram illustrating a system for distributed readout. It is a schematic diagram of a quantum device equipped with a conventional linear filter. It is a schematic diagram of a quantum device according to a first embodiment. It is a graph showing the relationship between the linewidth of a readout resonator and the dephasing rate. It is a graph showing the relationship between frequency and the transmittance of a filter according to an embodiment. It is a schematic diagram showing parameters related to the design of a filter qubit. It is a schematic diagram showing a nonlinear filter of a quantum device according to a second embodiment. It is a schematic diagram showing a quantum device according to a third embodiment. It is a schematic diagram showing a quantum device according to a fourth embodiment. It is a graph showing experimental results of the wavelength characteristics of a nonlinear filter according to the present disclosure. It is a graph showing numerical simulation results of the wavelength characteristics of a nonlinear filter according to the present disclosure. It is a graph showing the relationship between the amplitude of a readout signal and signal separation obtained from the experimental results of FIG. It is a graph showing the time change of a readout signal in an excited state and a ground state. (a) corresponds to a readout pulse period of 200 ns, and (b) corresponds to a readout pulse period of 40 ns. It is a graph showing the phase of the steady-state reflection coefficient of a nonlinear filter versus the frequency and amplitude of an input signal. 10A and 10B are graphs showing the observed measurement rate as a function of the amplitude of the readout pulse, and 10C are graphs showing the complex amplitude of the readout signal in the excited and ground states measured using a 2 microsecond rectangular pulse.

[0021] The present invention will be described below with reference to the drawings based on preferred embodiments. The embodiments are illustrative and do not limit the invention. Not all features or combinations thereof described in the embodiments are necessarily essential to the invention. The same or equivalent components, parts, and processes shown in the drawings are designated by the same reference numerals, and redundant descriptions are omitted where appropriate. The scale and shape of each part shown in the drawings are set for convenience to facilitate explanation and should not be interpreted as limiting unless otherwise specified. Furthermore, when terms such as "first" and "second" are used in this specification or claims, unless otherwise specified, these terms do not indicate any order or importance, but are merely used to distinguish one configuration from another. Furthermore, some components that are not important for explaining the embodiments are omitted from the drawings.

[0022] Before describing specific embodiments, we will first explain the basic findings. As mentioned above, when the distributed readout of quantum bits is made faster and more accurate, the quantum bits become sensitive to thermal noise in the readout resonator, which causes a problem of shortening the phase relaxation time T2. This problem has traditionally been solved by suppressing the thermal noise flowing in from the readout waveguide coupled to the readout resonator.

[0023] Here, we will explain distributed readout of quantum bits. Distributed readout uses a system in which a readout resonator is coupled to a quantum bit, and a readout waveguide is coupled to the readout resonator. Figure 2 shows a schematic diagram of a system 100 used for such distributed readout. System 100 includes a data quantum bit 101, a readout resonator 102, and a readout waveguide 103. Data quantum bit 101 is coupled to readout resonator 102, and readout resonator 102 is coupled to readout waveguide 103.

[0024] To read out, a microwave pulse (hereinafter referred to as the "readout pulse") having a frequency resonant with the readout resonator 102 is incident from the readout waveguide 103. Here, because the readout resonator 102 is coupled to the data quantum bit 101, the resonant frequency changes depending on the state of the data quantum bit 101. Therefore, the reflection coefficient of the readout pulse also changes. In this way, the state of the data quantum bit 101 can be determined by measuring the phase and amplitude of the reflected wave (hereinafter referred to as the "readout signal") after the readout pulse is incident on the readout resonator 102.

[0025] The readout signal must be measured using a waveform measuring device placed in a room temperature environment. Meanwhile, the data quantum bit 101 and readout resonator 102 must be cooled to several tens of millikelvins (mK) using a dilution refrigerator and maintained in a low-temperature environment. Therefore, if the readout resonator 102 and the waveform measuring device are directly connected via the readout waveguide 103, thermal radiation from the room temperature environment will flow back through the readout waveguide 103 and into the readout resonator 102. This causes thermal noise. To prevent this, microwave elements called isolators, which allow light to pass in the forward direction but attenuate it in the reverse direction, have traditionally been used. However, with current technology, it is difficult to miniaturize an isolator. Therefore, it is difficult to accommodate the required number of isolators in a practical-scale quantum computer dilution refrigerator. Furthermore, even in experiments using a large number of isolators connected together, the average number of thermal photons in the readout resonator 102 is currently only 10 －３ ~10 －４ However, the effect has only been suppressed to a certain extent (see, for example, Non-Patent Documents 12 to 14).

[0026] This value is 10, which is the average number of heat photons expected from the temperature of the dilution refrigerator, which is about 20 mK. －８This is more than 10,000 times larger than the conventional method. This is thought to be due to the difficulty of sufficiently dissipating heat from the various microwave elements connected to the readout waveguide 103 at extremely low temperatures (see, for example, Non-Patent Document 14). For these reasons, in order to continue improving the phase relaxation time T2 of the data quantum bit 101 in the future, it is thought that approaches other than suppressing the thermal noise flowing in from the readout waveguide 103 will also need to be used.

[0027] As a new approach to improving the quantum bit dephasing time T2, the inventors have devised a method of making the readout circuit itself resistant to thermal noise. This makes it possible to suppress quantum bit dephasing without suppressing the inflow of thermal noise into the readout resonator. In this disclosure, a nonlinear filter is used to achieve this. Below, we will explain the unique features that the nonlinear filter of this disclosure has compared to conventional linear filters.

[0028] 3 shows a schematic diagram of a quantum device 110 equipped with a conventional linear filter. The quantum device 110 includes a data qubit 101, a readout resonator 102, a readout waveguide 103, and a linear filter 104. The readout resonator 102 and the readout waveguide 103 are coupled via the linear filter 104.

[0029] The rate at which the data qubit 101 undergoes phase relaxation is expressed as the phase relaxation rate Γ, which is the reciprocal of the phase relaxation time T2. In particular, the phase relaxation rate Γ of the qubit due to thermal noise in the readout resonator 102 ｔｈ Φ is expressed by the following formula: where: is the average number of thermal photons in the readout resonator 102 under normal conditions. χ is the amount of change in the resonant frequency of the readout resonator 102 depending on the state of the data quantum bit 101 (hereinafter referred to as the "dispersion shift"). ｅｆｆ is the linewidth of the coupling between the readout resonator 102 and the readout waveguide 103 via the linear filter 104. To perform dispersed readout in this system, the dispersion shift χ of the readout resonator 102 and the linewidth κ ｅｆｆ(For example, see Non-Patent Document 15.) In this case, equation (1) can be approximated as follows: In other words, if the dispersion shift χ is increased to speed up and improve the accuracy of readout, the phase relaxation rate Γ due to thermal noise ｔｈ Φ also increases proportionally.

[0030] To understand the fundamental nature of this trade-off, we need to consider that reading out the state of a qubit is a deliberate dephasing of the qubit. When a qubit in a superposition of |g〉 and |e〉 is read, the information is converted to a classical bit, and the phase information of the superposition is lost. In distributed readout, this process occurs gradually and can be considered dephasing. This is called measurement-induced dephasing. Since the measurement-induced dephasing rate is the rate at which the qubit information is converted to a classical bit, a large rate is a necessary condition for fast and accurate readout.

[0031] The average number of photons in the readout cavity 102 generated by the readout pulse is Then the measurement-induced dephasing rate in the distributed readout is where the frequency of the readout pulse is the average of the resonant frequencies of the readout resonator when the data qubits are in the |g> and |e> states. Equation (1) has exactly the same form as equation (3), except for the factor of two. This is because phase relaxation due to thermal noise can be considered as measurement-induced phase relaxation due to a broadband readout pulse. In other words, the distributed readout of data qubits and phase relaxation due to thermal noise are thought to occur through the same mechanism.

[0032] From the above considerations, in order to achieve both high-speed and high-precision readout and a long phase relaxation time T2, the phase relaxation rate Γ during readout is ｍｅａｓ φ and the dephasing rate Γ due to thermal noise under normal conditions ｔｈ φAccording to equations (1) and (3), to achieve this, the average number of photons in the readout cavity due to the readout pulse must be increased by and the average number of photons under normal conditions The ratio needs to be increased.

[0033] However, distributed readout has a maximum strength of is 10 １ On the other hand, even with an isolator, the average number of thermal photons is is 10 －４ Therefore, at present, this ratio About 10 ５ Therefore, it is difficult to make the ratio of the dephasing rates during readout and normal operation, Γ ｍｅａｓ φ / Γ ｔｈ Φ In order to increase the average number of photons in the readout cavity 102 in the future, and the dephasing rate Γ φ It is necessary to break the proportionality between

[0034] 4 is a schematic diagram of a quantum device 10 equipped with a nonlinear filter according to a first embodiment. The quantum device 10 includes a data qubit 11, a readout resonator 12, a readout waveguide 13, and a nonlinear filter 14. The readout resonator 12 and the readout waveguide 13 are coupled via the nonlinear filter 14.

[0035] In this embodiment, the average number of photons in the readout cavity 12 is and the dephasing rate Γ ｍｅａｓ φ In order to break the proportional relationship between the readout resonator 12 and the readout waveguide 13, a nonlinear band-pass filter 14 is inserted between the readout resonator 12 and the readout waveguide 13. When a conventional linear band-pass filter is inserted, it is called a Purcell filter. To distinguish it from this, the nonlinear filter 14 of this embodiment is sometimes called a "nonlinear Purcell filter."

[0036] Existing linear Purcell filters selectively suppress the energy relaxation of quantum bits by making the coupling between the readout resonator and the readout waveguide frequency-dependent. This is possible because, in distributed readout, the quantum bit transition frequency differs from the frequency of the readout pulse. However, the thermal noise that is a problem in this embodiment has a broadband spectrum, and the component with the same frequency as the readout pulse causes phase relaxation. For this reason, it is not possible to distinguish between thermal noise and the readout pulse based on frequency. Therefore, in this embodiment, we focus on the difference in amplitude between thermal noise and the readout pulse. In other words, the novel idea of ​​the present invention is to selectively suppress the influence of thermal noise by using a nonlinear filter whose transmittance depends on the amplitude of the input signal.

[0037] Simply put, it may seem that using a filter that blocks small-amplitude input signals and transmits large-amplitude input signals would block only thermal noise. However, in this embodiment, on the contrary, a filter is used that easily transmits small-amplitude input signals and poorly transmits large-amplitude input signals. Below, we will explain how the effects of thermal noise can be suppressed by using such a filter.

[0038] To perform distributed readout, the linewidth κ of the coupling between the readout resonator 12 and the readout waveguide 13 via the nonlinear filter 14 is ｅｆｆ must be comparable to the dispersion shift χ of the readout cavity. This follows from equation (3) as follows: ｍｅａｓ φ (hereinafter referred to as "read rate") is κ ｅｆｆ This is because the phase relaxation rate is maximized at χ = ​​χ, which can be seen from Figure 5, which shows the relationship between the linewidth of the readout cavity and the phase relaxation rate.

[0039] Also, κ ｅｆｆ →∞, Γ ｍｅａｓ φ →0, the linewidth κ of the readout resonator 12 ｅｆｆ It can be seen that if is too large, the readout rate approaches 0. The reason for this is that the linewidth κ of the readout cavity 12 ｅｆｆIf Γ is too large, the readout pulse that enters the readout resonator 12 is immediately output as a readout signal, and therefore the time during which it can interact with the data quantum bit is short. Similarly, from equation (1), the dephasing rate Γ due to thermal noise is ｔｈ φ Also ｅｆｆ = χ and κ ｅｆｆ →∞, it approaches 0. In other words, the linewidth κ of the readout resonator 12 ｅｆｆ κ ｅｆｆ >>χ, κ during reading ｅｆｆ =χ, the influence of phase relaxation due to thermal noise can be suppressed without impairing the readout rate. To achieve this, in this embodiment, a nonlinear filter 14 that has high transparency to input signals with small amplitudes and low transparency to input signals with large amplitudes is inserted between the readout resonator 12 and the readout waveguide 13. As a result, during normal times (when no readout is being performed), the coupling between the readout resonator 12 and the readout waveguide 13 is strong, and κ ｅｆｆ On the other hand, during the read pulse, the coupling is weaker and κ ｅｆｆ It is possible to realize a readout circuit that satisfies the condition:

[0040] The inventors have discovered that, in the present invention, by using a superconducting quantum bit, it is possible to realize a nonlinear filter 14 that has high transparency for input signals with small amplitudes and low transparency for input signals with large amplitudes. A superconducting quantum bit coupled to an input port and an output port operates as a nonlinear bandpass filter. When the amplitude of the input signal is sufficiently small, this filter transmits only signals near the transition frequency of the quantum bit. On the other hand, as the amplitude of the input signal is increased, the pass frequency shifts according to the anharmonicity of the quantum bit. An explanation will be given of the anharmonicity. A nonlinear LC circuit such as a Josephson junction has a cosine-type potential, and the difference appears in the level structure. The deviation from the harmonic potential is expressed as an anharmonicity α = E １２ -E ０１ This is an index showing how close the system is to an ideal two-level system. ０１is the level difference between the ground state and the first excited state, and E １２ is the level difference between the second excited state and the first excited state. Figure 6 shows the relationship between frequency and the transmittance of the nonlinear filter of this embodiment. Such a filter can be realized by using a quantum bit whose transition frequency is equal to the frequency of the readout pulse and whose anharmonicity is sufficiently large. Hereinafter, a nonlinear Purcell filter realized using such quantum bits will be referred to as a "filter quantum bit" to distinguish it from a data quantum bit.

[0041] The filter qubit is defined by the following four parameters: ｆ , anharmonicity α ｆ , the coupling strength g with the readout resonator 12, and the linewidth κ of the coupling with the readout waveguide 13. Figure 7 shows a schematic of these parameters relevant to the design of the filter qubit 15.

[0042] The conditions for this filter to operate as a nonlinear Purcell filter are given by the following four equations. Equation (4) expresses that the normal transmission band of the filter is the resonant frequency ω ｒ The condition is that the filter includes a frequency domain that is larger than the passband width. Equation (5) is the condition that the shift in the passband width of the filter is greater than the passband width. These two conditions realize a nonlinear filter that is highly transparent to small-amplitude input signals and is less transparent to large-amplitude input signals. In addition, equations (6) and (7) must be satisfied to reduce the influence of thermal noise under normal conditions. When equation (6) is satisfied, the two resonant modes that are generated by coupling the readout resonator and the filter qubit both have a resonant frequency ≒ ω ｒ , line width κ ｅｆｆ In this case, if equation (7) is further satisfied, the linewidths of the two resonant modes are both κ ｅｆｆ >>χ is satisfied, so phase relaxation due to thermal noise is suppressed.

[0043] According to this embodiment, it is possible to lengthen the phase relaxation time while shortening the readout time of the quantum bit.

[0044] [Implementation Advantages of Nonlinear Purcell Filter] The fundamental advantages of this embodiment have been described above. In addition, the nonlinear Purcell filter also has implementation advantages. That is, in realizing a large-scale quantum computer consisting of a large number of superconducting quantum bits, it is desirable that the implementation of the readout circuit for each quantum bit be as simple as possible. In this respect, the nonlinear Purcell filter has the following three advantages.

[0045] First, because the filter is implemented using superconducting qubits, the chip fabrication recipe is not complicated. Typically, implementing nonlinear elements with different functions on the same chip requires Josephson junctions with different characteristics, necessitating multiple electron beam lithography processes. This reduces the overall chip yield and performance due to the increase in impurities on the chip with each lithography process and the fact that the yield in fabricating Josephson junctions is not 100%. On the other hand, because the characteristics of the filter qubits required to implement the nonlinear Purcell filter are nearly identical to those of the qubits responsible for quantum computing (hereafter referred to as "data qubits"), the filter qubits and data qubits can be fabricated simultaneously. Therefore, a chip with a nonlinear Purcell filter can be fabricated using a recipe optimized for yield and performance of the data qubits. This is becoming increasingly important in recent years as chip fabrication recipes become highly optimized.

[0046] Second, a nonlinear Purcell filter can also fulfill the role of an existing linear Purcell filter. Existing bandpass Purcell filters suppress energy relaxation of the quantum bit to the readout waveguide by inserting a filter between the readout resonator and the readout waveguide to impart frequency-dependent coupling. A nonlinear Purcell filter suppresses phase relaxation due to quantum bit thermal noise by utilizing differences in transmittance depending on the amplitude of the input signal. However, it also has the same frequency dependence as an existing bandpass Purcell filter. Therefore, the nonlinear Purcell filter alone can improve both the energy relaxation time T1 and the phase relaxation time T2 without the need for a separate filter to suppress energy relaxation. Since many recent chips already incorporate bandpass Purcell filters, simply replacing them with a nonlinear Purcell filter can provide additional thermal noise resistance. This is important in terms of saving chip area when scaling up superconducting quantum computers.

[0047] Third, no additional control is required beyond the injection of the readout pulse. Looking at equation (1), which gives the dephasing rate of a qubit due to thermal noise, the dispersion shift or linewidth κ of the readout cavity ｅｆｆ For example, it is possible to control the χ and κ during normal operation and during readout by using a superconducting quantum interference device (SQUID) and a magnetic flux bias line. ｅｆｆ By changing the value of κ, it is possible to achieve both high-speed and high-precision readout and thermal noise resistance. However, adding one flux bias line per quantum bit not only consumes chip area, but also increases the wiring density and heat inflow of the refrigerator, which is a barrier to the scale-up of quantum computers. In contrast, the nonlinear Purcell filter automatically adjusts κ depending on the presence or absence of a readout pulse. ｅｆｆSince the Purcell filter is an element that changes the signal, no additional control lines are required. In other words, the wiring and experimental equipment designed for distributed readout of superconducting qubits can be used as is, and the nonlinear Purcell filter can be introduced simply by changing the chip design. In recent years, rapid progress has been made in the development of experimental equipment specialized for the control and distributed readout of superconducting qubits, so being able to use this equipment as is is a major advantage.

[0048] 8 is a schematic diagram of a nonlinear filter 20 of a quantum device according to a second embodiment of the present invention. This nonlinear filter is composed of a transmon in which a capacitor 21 and a Josephson junction 22 are coupled in parallel.

[0049] According to this embodiment, a nonlinear filter can be easily fabricated as a superconducting quantum bit.

[0050] 9 schematically shows a quantum device 30 according to a third embodiment. The quantum device 30 includes a data qubit 31, a readout resonator 32, a readout waveguide 33, and a nonlinear filter 34.

[0051] The data quantum bit 31 and the readout resonator 32 are capacitively coupled via a capacitor 35. The readout resonator 32 and the nonlinear filter 34 are capacitively coupled via a capacitor 36. The readout waveguide 33 and the nonlinear filter 34 are capacitively coupled via a capacitor 37.

[0052] 10 is a schematic diagram of a quantum device 40 according to a fourth embodiment. The quantum device 40 includes a data quantum bit 41, a readout resonator 42, a readout waveguide 43, and a nonlinear filter 44.

[0053] The data quantum bit 41 and the readout resonator 42 are capacitively coupled via a capacitor 45. The readout resonator 42 and the nonlinear filter 44 are capacitively coupled via a capacitor 46. The readout waveguide 43 and the nonlinear filter 44 are inductively coupled via an inductor 47.

[0054] [Verification] The inventors conducted verification experiments to confirm the effects of the quantum device according to the embodiment. (Experiment 1) Fig. 11 shows the experimental results of the wavelength characteristics of the nonlinear filter according to the present disclosure. Fig. 12 shows the numerical simulation results of the wavelength characteristics of the nonlinear filter according to the present disclosure. Fig. 13 shows the relationship between the amplitude of the readout signal and signal separation obtained from the experimental results of Fig. 11.

[0055] (Experiment 2) The parameters of the quantum device used in the experiment are as follows: Data qubit transition frequency: ω ｑ / 2π=8.4969 GHz. Energy relaxation time: T1=17±1 μsec. The readout resonator is a λ / 2 resonator with a built-in Purcell filter as described in Non-Patent Document 8, and the Dressed Qubit resonant frequency ω ｃ / 2π=9.7927 GHz. Dispersion shift: χ=-11.8 MHz. Nonlinear filter anharmonicity: α ｆ / 2π=-0.12 GHz. Coupling coefficient between the readout resonator and the nonlinear filter: g / 2π=88 MHz. Linewidth of the nonlinear filter: κ ｆ = 0.31 GHz. In the following, experiments were carried out using two read pulses with periods of 200 ns and 40 ns.

[0056] FIG. 14 shows the readout signal b in the excited state (|e>) and the ground state (|g>). ｏｕｔ (| b ｏｕｔ | ２ The graphs show the time evolution of the photon flux (normalized so that the photon flux is equal to the photon flux). Figure 14(a) corresponds to a readout pulse length of 200 ns, and Figure 14(b) corresponds to a readout pulse length of 40 ns.

[0057] FIG. 15 shows the steady-state reflection coefficient S of the nonlinear filter as a function of the frequency and amplitude of the input signal. １１ Specifically, this is the reflection spectrum of the nonlinear filter measured using 2 microsecond rectangular pulses of various frequencies and amplitudes. The theoretical curves were calculated using a steady-state solution of the classical equations of motion that approximate the mean-field dynamics of the readout resonator. The frequency of the readout pulse, ω, ｒｏ and amplitude Ωｒｏ The reflection coefficient measured at is indicated by an asterisk.

[0058] When the amplitude of the input signal is small, the measured spectrum agrees well with the classical model, which can be used to determine the anharmonicity of the filter. However, near the frequency and amplitude of the readout pulse, the classical model bifurcates. The readout signal for the ground state |g〉 lies on the low-excitation branch. In contrast, the readout signal for the excited state |e〉 does not strictly follow the classical model, but is considered to be on the high-excitation branch.

[0059] FIG. 16 shows the observed measurement rate Γ ｍｅａｓ as a function of the amplitude of the read pulse. ｍｅａｓ is calculated as follows: ｍｅａｓ = | b ｅ ｏｕｔ -b ｇ ｏｕｔ | / 2 where b ｅ ｏｕｔ and b ｇ ｏｕｔ are the complex amplitudes of the readout signals in the excited state |e〉 and the ground state |g〉, respectively (where |b ｏｕｔ | ２ (Normalized so that is equal to the photon flux.) These complex amplitudes were measured using a 2 microsecond rectangular pulse. The results are shown in Figure 17.

[0060] As shown in FIG. 16, around the read pulse, Γ ｍｅａｓ (i.e., the difference in amplitude of the readout signal between the excited state |e〉 and the ground state |g〉 |b ｅ ｏｕｔ -b ｇ ｏｕｔ |) becomes larger. This is thought to be due to the fact that the two signals are on different branches. This improves the measurement rate by approximately 9 times compared to a device using a linear filter with equivalent noise immunity.

[0061] The present invention has been described above based on the embodiments. These embodiments are merely examples, and it will be understood by those skilled in the art that various modifications are possible in the combination of the respective components and treatment processes, and that such modifications are also within the scope of the present invention.

[0062] Any combination of the above-described embodiments and modifications is also useful as an embodiment of the present invention. A new embodiment resulting from the combination has the combined effects of each of the combined embodiments and modifications.

[0063] The present invention can be used in quantum devices and quantum computers.

[0064] 10. Quantum device, 11. Qubit, 12. Readout resonator, 13. Readout waveguide, 14. Nonlinear filter, 15. Filter qubit, 20. Transmon nonlinear filter, 21. Capacitor, 22. Josephson junction, 30. Quantum device, 31. Data qubit, 32. Readout resonator, 33. Readout waveguide, 34. Nonlinear filter, 35. Capacitor, 36. Capacitor, 37. Capacitor, 40. Quantum device, 41. Data qubit, 42. Readout resonator, 43. Readout waveguide, 44. Nonlinear filter, 45. Capacitor, 46. Capacitor, 47. Inductor, 100. System for distributed readout, 110. Quantum device, 101: quantum bit; 102: readout resonator; 103: readout waveguide; 104: linear filter.

Claims

1. A quantum device comprising: a data quantum bit; a readout resonator coupled to the data quantum bit; and a nonlinear filter inserted between the readout resonator and a readout waveguide, wherein the nonlinear filter has different transmission characteristics depending on the amplitude of a readout pulse input to the readout waveguide.

2. The quantum device according to claim 1, wherein said nonlinear filter has high transparency to input signals with small amplitudes and low transparency to signals with large amplitudes.

3. The linewidth of the coupling between the readout resonator and the readout waveguide via a nonlinear filter is defined as κ ｅｆｆ , the dispersion shift of the readout resonator due to the data qubit is χ, the nonlinear filter has a dispersion shift of κ when there is no readout of the data qubit. ｅｆｆ >>χ, during reading κ ｅｆｆ 3. The quantum device according to claim 2, characterized in that it has a transmission characteristic such that:

4. The quantum device according to claim 3, wherein the nonlinear filter is constructed using a superconducting quantum bit.

5. Set the center frequency of the nonlinear filter to ω ｆ , the inharmonicity of the nonlinear filter is α ｆ , the resonant frequency of the readout resonator is ω ｒ When the coupling strength between the readout resonator and the nonlinear filter is g and the line width of the coupling between the nonlinear filter and the readout waveguide is κ, the nonlinear filter satisfies the following condition: The quantum device according to claim 4, wherein 6. The quantum device according to claim 5, wherein the superconducting quantum bit is composed of a transmon in which a Josephson junction and a capacitor are coupled in parallel.

7. The quantum device according to claim 6, wherein said nonlinear filter and said readout waveguide are capacitively coupled.

8. The quantum device according to claim 6, wherein said nonlinear filter and said readout waveguide are inductively coupled.

9. A quantum computer comprising the quantum device according to any one of claims 1 to 8.

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