Quantum gate device, superconducting quantum gate device, quantum computer, and quantum gate operating method
Patent Information
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- RIKEN CO LTD
- Filing Date
- 2025-11-26
- Publication Date
- 2026-06-04
Smart Images
Figure JP2025041212_04062026_PF_FP_ABST
Abstract
Description
Quantum gate device, superconducting quantum gate device, quantum computer, and quantum gate operation method
[0001] This disclosure relates to a quantum gate device, a superconducting quantum gate device, a quantum computer, and a quantum gate manipulation method.
[0002] In superconducting quantum computers currently under development, the mainstream approach is to use transmons, which are Josephson junctions with capacitances connected in parallel, as qubits. Transmons possess high performance among superconducting qubits due to their simple circuitry and excellent phase and charge noise immunity. For these reasons, transmons are considered a promising basic element for building superconducting quantum computers.
[0003] Incidentally, one of the essential elements for performing calculations using a quantum computer is an operation that spans two qubits (hereinafter referred to as a "two-qubit gate"). When transmons are used as qubits, there are two main ways to execute a two-qubit gate.
[0004] One method involves modulating the frequency of a transmon with an external magnetic field to control the frequency difference (i.e., detuning) between adjacent transmons, thereby executing a two-qubit gate (hereinafter, this method will be referred to as the "frequency-tunable method").
[0005] Another method involves fixing the frequency of the transmon and applying an external microwave pulse to induce a parametric interaction between adjacent transmons, originating from the nonlinearity of the Josephson junction, thereby executing a two-qubit gate (hereinafter, this method will be referred to as the "fixed frequency method").
[0006] International Publication No. 2014 / 058208
[0007] Chow, Jerry M., et al. "A Simple all-microwave entangling gate for fixed-frequency superconducting qubits." Physical Review Letters 107.8 (2011): 080502.Kandala, Abhinav, et al. "Demonstration of a high-fidelity cnot gate for fixed-frequency transmons with engineered zz suppression." Physical Review Letters 127.13 (2021): 130501.Krinner, Sebastian, et al. "Demonstration of an all-microwave controlled-phase gate between far-detuned qubits." Physical Review Applied 14.4 (2020): 044039.Ficheux, Quentin, et al. "Fast logic with slow qubits: microwave-activated controlled-Z gate on low-frequency fluxoniums." Physical Review X 11.2 (2021): 021026.Shirai, Shotaro, et al. "All-microwave manipulation of superconducting qubits with a fixed-frequency transmon coupler." Physical Review Letters 130.26 (2023): 260601.
[0008] The variable frequency method allows for the execution of high-speed 2-qubit gates, such as those with execution times of 100 ns or less. Furthermore, because the transmon frequency is variable, the interaction between adjacent transmons can be made negligibly small when a 2-qubit gate is not being executed. This prevents errors from propagating between transmons or the reduction in computational accuracy caused by unnecessary interactions (residual interactions) during 1-qubit gate execution or idle periods.
[0009] On the other hand, the variable frequency method has several drawbacks, such as requiring additional magnetic field wiring to modulate the frequency by applying a magnetic field, being susceptible to magnetic field noise, and having a shortened qubit coherence time.
[0010] In contrast, the fixed-frequency method has the advantages of not requiring additional magnetic field wiring, thus simplifying the wiring and allowing for a more compact circuit, as well as having low sensitivity to magnetic field noise and long coherence.
[0011] However, in the fixed-frequency method, it is difficult to control the magnitude of the interaction because the frequency is fixed. In other words, the transmon is always coupled with surrounding transmons by residual interaction. This causes a decrease in the precision of the two-qubit gate. In addition, the execution time of the two-qubit gate is currently limited to around 100-500 ns, which presents a challenge in terms of speed compared to the variable-frequency method.
[0012] In fixed-frequency systems, achieving high gate speeds while suppressing residual interaction requires high fabrication precision and strong coupling between transmons. However, generally, increasing the coupling between transmons also increases residual interaction. As a result, even with high gate speeds, the effects of residual interaction become significant. To prevent this, one idea is to fabricate devices in a region (stradiling region) where the frequency difference between adjacent transmons is smaller than the anharmonicness of one transmon. However, integrating this method requires higher fabrication precision than current Josephson junctions. Therefore, a challenge arises in terms of device yield.
[0013] In light of the above, this disclosure focuses on fixed-frequency systems, aiming to solve their problems while leveraging their advantages.
[0014] Now, there are three main types of fixed-frequency systems.
[0015] The first method is called a cross-response gate (see, for example, Non-Patent Documents 1 and 2). This method executes a CNOT gate by applying a microwave pulse at the frequency of the other transmon coupled to the target transmon. However, in order to improve the gate speed while suppressing residual interaction, it is necessary to fabricate the device in the straddlering region, which requires high fabrication precision. Cross-response gates can also be executed outside the straddlering region. However, the residual interaction here is proportional to the square of the coupling between transmons, and the speed of a cross-response gate outside the straddlering region is proportional to the coupling. Therefore, there is a problem that the residual interaction becomes larger than the increase in gate speed.
[0016] The second method is called the fg-ge transition between coupled transmons. This uses a parametric transition caused by a second-order perturbation (see, for example, Non-Patent Documents 3 and 4). The state in computational space undergoes a Rabi oscillation with an auxiliary level outside of computational space via the parametric transition. After one period of this Rabi oscillation, the state in computational space acquires a geometric phase π. This realizes a controlled phase gate. This method can operate both inside and outside the Stradling domain. However, similar to the cross-resonance gate, the gate speed is proportional to the coupling between transmons, so there is a trade-off between increasing the gate speed and decreasing residual interaction.
[0017] Furthermore, there are reported examples of this method using fraxonium, a type of superconducting qubit. Fraxonium has greater nonlinearity than transmons. Therefore, even if the coupling constant is increased, the residual interaction does not tend to increase significantly. This makes it possible to achieve both high-speed two-qubit gates and small residual interactions. However, it requires additional control wiring to apply a magnetic field, which makes it more difficult to fabricate compared to transmons.
[0018] The third method is called the CAS gate (see, for example, Patent Document 1 and Non-Patent Document 5). Like the second method (fg-ge transition), this also uses a parametric transition. Here, an additional frequency-fixed transmon (coupler transmon) for coupling is introduced between the two transmons (data transmons) that are the targets of the two-qubit gate. Then the gate velocity is determined by the coupling of the coupler transmon and the data transmon. As a result, the residual interaction is determined by the coupling between the data transmons. This eliminates the trade-off between gate velocity and residual interaction. However, this parametric transition is caused by a third-order perturbation, which is a higher order than that of the Cross-Resonance gate. Therefore, the Rabi oscillation itself is slow, and although a gate velocity of around 200-300 ns can be expected, there is a problem that it is difficult to increase the speed further due to design constraints.
[0019] This invention was made in view of these circumstances, and its purpose is to increase the gate speed while taking advantage of the benefits of the fixed-frequency method, such as the compactness of the circuit and the long coherence.
[0020] In order to solve the above problems, a quantum gate device according to an aspect of the present invention includes a qubit substrate unit equipped with at least two data qubits, namely a first data qubit and a second data qubit, and a coupler qubit disposed between the first data qubit and the second data qubit, and a drive microwave irradiation unit that irradiates the coupler qubit with a drive microwave that causes an fg-ge transition between the first data qubit and the coupler qubit. The first data qubit, the second data qubit, and the coupler qubit each have a ground state, a first excited state with energy higher than the ground state, and a second excited state with energy higher than the first excited state. When the second data qubit is in the ground state, the transition frequency of the fg-ge transition between the first data qubit and the coupler qubit is ω ｆｇｇｅ ｇ Let it be, and when the second data qubit is in the first excited state, the transition frequency of the fg-ge transition between the first data qubit and the coupler qubit is ω ｆｇｇｅ ｅ When set as, the frequency ω of the drive microwave ｄ is, ω ｆｇｇｅ ｇ And ω ｆｇｇｅ ｅ Takes a value between.
[0021] In a certain embodiment, when the second data qubit is in the ground state, the control phase obtained by the Rabi oscillation for one period of the fg-ge transition between the first data qubit and the coupler qubit is Φ ｅｇｇ Let it be, and when the second data qubit is in the first excited state, the control phase obtained by the Rabi oscillation for one period of the fg-ge transition between the first data qubit and the coupler qubit is Φ ｅｅｇ When set as, Φ ｅｇｇ +Φ ｅｅｇ May be = ±π.
[0022] The quantum gate device according to a certain embodiment may realize a control phase gate.
[0023] In one embodiment, the Rabi frequency of the fg-ge transition between the first data qubit and the coupler qubit when the second data qubit is in the ground state is Ω ｆｇｇｅ ｇ Assuming that the Rabi frequency of the fg-ge transition between the first data qubit and the coupler qubit when the second data qubit is in the first excited state is Ω ｆｇｇｅ ｅ To that end, Ω ｆｇｇｅ ｇ = Ω ｆｇｇｅ ｅ That's fine.
[0024] In one embodiment, the frequency of the drive microwave is ω ｄ = (ω ｆｇｇｅ ｇ +ω ｆｇｇｅ ｅ ) / 2 is also acceptable.
[0025] In one embodiment, the energy of the first excited state of the first data qubit when the second data qubit is in the ground state may be higher than the energy of the first excited state of the second data qubit when the first data qubit is in the ground state.
[0026] In one embodiment, the energy of the first excited state of the first data qubit when the second data qubit is in the ground state may be lower than the energy of the first excited state of the second data qubit when the first data qubit is in the ground state.
[0027] In one embodiment, let r be a positive real number, and r = Ω ｆｇｇｅ ｇ / Ω ｆｇｇｅ ｅ When this is the case, the frequency of the drive microwave is ω ｄ is, ω ｆｇｇｅ ｇ -ω ｆｇｇｅ ｅ =Δ, δ=ω ｆｇｇｅ ｇ -ω ｄ , calculated from Using It may be defined as follows.
[0028] In one embodiment, the first data qubit, the second data qubit, and the coupler qubit may be superconducting qubits.
[0029] In one embodiment, the superconducting qubit may be a transmon.
[0030] Another aspect of the present invention is a superconducting quantum gate device. This superconducting quantum gate device comprises the aforementioned quantum gate device and a refrigerator for cooling and operating the qubit substrate.
[0031] Yet another aspect of the present invention is a quantum computer. This quantum computer comprises the aforementioned quantum gate device and a control unit for controlling the quantum gate device.
[0032] A further aspect of the present invention is a quantum gate operation method. This method is a quantum gate operation method for a qubit system comprising at least two data qubits, namely a first data qubit and a second data qubit, and a coupler qubit positioned between the first data qubit and the second data qubit. This method includes the step of irradiating the coupler qubit with a drive microwave that induces an fg-ge transition between the first data qubit and the coupler qubit. The first data qubit, the second data qubit, and the coupler qubit each have a ground state, a first excited state with higher energy than the ground state, and a second excited state with higher energy than the first excited state. The transition frequency of the fg-ge transition between the first data qubit and the coupler qubit when the second data qubit is in the ground state is ω ｆｇｇｅ ｇ Let ω be the transition frequency of the fg-ge transition between the first data qubit and the coupler qubit when the second data qubit is in the first excited state. ｆｇｇｅ ｅ In this case, the frequency of the drive microwave is ω ｄ is, ω ｆｇｇｅ g and ω ｆｇｇｅ It takes a value between e and the specified value.
[0033] Furthermore, any combination of the above components, as well as conversions of the expressions of this disclosure between methods, apparatus, systems, recording media, computer programs, etc., are also valid forms of this disclosure.
[0034] According to the present invention, it is possible to increase the gate speed while taking advantage of the benefits of the fixed-frequency method, such as the compactness of the circuit and the long coherence.
[0035] This is a functional block diagram of a quantum gate device according to the first embodiment. This is an energy level diagram of the system in Figure 1. This is a schematic diagram showing what happens when a drive microwave is irradiated onto a coupler qubit. This is a schematic diagram of the geometric phase obtained by the fg-ge transition caused by the drive microwave irradiation. This is a projection of Figure 4 onto the xy plane. This is a schematic diagram of a controlled phase gate realized by the quantum gate device of this embodiment. This is a functional block diagram of a superconducting quantum gate device according to the second embodiment. This is a functional block diagram of a quantum computer according to the third embodiment. This is a flowchart showing the processing of a quantum gate operation method according to the fourth embodiment. This is a schematic diagram showing the time change of the pulse intensity of the microwave drive pulse used in the experiment. This is a graph showing the extracted resonance frequency. This is a graph showing the frequency difference between subspaces. This is a graph showing the relationship between the Rabi frequency of the fg-ge transition and the intensity of the drive pulse. This is a photograph showing the Rabi oscillation of each subspace under the above crossover conditions. |e> at the above drive pulse frequency ２ and |f> ｃ This is a graph showing the population. This is a schematic diagram showing the gate sequence (upper panel) and the pulse sequence of the CZ gate (lower panel) in this experiment. This is a graph showing the sequence fidelity obtained from the SRB and IRB. This is a graph showing the population in the computational space while the SRB and IRB are being executed. This is a graph showing the error rate of the CZ gate obtained from measurements over approximately one day. This is a graph showing the leak rate of the CZ gate obtained from measurements over approximately one day.
[0036] [First Embodiment] Figure 1 is a functional block diagram of a quantum gate device 1 according to the first embodiment. The quantum gate device 1 comprises a qubit substrate section 10 and a drive microwave irradiation section 20.
[0037] The qubit substrate 10 is equipped with a first data qubit 11, a second data qubit 12, and a coupler qubit 13. The coupler qubit 13 is positioned between the first data qubit 11 and the second data qubit 12. The first data qubit 11 and the second data qubit 12 are capacitance-coupled to each other via a capacitor 101. The coupling strength of this capacitance coupling is set to g １２ The first data qubit 11 and the coupler qubit 13 are capacitance-coupled to each other via the capacitor 102. The coupling strength of this capacitance coupling is given by g. １３ The second data qubit 12 and the coupler qubit 13 are capacitance-coupled to each other via the capacitor 103. The coupling strength of this capacitance coupling is given by g. ２３ In this configuration, the first data qubit 11 is formed by connecting a Josephson element 1001 and a capacitor 1101 in parallel to form a resonant circuit. The second data qubit 12 is formed by connecting a Josephson element 1002 and a capacitor 1102 in parallel to form a resonant circuit. The coupler qubit 13 is formed by connecting a Josephson element 1003 and a capacitor 1103 in parallel to form a resonant circuit. In other words, in the example shown in Figure 1, the first data qubit 11, the second data qubit 12, and the coupler qubit 13 are all composed of frequency-fixed transmon qubits.
[0038] The first data qubit 11, the second data qubit 12, and the coupler qubit 13 each have a ground state, a first excited state with higher energy than the ground state, and a second excited state with higher energy than the first excited state. Hereinafter, the ground state will be denoted as g, the first excited state as e, and the second excited state as f. The state when a qubit is in the ground state g will be denoted as |g>, the state when it is in the first excited state e as |e>, and the state when it is in the second excited state as |f>. Furthermore, in the case of a three-quantum system as shown in Figure 1, the first data qubit is Q １ , the second data qubit is Q ２ , coupler qubit is Q ｃ The state when in this state is | Q １ Q ２ Q ｃ This is represented as >. For example, |g, e, f> means that the first data qubit is in the ground state g, the second data qubit is in the first excited state e, and the coupler qubit is in the second excited state f.
[0039] The drive microwave irradiation unit 20 irradiates a drive microwave that causes an fg-ge transition between the first data qubit 11 and the coupler qubit 13. The frequency of this drive microwave is ω ｄ Let ω be the transition frequency of the fg-ge transition between the first data qubit 11 and the coupler qubit 13 when the second data qubit 12 is in the ground state g. ｆｇｇｅ ｇ When the second data qubit 12 is in the first excited state e, the transition frequency of the fg-ge transition between the first data qubit 11 and the coupler qubit 13 is ω. ｆｇｇｅ ｅ When that happens, ω ｄ is, ω ｆｇｇｅ ｅ and ω ｆｇｇｅ ｇ It takes a value between ω. ｆｇｇｅ ｅ <ω ｄ <ω ｆｇｇｅ ｇ The fg-ge transition will be explained in detail below.
[0040] Consider a two-qubit system consisting of a first qubit and a second qubit. In this case, the transition between the state |g,e> where the first qubit is in the ground state g and the second qubit is in the first excited state e, and the state |f,g> where the first qubit is in the second excited state f and the second qubit is in the ground state g, is called an fg-ge transition (needless to say, the transition between the state |e,g> where the first qubit is in the first excited state e and the second qubit is in the ground state g, and the state |g,f> where the first qubit is in the ground state g and the second qubit is in the second excited state f, is also an fg-ge transition). In general, the transition frequency of an fg-ge transition is ω ｆｇｇｅ This is expressed as follows, and the transition frequency of the fg-ge transition is ω ｆｇｇｅ This is expressed as Ω, and the Rabi frequency of the fg-ge transition is Ω ｆｇｇｅ It is represented as follows.
[0041] Figure 2 is the energy level diagram of the system in Figure 1. The bracket notation |> indicates the states of the first data qubit, the second data qubit, and the coupler qubit, respectively, from left to right, as described above. When the second data qubit 12 is in the ground state g, the fg-ge transition between the first data qubit 11 and the coupler qubit 13 is given by |e, g, g> ⇔ |g, g, f>. The transition frequency at this time is ω ｆｇｇｅ ｇ This is expressed as follows. When the second data qubit 12 is in the first excited state e, the transition frequency of the fg-ge transition between the first data qubit 11 and the coupler qubit 13 is given by |e, e, g> ⇔ |g, e, f>. The transition frequency at this time is given by ω ｆｇｇｅ ｅ This is how it is expressed.
[0042] Under the circumstances described above, when the drive microwave is irradiated onto the coupler qubit 13, Rabi oscillations occur between the states |e, g, g> and |g, g, f>, or between the states |e, e, g> and |g, e, f>.
[0043] With respect to the first data qubit 11 and coupler qubit 13, which are an fg-ge transition pair, if there is a coupling between the second data qubit 12 and the coupler qubit 13 (coupling constant g ２３), if not, regardless of the state of the second data qubit 12, ω ｆｇｇｅ ｇ = ω ｆｇｇｅ ｅ holds. However, in reality, due to the coupling, ω ｆｇｇｅ ｇ ≠ω ｆｇｇｅ ｅ . In reality, since the difference between ω ｆｇｇｅ ｇ and ω ｆｇｇｅ ｅ is small, it can also be written as ω ｆｇｇｅ ｇ ≒ω ｆｇｇｅ ｅ . Let the difference between ω ｆｇｇｅ ｇ and ω ｆｇｇｅ ｅ be represented by Δ. That is, Δ = ω ｆｇｇｅ ｇ −ω ｆｇｇｅ ｅ . This Δ is calculated as follows using perturbation theory. Here, each parameter is as follows. Δ ３２ = ω ３ −ω ２ ω ２ : The frequency ω of the second data qubit ３ : The frequency α of the coupler qubit ２ : The anharmonicity α of the second data qubit ３ : The anharmonicity of the coupler qubit
[0044] In this situation, the drive microwave irradiation unit 20 irradiates the coupler qubit 13 with a drive microwave whose frequency ω ｄ takes a value between ω ｆｇｇｅ ｇ and ω ｆｇｇｅ ｅ . That is, ω ｆｇｇｅ ｅ <ω ｄ <ω ｆｇｇｅ ｇ . When the second data qubit 12 is in the ground state g, the transition frequency of the fg - ge transition between the first data qubit 11 and the coupler qubit 13 is ω ｆｇｇｅ ｇAnd the frequency of the drive microwave ω ｄ As the difference, we define the detuning δ as follows: δ = ω ｆｇｇｅ ｇ -ω ｄ Figure 3 schematically shows what happens when such drive microwaves are irradiated onto the coupler qubit 13.
[0045] Figure 4 is a schematic diagram of the geometric phase obtained by the fg-ge transition caused by the drive microwave irradiation described above. In this example, ω ｄ = (ω ｆｇｇｅ ｇ +ω ｆｇｇｅ ｅ Let ) / 2. That is, the frequency of the drive microwave ω ｄ is, ω ｆｇｇｅ ｅ and ω ｆｇｇｅ ｇ It is assumed to take the value exactly in the middle between [the specified values].
[0046] The left diagram of Figure 4 shows the Bloch sphere of the subspace in the fg-ge transition between |e,g,g> and |g,g,f>. When the fg-ge transition is driven starting from the initial state |e,g,g> belonging to the computation space, the two-qubit system consisting of the first data qubit 11 and the coupler qubit 13 evolves in time counterclockwise (negative direction) along the circumference shown by the solid line on the surface of the Bloch sphere. As a result, this system acquires a geometric phase of -π / 2 after completing one revolution around the Bloch sphere (i.e., after one period of Rabi oscillation in the fg-ge subspace). That is, Φ ｅｇ = -π / 2.
[0047] The right-hand figure of Figure 4 shows the Bloch sphere of the subspace in the fg-ge transition between |e,e,g> and |g,e,f>. When the fg-ge transition is driven starting from the initial state |e,e,g> belonging to the computation space, the two-qubit system consisting of the first data qubit 11 and the coupler qubit 13 evolves in time clockwise (positive direction) along the circumference shown by the dotted line on the surface of the Bloch sphere. As a result, this system acquires a geometric phase π / 2 after completing one revolution around the Bloch sphere (i.e., after one period of Rabi oscillation in the fg-ge subspace). That is, Φｅｅ = π / 2.
[0048] The geometric phases obtained by the states |e, g, g> and |e, e, g> in computational space through one period of Rabi oscillation are as follows: A control phase gate for two qubits is generally a diagonal matrix U(Φ ＣＰ ) using This can be written as follows. At this time, the control phase Φ ＣＰ and the phase φ assigned to each state ｉｊ The following relationship holds between i and j ∈ {gg, ee, ge, eg}: Φ ＣＰ =Φ ｇｇ +Φ ｅｅ -Φ ｇｅ -Φ ｅｇ To realize a controlled phase gate, Φ ＣＰ = ±π, that is, Φ ＣＰ = π or Φ ＣＰ It should be equal to -π.
[0049] Figure 5 is a projection of Figure 4 onto the xy-plane. As shown in this figure, the direction of the path along the Bloch sphere reverses depending on the positive or negative sign of detuning from the resonance condition. At this time, the control phase Φ ＣＰ As mentioned above, Φ ＣＰ =Φ ｇｇ +Φ ｅｅ -Φ ｇｅ -Φ ｅｇ Therefore, Φ ｇｇ = 0 Φ ｅｅ = π / 2 Φ ｇｅ = -π / 2 Φ ｅｇ Substituting = 0, we get Φ ＣＰ As we see that = π, we can realize a controlled phase gate. In this way, the two fg-ge transitions traverse the Bloch sphere in opposite directions depending on the positive and negative signs of detuning, causing a "constructive interference" of the phase. The quantum gate device of this embodiment realizes a controlled phase gate by utilizing this phenomenon.
[0050] As mentioned above, in order to realize a controlled phase gate, Φ ＣＰIt is sufficient that the value is ±π. In this embodiment, only states |e, g, g> and states |e, e, g> acquire phase. Therefore, the conditions for realizing a controlled phase gate are: Here, Ω ｇ and Ω ｅ These are, It can be written as Ω. ｆｇｇｅ ｇ , Ω ｆｇｇｅ ｅ Regarding That is the case.
[0051] Figure 6 schematically shows a controlled phase gate realized by the quantum gate device of this embodiment.
[0052] Regardless of whether the initial state was |e, g, g> or |e, e, g>, it is desirable that the state returns to computational space after one period of Rabi oscillation. Otherwise, a state leak error occurs, reducing gate fidelity. The condition for minimizing this leak error is that the following relationship holds.
[0053] The Rabi frequency of the fg-ge transition in each subspace when driven by resonance is ideally Ω ｆｇｇｅ ｇ = Ω ｆｇｇｅ ｅ This is because, under certain conditions, ω ｄ = (ω ｆｇｇｅ ｇ +ω ｆｇｇｅ ｅ This can be achieved by setting ) / 2.
[0054] However, in reality, due to interactions with other nearby levels, Ω ｆｇｇｅ ｇ and Omega ｆｇｇｅ ｅ A difference arises between these two. Therefore, to evaluate this difference, we use a positive real number r and write r = Ω ｆｇｇｅ ｇ / Ω ｆｇｇｅ ｅThis is expressed as follows. r is a value determined by the fabricated device and can be obtained experimentally. Needless to say, r=1 is the ideal case, in which case, ω ｄ = (ω ｆｇｇｅ ｇ +ω ｆｇｇｅ ｅ ) / 2 is achieved. However, in actual devices, r does not necessarily equal 1. Therefore, as follows, ω ｆｇｇｅ ｇ By appropriately adjusting the detuning of the drive frequency, a control phase gate with minimized leakage error can be realized.
[0055] First, ω ｆｇｇｅ ｇ -ω ｆｇｇｅ ｅ =Δ δ=ω ｆｇｇｅ ｇ -ω ｄ Let δ be ω ｆｇｇｅ ｇ This is the detuning of the drive frequency from the original frequency, and Δ is the dispersion shift of the fgge transition. At this time, δ / Δ is calculated using the following equation, where r is an experimentally obtained value. Based on the k calculated in this way, (Δ / 2) * (1 - 2k) = (ω ｆｇｇｅ ｇ +ω ｆｇｇｅ ｅ By adding this to ) / 2, the microwave drive frequency required to realize a controlled phase gate while minimizing leakage error can be determined. That is, when r≈1, That is the case.
[0056] According to this embodiment, Ω ｆｇｇｅ ｇ and Omega ｆｇｇｅ ｅ Even if they do not exactly match, the system can return to the computational space with high accuracy after the fgge transition has occurred, starting from the initial state. Also, the gate velocity at this time is the condition realized for the controlled phase gate to hold, and twist, It can be written as follows.
[0057] In the above example, an fg-ge transition was used between the first data qubit 11 and the coupler qubit 13. However, instead of the fg-ge transition between the first data qubit 11 and the coupler qubit 13, an fg-ge transition between the second data qubit 112 and the coupler qubit 13 may be used. In this case, the transition frequency of the fg-ge transition between the second data qubit 12 and the coupler qubit 13 will vary depending on the state of the first data qubit (i.e., whether the first data qubit is in the ground state or the first excited state).
[0058] In the example above, as shown in Figure 2, the energy of the first excited state e of the first data qubit 11 when the second data qubit 12 is in the ground state g (i.e., the energy when the state |e, g, g> is defined as E) is the energy of the first excited state e of the first data qubit 11. ｅｇｇ (represented as E) is the energy of the first excited state e of the second data qubit 12 when the first data qubit 11 is in the ground state g (i.e., the energy when the states |g, e, g> are equal, let E be the energy of the first excited state e of the second data qubit 12). ｇｅｇ It is higher than (expressed as E). ｅｇｇ > E ｇｅｇ
[0059] However, this is not limited to this, and the energy (E) of the first excited state e of the first data qubit 11 when the second data qubit 12 is in the ground state g. ｅｇｇ ) may be lower than the energy of the first excited state e of the second data qubit 12 when the first data qubit 11 is in the ground state e. That is, E ｅｇｇ <E ｇｅｇ That's fine.
[0060] (Comparison with prior art) Below, in order to verify the effects of this embodiment, we will compare this embodiment with two comparative examples (prior art).
[0061] (Comparative Example 1) The first comparative example is the technology disclosed in Non-Patent Document 3. Non-Patent Document 3 describes a controlled phase gate realized using an fg-ge transition between two data qubits. Here, an fg-ge transition (a transition between |g,e> and |f,g>) is induced by irradiating one of two capacitance-coupled qubits (each qubit having a ground state, a first excited state, and a second excited state) with a drive microwave. At this time, after one period of Rabi oscillation in the fg-ge subspace (i.e., after the two quantum states have just completed one revolution on the surface of the Bloch sphere), the state |g,e> acquires a geometric phase π, and a controlled phase gate is realized.
[0062] The Rabi frequency Ω of the fg-ge transition at this time ｆｇｇｅ (Equivalent to the gate velocity of a controlled phase gate) is calculated using perturbation theory. This is calculated as follows: The residual interaction ξ of these two quantum systems. ＺＺ This is done by using perturbation theory. This is calculated as follows: Here, g １２ α is the coupling constant of the capacitance coupling between the first qubit and the second qubit. １ and α ２ Δ represents the anharmonics of the first and second qubits, respectively. １２ is, ω １ and ω ２ When these are the frequencies of the first qubit and the second qubit, respectively, Δ １２ = ω １ -ω ２ It is defined as follows.
[0063] As can be seen from the two equations above, both the gate velocity and the residual interaction are g １２ It is an increasing function. Therefore, the method in Non-Patent Document 3 has a trade-off in that increasing the gate speed also increases the residual interaction.
[0064] In contrast, the gate velocity Ω of this embodiment ｇａｔｅ The following applies: however, Furthermore, the residual interaction ξ of this embodimentＺＺ Using perturbation theory, this can be expressed as follows: This is calculated as follows, where g is the effective coupling constant. ｅｆｆ The following applies:
[0065] Thus, in this embodiment, the gate velocity Ω ｇａｔｅ is g １２ It does not depend on the gate speed. Therefore, in this embodiment, the effective coupling constant g is independent of the gate speed. ｅｆｆ Minimize g １２ By designing it this way, the trade-off observed in Non-Patent Document 3, where increasing the gate speed also increases the residual interaction, is eliminated.
[0066] (Comparative Example 2) As a second comparative example, the technology disclosed in Patent Document 1 will be described. Patent Document 1 describes two data qubits Q ０ Q １ And the coupler qubit Q connected between them ｃ In a configuration consisting of the above, a method for realizing a controlled phase gate is disclosed by irradiating a coupler qubit with a microwave pulse called a cross-rabbit transition drive pulse.
[0067] The gate velocity Ω obtained by the method of Comparative Example 2 ＣＡＳ The following applies: Furthermore, the residual interaction ξ of Comparative Example 2 ＺＺ The following applies:
[0068] Similar to this embodiment, the gate velocity Ω ＣＡＳ is, g ０１ (Data qubit Q ０ and data qubit Q １ It does not depend on the coupling constant between the gate and the residual interaction. Therefore, Comparative Example 2 does not have the trade-off between gate velocity and residual interaction that existed in Comparative Example 1.
[0069] On the other hand, gate velocity Ω ＣＡＳ This represents a third-order perturbation of (1 / Δ).
[0070] In contrast, the gate velocity Ω of this embodiment ｇａｔｅThis represents a first-order perturbation of (1 / Δ), which is two orders lower than that of Comparative Example 2. Therefore, according to this embodiment, a control phase gate that is fundamentally faster than that of Comparative Example 2 can be realized.
[0071] As described above, this embodiment makes it possible to realize a quantum gate device with a higher gate speed while taking advantage of the benefits of the fixed-frequency method, such as the compactness of the circuit and the long coherence.
[0072] [Second Embodiment] The technology described above is expected to be applicable to various qubits. However, it is particularly desirable that the first data qubit, the second data qubit, and the coupler qubit be superconducting qubits.
[0073] Figure 7 is a functional block diagram of a superconducting quantum gate device 2 according to a second embodiment. The superconducting quantum gate device 2 comprises the aforementioned qubit substrate section 10, which is configured using superconducting qubits, and a refrigerator 30 for cooling and operating the qubit substrate section 10.
[0074] The refrigerator 30 consists of a dilution refrigerator (cryostat), etc. The inside of the refrigerator 30 is kept at a low temperature of several K (K) to several tens of mK (millikelvin). Equipment other than the qubit substrate section 10, such as the drive microwave irradiation section 20, is placed outside the refrigerator 30.
[0075] According to this embodiment, it is possible to realize a superconducting quantum gate device with a higher gate speed while taking advantage of the benefits of the fixed-frequency method, such as the compactness of the circuit and the long coherence.
[0076] [Third Embodiment] Figure 8 is a functional block diagram of the quantum computer 3 according to the third embodiment. The quantum computer 3 comprises the superconducting quantum gate device 2 configured using superconducting qubits, and a control unit 40 that controls the superconducting quantum gate device 2. The control unit 40 performs, for example, syndrome extraction operations and logic quantum gate operations for quantum error correction processing, and is implemented by a control device or PC located outside the refrigerator 30.
[0077] According to this embodiment, it is possible to realize a quantum computer with a faster gate speed while taking advantage of the benefits of the fixed-frequency method, such as the compactness of the circuit and the long coherence.
[0078] [Fourth Embodiment] Figure 9 is a flowchart showing the processing of a quantum gate operation method according to the fourth embodiment. This method is a quantum gate operation method for a qubit system comprising at least two data qubits, namely a first data qubit and a second data qubit, and a coupler qubit positioned between the first data qubit and the second data qubit. This method includes step S1 of irradiating the coupler qubit with a drive microwave that induces an fg-ge transition between the first data qubit and the coupler qubit. The first data qubit, the second data qubit, and the coupler qubit each have a ground state, a first excited state with higher energy than the ground state, and a second excited state with higher energy than the first excited state. The transition frequency of the fg-ge transition between the first data qubit and the coupler qubit when the second data qubit is in the ground state is ω ｆｇｇｅ ｇ Let ω be the transition frequency of the fg-ge transition between the first data qubit and the coupler qubit when the second data qubit is in the first excited state. ｆｇｇｅ ｅ In this case, the frequency of the drive microwave is ω ｄ is, ω ｆｇｇｅ g and ω ｆｇｇｅ It takes a value between e and the specified value.
[0079] According to this embodiment, by using a quantum gate device, it is possible to perform quantum gate operations with a higher gate speed while taking advantage of the benefits of the fixed-frequency method, such as the compactness of the circuit and the long coherence.
[0080] As described above, the technology disclosed herein is extremely novel and industrially useful in that it realizes quantum gate operations by applying a detuning microwave drive to a coupler qubit, which causes two fg-ge transitions to traverse the Bloch sphere in opposite directions depending on the positive and negative signs of detuning, resulting in constructive phase interference.
[0081] (Verification Experiment) The inventors conducted a verification experiment to confirm the effectiveness of the above-described embodiment. The results are shown below.
[0082] This experiment demonstrates that a CZ gate (controlled Z gate) can be realized using the method described above. First, the calibration procedure for the experimental system is shown.
[0083] Figure 10 is a schematic diagram showing the time variation of the pulse intensity of the microwave drive pulse used in the experiment. This pulse has a flat top in the center at time τ and cosine edges at the rising and falling edges at time 20 ns.
[0084] In the initial state of |e, g, g> or |e, e, g>, the above microwave drive pulse is irradiated onto the coupler qubit. At this time, the frequency, amplitude, and pulse length of the microwave drive pulse are swept, and the time-domain Rabi oscillation pattern is recorded. This is then fitted to an exponentially decaying cosine curve to extract the Rabi oscillation pattern. The fg-ge transition is determined by the drive frequency that minimizes the frequency of the Rabi oscillation in each subspace.
[0085] Figure 11 shows the extracted resonance frequencies. Figure 12 shows the frequency difference between the subspaces. Figure 13 shows the relationship between the Rabi frequency of the fg-ge transition and the intensity of the drive pulse.
[0086] As mentioned above According to this, Δ(=ω ｆｇｇｅ ｇ -ω ｆｇｇｅ ｅ ) shows no dependence on the intensity of the drive pulse. However, a clear intensity dependence is observed in Figures 11 and 12. This is thought to be due to AC Stark shifts that have amplitude dependence for each subspace.
[0087] According to theory When the following conditions are met, the CZ gate is realized. The horizontal line in Figure 13 represents the frequency shift fit in Figure 12, with respect to A ｄ We substituted 0 and evaluated it. This indicates Q. The black vertical line represents Q. １ This shows the drive strength when the frequency fit of the Rabi oscillation intersects the horizontal line when |g>. At this drive strength, the frequency ratio of the Rabi oscillations between subspaces r ≈ 1.03, and Δ ｆｇｇｅ The detuning deviation δ' from / 2 is approximately 0.2 MHz. Since this deviation is small, we can ignore the subspace dependence of the Rabi oscillation frequency of the fg-ge transition and Q １ The value obtained when |g> was used as the basis for the following analysis.
[0088] Figure 14 is a photograph showing the Rabi oscillations of each subspace under this crossover condition. The white dashed line indicates that when viewed over one period of the Rabi oscillation of the fg-ge transition, |f> in the two subspaces. Ｃ This indicates the drive pulse frequency that minimizes the population simultaneously.
[0089] Figure 15 shows the |e> at these drive pulse frequencies. ２ and |f> ｃ This shows the population. From these fits, an initial estimate of the flat-top duration of the drive pulse required for implementing the CZ gate can be obtained.
[0090] Next, the inventors conducted an experiment to verify the performance of the CZ gate calibrated using the procedure described above. Figure 16 is a schematic diagram showing the SRB (Standard Randomized Benchmarking) gate sequence (upper panel) and the CZ gate pulse sequence (lower panel) in this experiment.
[0091] While the drive pulse is being irradiated, a VZ gate is applied to the two data qubits simultaneously to correct for local phase shifts. All single-qubit Clifford gates are applied to the two X π／２It is implemented using pulses and three VZ gates. A two-qubit Clifford gate contains 0 to 3 CZ gates and one-qubit Clifford gates, with an average of 1.5 CZ gates and 5 one-qubit Clifford gates per two-qubit Clifford gate. In IRB (Interleaved RB), a CZ gate is inserted after every two-qubit Clifford gate except the last one. In all benchmark measurements, |g>, |e>, and |f> are classified and the population of all 27 coupled states is calculated.
[0092] Figure 17 is a graph showing the sequence fidelity obtained from SRB and IRB. Sequence fidelity is a function Aλ that decays exponentially. ＳＲＢ／ＩＲＢ ｍ It was fitted to +B. λ ＳＲＢ／ＩＲＢ λ is the damping parameter. ＳＲＢ／ＩＲＢ From the Clifford gate error This was calculated using the formula d=2. ２ is the dimension of the computational space.
[0093] Figure 18 is a graph showing the population in the computational space while SRB and IRB are being executed. The population in the computational space is C ＳＲＢ／ＩＲＢ +D ＳＲＢ／ＩＲ ・l ＳＲＢ／ＩＲＢ ｍ It was fitted to this. From this, the leak rate It was calculated using the method described above.
[0094] Based on the above results, the error rate r of the CZ gate ＣＺ and leak rate L ＣＺ These are given as follows: r ＣＺ and leak rate L ＣＺ The total error rate e including both contributions ＣＺ It is given as follows:
[0095] Figure 19 is a graph showing the error rate of the CZ gate obtained from measurements over approximately one day. Figure 20 is a graph showing the leak rate of the CZ gate obtained from measurements over approximately one day.
[0096] The fidelity of the CZ gate, as determined from the experimental data, is F ＣＺ = 1 - e ＣＺ This results in 99.7(1)%. From this result, it has been experimentally verified that the CZ gate can be realized with high fidelity in this embodiment.
[0097] The present invention has been described based on embodiments. These embodiments are illustrative, and it will be understood by those skilled in the art that various modifications are possible in combinations of their components and processing processes, and that such modifications also fall within the scope of the present invention.
[0098] The first data qubit, the second data qubit, and the coupler qubit are not limited to superconducting qubits, but may be any suitable qubit, such as a quantum dot or an ion trap.
[0099] This modified version allows for greater flexibility in configuration.
[0100] Any combination of the embodiments and modifications described above is also useful as an embodiment of the present invention. The new embodiments resulting from these combinations possess the combined effects of each of the embodiments and modifications that are combined.
[0101] The embodiments and modifications have been described above. In understanding the technical concept abstracted from the embodiments and modifications, the technical concept should not be interpreted as being limited to the content of the embodiments and modifications. The embodiments and modifications described above are merely examples, and many design changes such as changes, additions, and deletions of components are possible. In the embodiments, the content in which such design changes are possible is emphasized with the notation "embodiment." However, design changes are also permitted in content without such notation.
[0102] This disclosure relates to a quantum gate device, a superconducting quantum gate device, a quantum computer, and a quantum gate manipulation method.
[0103] 1. Quantum gate device. 2. Superconducting quantum gate device. 3. Quantum computer. 10. Qubit substrate section. 11. First data qubit. 12. Second data qubit. 13. Coupler qubit. 20. Drive microwave irradiation section. 30. Refrigerator. 40. Control section. 101. Capacitor. 102. Capacitor. 103. Capacitor. 1001. Josephson element. 1101. Capacitor. 1002. Josephson element. 1102. Capacitor. 1003. Josephson element. 1103. Capacitor. S1. Step of irradiating the coupler qubit with an fg-ge transition induced microwave drive pulse.
Claims
1. A qubit substrate unit including at least two data qubits, namely a first data qubit and a second data qubit, and a coupler qubit disposed between the first data qubit and the second data qubit, and a drive microwave irradiation unit that irradiates the coupler qubit with a drive microwave that causes an fg-ge transition between the first data qubit and the coupler qubit. The first data qubit, the second data qubit, and the coupler qubit each have a ground state, a first excited state with energy higher than the ground state, and a second excited state with energy higher than the first excited state. When the second data qubit is in the ground state, the transition frequency of the fg-ge transition between the first data qubit and the coupler qubit is ω ｆｇｇｅ ｇ is denoted as ω, and when the second data qubit is in the first excited state, the transition frequency of the fg-ge transition between the first data qubit and the coupler qubit is ω ｆｇｇｅ ｅ is denoted as ω. When the frequency of the drive microwave is ω ｄ is ω ｆｇｇｅ ｅ and ω ｆｇｇｅ ｇ A quantum gate device characterized by taking a value between them.
2. The control phase obtained by the Rabi oscillation for one period of the fg-ge transition between the first data qubit and the coupler qubit when the second data qubit is in the ground state is Φ ｅｇｇ The control phase obtained by the Rabi oscillation for one period of the fg-ge transition between the first data qubit and the coupler qubit when the second data qubit is in the first excited state is defined as Φ. ｅｅｇ When that happens, Φ ｅｇｇ +Φ ｅｅｇ The quantum gate device according to claim 1, characterized in that = ±π.
3. The quantum gate device according to claim 1, characterized in that it realizes a controlled phase gate.
4. The Rabi frequency of the fg-ge transition between the first data qubit and the coupler qubit when the second data qubit is in the ground state is Ω ｆｇｇｅ ｇ The Rabi frequency of the fg-ge transition between the first data qubit and the coupler qubit when the second data qubit is in the first excited state is Ω ｆｇｇｅ ｅ To that end, Ω ｆｇｇｅ ｇ = Ω ｆｇｇｅ ｅ The quantum gate device according to claim 1, characterized in that it is the same as described in claim 1.
5. The frequency ω of the drive microwave ｄ ω ｄ = (ω ｆｇｇｅ ｇ +ω ｆｇｇｅ ｅ The quantum gate device according to claim 1, characterized in that it is ) / 2.
6. The quantum gate device according to claim 1, characterized in that the energy of the first excited state of the first data qubit when the second data qubit is in the ground state is higher than the energy of the first excited state of the second data qubit when the first data qubit is in the ground state.
7. The quantum gate device according to claim 1, characterized in that the energy of the first excited state of the first data qubit when the second data qubit is in the ground state is lower than the energy of the first excited state of the second data qubit when the first data qubit is in the ground state.
8. Let r be a positive real number, then r = Ω ｆｇｇｅ ｇ / Ω ｆｇｇｅ ｅ When this is the case, the frequency ω of the drive microwave ｄ is, ω ｆｇｇｅ ｇ -ω ｆｇｇｅ ｅ =Δ, δ=ω ｆｇｇｅ ｇ -ω ｄ , calculated from Using The quantum gate device according to claim 1, characterized in that it is defined as follows.
9. The quantum gate device according to claim 1, characterized in that the first data qubit, the second data qubit, and the coupler qubit are superconducting qubits.
10. The quantum gate device according to claim 9, characterized in that the superconducting qubit is a transmon.
11. A superconducting quantum gate device comprising the quantum gate device according to claim 9, and a refrigerator for cooling and operating the qubit substrate portion.
12. A quantum computer comprising a quantum gate device as described in claim 1, and a control unit for controlling the quantum gate device.
13. A quantum gate operation method for a qubit system comprising at least two data qubits, namely a first data qubit and a second data qubit, and a coupler qubit positioned between the first data qubit and the second data qubit, the method comprising the step of irradiating the coupler qubit with a drive microwave that induces an fg-ge transition between the first data qubit and the coupler qubit, wherein the first data qubit, the second data qubit and the coupler qubit each have a ground state, a first excited state with higher energy than the ground state and a second excited state with higher energy than the first excited state, and the transition frequency of the fg-ge transition between the first data qubit and the coupler qubit when the second data qubit is in the ground state is ω ｆｇｇｅ ｇ The transition frequency of the fg-ge transition between the first data qubit and the coupler qubit when the second data qubit is in the first excited state is ω. ｆｇｇｅ ｅ When the frequency of the drive microwave is ω ｄ is, ω ｆｇｇｅ ｇ and ω ｆｇｇｅ ｅ A method characterized by taking a value between [a certain value] and [another value].