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JP6765656B2 - Quantum gate device - Google Patents
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JP6765656B2 - Quantum gate device - Google Patents

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JP6765656B2
JP6765656B2 JP2017075138A JP2017075138A JP6765656B2 JP 6765656 B2 JP6765656 B2 JP 6765656B2 JP 2017075138 A JP2017075138 A JP 2017075138A JP 2017075138 A JP2017075138 A JP 2017075138A JP 6765656 B2 JP6765656 B2 JP 6765656B2
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徳永 裕己
裕己 徳永
泰信 中村
泰信 中村
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Description

この発明は、量子計算技術に関する。 The present invention relates to quantum computing technology.

近年、超伝導回路により構成された人工的な原子構造を量子ビットとして用いることにより量子情報処理を行うことが検討されている。これまで超伝導量子ビットと伝搬するマイクロ波光子間の量子ゲート装置が非特許文献1で提案されている。 In recent years, it has been studied to perform quantum information processing by using an artificial atomic structure composed of a superconducting circuit as a qubit. So far, Non-Patent Document 1 has proposed a quantum gate device between a superconducting qubit and a propagating microwave photon.

非特許文献1には、ラムダ型の3準位系を構成することによりマイクロ波光子・超伝導量子ビット間のSWAPゲートを行う方法が示されている。 Non-Patent Document 1 discloses a method of performing SWAP gate between microwave photons and superconducting qubits by constructing a lambda type three-level system.

Koshino, K., Inomata, K., Yamamoto, T., & Nakamura, Y. "Implementation of an Impedance-Matched Λ System by Dressed-State Engineering", Physical Review Letters, 111, 153601, (2013).Koshino, K., Inomata, K., Yamamoto, T., & Nakamura, Y. "Implementation of an Impedance-Matched Λ System by Dressed-State Engineering", Physical Review Letters, 111, 153601, (2013).

非特許文献1の方法ではマイクロ波光子・超伝導量子ビット間のSWAPゲートのみが可能であり、マイクロ波光子・超伝導量子ビット間でSWAPゲート以外の量子計算はできなかった。 In the method of Non-Patent Document 1, only SWAP gate between microwave photon and superconducting qubit is possible, and quantum calculation other than SWAP gate is not possible between microwave photon and superconducting qubit.

本発明は、このような問題点に鑑みてなされたものであり、その目的は、マイクロ波光子・超伝導量子ビット間でSWAPゲート以外の量子計算を行うことができる量子ゲート装置を提供することである。 The present invention has been made in view of such problems, and an object of the present invention is to provide a quantum gate device capable of performing quantum calculations other than SWAP gates between microwave photons and superconducting qubits. Is.

この発明の一態様による量子ゲート装置は、共振器に結合している超伝導量子ビットと、共振器に結合しており、マイクロ波光子が入射される第一導波路と、超伝導量子ビットに結合しており、マイクロ波ドライブ光が入射される第二導波路と、マイクロ波ドライブ光の周波数、マイクロ波ドライブ光の強度、共振器の周波数、超伝導量子ビットの周波数及び超伝導量子ビットと共振器の結合強度の少なくとも1つを制御可能な操作部と、を備えており、所望の量子ゲートに対応するように、マイクロ波ドライブ光の周波数、マイクロ波ドライブ光の強度、共振器の周波数、超伝導量子ビットの周波数及び超伝導量子ビットと共振器の結合強度の少なくとも1つの値を決定する決定部を更に含み、操作部は、決定された値となるように、マイクロ波ドライブ光の周波数、マイクロ波ドライブ光の強度、共振器の周波数、超伝導量子ビットの周波数及び超伝導量子ビットと共振器の結合強度の少なくとも1つを制御する
この発明の一態様による量子ゲート装置は、共振器に結合している超伝導量子ビットと、共振器に結合しており、マイクロ波光子が入射される第一導波路と、超伝導量子ビットに結合しており、マイクロ波ドライブ光が入射される第二導波路と、マイクロ波ドライブ光の周波数、マイクロ波ドライブ光の強度、共振器の周波数、超伝導量子ビットの周波数及び超伝導量子ビットと共振器の結合強度の少なくとも1つを制御可能な操作部と、を備えており、マイクロ波ドライブ光の周波数をω d とし、マイクロ波ドライブ光の強度をΩ d とし、共振器の周波数を - ω r とし、超伝導量子ビットの周波数を - ω a とし、χ=g 2 /( - ω r - - ω a )とし、ω r = - ω r +χ、ω a = - ω a -χとし、超伝導量子ビットと共振器の結合強度をgとし、マイクロ波ドライブ光の影響を受けた超伝導量子ビット及び共振器が構成する着衣状態の中のエネルギー準位が低い2個の着衣状態を|~1>,|~2>とし、ωをマイクロ波光子の周波数とし、ω=ω l h とし、(ω l h )=(~ω 32 ,~ω 31 )又は(~ω 42 ,~ω 41 )とし、~ω 32 =~ω 3 -~ω 2 とし、~ω 31 =~ω 3 -~ω 1 とし、~ω 42 =~ω 4 -~ω 2 とし、~ω 41 =~ω 4 -~ω 1 とし、Δω=ω h l とし、~ω 1 ,~ω 2 ,~ω 3 ,~ω 4 は式(6)-(7')により定義されるとし、量子ゲートは式(10),(11)の変換を行うとし、量子ゲートに対応する係数ξ 11 (ω),ξ 12 (ω),ξ 21 (ω),ξ 22 (ω)は式(12)-(15)で定義されるとし、κを所定の定数とし、θ t l h とし、θ l h は式(5'),(5'')により定義されるとして、

Figure 0006765656
量子ゲートに対応する係数ξ 11 (ω),ξ 12 (ω),ξ 21 (ω),ξ 22 (ω)を所与として、式(12)-(15)を満たす、マイクロ波ドライブ光の周波数ω d 、マイクロ波ドライブ光の強度Ω d 、共振器の周波数 - ω r 、超伝導量子ビットの周波数 - ω a 及び超伝導量子ビットと共振器の結合強度gの少なくとも1つの値を決定する決定部を更に含み、操作部は、決定された値となるように、マイクロ波ドライブ光の周波数ω d 、マイクロ波ドライブ光の強度Ω d 、共振器の周波数 - ω r 、超伝導量子ビットの周波数 - ω a 及び超伝導量子ビットと共振器の結合強度gの少なくとも1つを制御する。
The quantum gate device according to one aspect of the present invention has a superconducting quantum bit coupled to a resonator, a first waveguide coupled to a resonator and in which microwave photons are incident, and a superconducting quantum bit. The second waveguide on which the microwave drive light is incident and the frequency of the microwave drive light, the intensity of the microwave drive light, the frequency of the resonator, the frequency of the superconducting quantum bit and the superconducting quantum bit It is equipped with an operation unit that can control at least one of the coupling strengths of the resonator, and corresponds to the desired quantum gate, the frequency of the microwave drive light, the intensity of the microwave drive light, and the frequency of the resonator. Further includes a determination unit for determining at least one value of the frequency of the superconducting quantum bit and the coupling strength between the superconducting quantum bit and the resonator, and the operation unit is of the microwave drive light so as to have the determined value. It controls at least one of the frequency, the intensity of the microwave drive light, the frequency of the resonator, the frequency of the superconducting quantum bit, and the coupling strength of the superconducting quantum bit and the resonator .
The quantum gate device according to one aspect of the present invention has a superconducting qubit coupled to a resonator, a first waveguide coupled to a resonator and in which microwave photons are incident, and a superconducting qubit. Combined, the second waveguide on which the microwave drive light is incident, the frequency of the microwave drive light, the intensity of the microwave drive light, the frequency of the resonator, the frequency of the superconducting qubit and the superconducting qubit and at least one controllable operation of the coupling strength of the resonator comprises a, the frequency of the microwave drive light is omega d, the intensity of the microwave drive light is omega d, the frequency of the resonator - and omega r, the frequency of superconducting qubits - and ω a, χ = g 2 / a (- - ω r - ω a ), ω r = - ω r + χ, ω a = - and ω a , The coupling strength between the superconducting qubit and the resonator is g, and the two clothing states with low energy levels in the clothing state composed of the superconducting qubit and the resonator affected by the microwave drive light are defined. | ~ 1>, | ~ 2>, ω is the frequency of the microwave photon, ω = ω l , ω h , (ω l , ω h ) = (~ ω 32 , ~ ω 31 ) or (~ ω) 42, and ~ ω 41), ~ ω 32 = ~ ω 3 - and ~ ω 2, ~ ω 31 = ~ ω 3 - and ~ ω 1, ~ ω 42 = ~ ω 4 - and ~ ω 2, ~ ω 41 = ~ omega 4 - and ~ omega 1, and Δω = ω h -ω l, ~ ω 1, ~ ω 2, ~ ω 3, is ~ omega 4 (6) - as defined by (7 '), Assuming that the quantum gate performs the conversion of equations (10) and (11), the frequencies ξ 11 (ω), ξ 12 (ω), ξ 21 (ω), ξ 22 (ω) corresponding to the qubit gate are given by equation (12). )-(15), κ is a predetermined constant, θ t = θ l + θ h, and θ l , θ h are defined by equations (5'), (5''). ,
Figure 0006765656
Given the frequencies ξ 11 (ω), ξ 12 (ω), ξ 21 (ω), ξ 22 (ω) corresponding to the quantum gate , the microwave drive light satisfying equations (12)-(15). Determine at least one value of frequency ω d , microwave drive light intensity Ω d , resonator frequency - ω r , superconducting quantum bit frequency - ω a and superconducting quantum bit-resonator coupling strength g. determining portion further includes an operation unit, as a determined value, the frequency omega d of the microwave drive light intensity omega d of the microwave drive light, the resonator frequency - omega r, superconducting qubits It controls at least one of the frequency - ω a and the coupling strength g between the superconducting quantum bit and the resonator.

SWAPゲート以外の量子計算を行うことができる。 Quantum calculations other than SWAP gates can be performed.

量子ゲート装置の例を説明するためのブロック図。A block diagram for explaining an example of a quantum gate device.

[実施形態]
以下、図面を参照して、この発明の一実施形態の量子ゲート装置について説明する。
[Embodiment]
Hereinafter, the quantum gate device according to the embodiment of the present invention will be described with reference to the drawings.

量子ゲート装置は、図1に示すように、第一導波路1、第二導波路2、共振器3、超伝導量子ビット4、操作部5、入力部6、サーキュレータ7、出力部8及び決定部9を例えば備えている。操作部5は、第一操作部51、第二操作部52、第三操作部53及び第四操作部54を例えば備えている。 As shown in FIG. 1, the quantum gate device includes a first waveguide 1, a second waveguide 2, a resonator 3, a superconducting qubit 4, an operation unit 5, an input unit 6, a circulator 7, an output unit 8, and a determination. A unit 9 is provided, for example. The operation unit 5 includes, for example, a first operation unit 51, a second operation unit 52, a third operation unit 53, and a fourth operation unit 54.

超伝導量子ビット4は、2準位系を持ち、共振器3に結合している(例えば、参考文献1参照。)。超伝導量子ビット4は、実際はさらに上の準位を有する場合も多いが、そのようなときは一番下の2準位を用いることにする。 The superconducting qubit 4 has a two-level system and is coupled to the resonator 3 (see, for example, Reference 1). In many cases, the superconducting qubit 4 actually has a higher level, but in such a case, the lowest two levels are used.

〔参考文献1〕K. Koshino, K. Inomata, Z. R. Lin, Y. Tokunaga, T. Yamamoto, Y. Nakamura, "Tunable quantum gate between a superconducting atom and a propagating microwave photon", (2016) [Reference 1] K. Koshino, K. Inomata, Z. R. Lin, Y. Tokunaga, T. Yamamoto, Y. Nakamura, "Tunable quantum gate between a superconducting atom and a propagating microwave photon", (2016)

共振器3及び超伝導量子ビット4は、それぞれ第一導波路1及び第二導波路2と結合している。 The resonator 3 and the superconducting qubit 4 are coupled to the first waveguide 1 and the second waveguide 2, respectively.

第一操作部51は、マイクロ波ドライブ光を出射可能である。また、第一操作部51は、出射するマイクロ波ドライブ光の周波数及び強度を制御可能である。第一操作部51は、例えば、決定部9で決定された値となるように、マイクロ波ドライブ光の周波数及び強度を制御する。マイクロ波ドライブ光の周波数及び強度の制御については、例えば参考文献2を参照のこと。 The first operation unit 51 can emit microwave drive light. Further, the first operation unit 51 can control the frequency and intensity of the emitted microwave drive light. The first operation unit 51 controls the frequency and intensity of the microwave drive light so that the values are determined by the determination unit 9, for example. For controlling the frequency and intensity of microwave drive light, see, for example, Reference 2.

〔参考文献2〕K. Inomata, Z. R. Lin, K. Koshino, W. D. Oliver, J. S. Tsai, T. Yamamoto and Y. Nakamura, "Single microwave-photon detector using an artificial Λ-type three-level system", Nature Communications 7 (2016) 12303 [Reference 2] K. Inomata, ZR Lin, K. Koshino, WD Oliver, JS Tsai, T. Yamamoto and Y. Nakamura, "Single microwave-photon detector using an artificial Λ-type three-level system", Nature Communications 7 (2016) 12303

第一操作部51により出射されたマイクロ波ドライブ光は、第二導波路2に入射される。第二導波路2に入射されたマイクロ波ドライブ光の周波数及び強度に応じて、超伝導量子ビット4とマイクロ波光子間の量子ゲートの作用は変化する。言い換えれば、マイクロ波ドライブ光は、超伝導量子ビット4と共振器3からなる着衣状態に影響を及ぼす。 The microwave drive light emitted by the first operation unit 51 is incident on the second waveguide 2. The action of the quantum gate between the superconducting qubit 4 and the microwave photon changes depending on the frequency and intensity of the microwave drive light incident on the second waveguide 2. In other words, the microwave drive light affects the clothing state of the superconducting qubit 4 and the resonator 3.

入力部6から出射されるマイクロ波光子は、サーキュレータ7を介して第一導波路1に入射される。第一導波路1に入射されたマイクロ波光子は、上記の着衣状態に応じて超伝導量子ビット4と作用し、第一導波路1に戻る。第一導波路1に戻ったマイクロ波光子は、サーキュレータ7を介して出力部8に出力される。 The microwave photon emitted from the input unit 6 is incident on the first waveguide 1 via the circulator 7. The microwave photon incident on the first waveguide 1 interacts with the superconducting qubit 4 according to the above-mentioned clothing state, and returns to the first waveguide 1. The microwave photon returned to the first waveguide 1 is output to the output unit 8 via the circulator 7.

第二操作部52、第三操作部53及び第四操作部54は、それぞれ共振器3の周波数、超伝導量子ビット4の周波数及び超伝導量子ビット4と共振器3の結合強度を制御可能である。第二操作部52、第三操作部53及び第四操作部54は、例えば、決定部9で決定された値となるように、それぞれ共振器3の周波数、超伝導量子ビット4の周波数及び超伝導量子ビット4と共振器3の結合強度を制御する。超伝導量子ビット4の周波数は、より正確には超伝導量子ビット4の2準位間の周波数である。 The second operation unit 52, the third operation unit 53, and the fourth operation unit 54 can control the frequency of the resonator 3, the frequency of the superconducting qubit 4, and the coupling strength between the superconducting qubit 4 and the resonator 3, respectively. is there. The second operation unit 52, the third operation unit 53, and the fourth operation unit 54 have, for example, the frequency of the resonator 3, the frequency of the superconducting qubit 4, and the superconducting unit 54 so as to have values determined by the determination unit 9. The coupling strength between the conduction qubit 4 and the resonator 3 is controlled. The frequency of the superconducting qubit 4 is more accurately the frequency between the two levels of the superconducting qubit 4.

第二操作部52、第三操作部53及び第四操作部54は、例えば、共振器3及び超伝導量子ビット4に接続された直流電流の強度や、共振器3及び超伝導量子ビット4に接続された図示していない超伝導量子干渉計(SQUID)に与える外部磁場の強度を制御することにより、それぞれ共振器3の周波数、超伝導量子ビット4の周波数及び超伝導量子ビット4と共振器3の結合強度を制御することができる。 The second operation unit 52, the third operation unit 53, and the fourth operation unit 54 are, for example, the strength of the DC current connected to the resonator 3 and the superconducting qubit 4, and the resonator 3 and the superconducting qubit 4. By controlling the strength of the external magnetic field applied to the connected superconducting qubit (SQUID), the frequency of the resonator 3, the frequency of the superconducting qubit 4, and the superconducting qubit 4 and the resonator, respectively. The bond strength of 3 can be controlled.

第二操作部52による共振器3の周波数の制御の詳細については、例えば参考文献3を参照のこと。 For details on controlling the frequency of the resonator 3 by the second operation unit 52, refer to, for example, Reference 3.

〔参考文献3〕Martin Sandberg, CM Wilson, Fredrik Persson, Thilo Bauch, Goran Johansson, Vitaly Shumeiko, Tim Duty, Per Delsing, "Tuning the field in a microwave resonator faster than the photon lifetime", Appl. Phys. Lett. 92, 203501 (2008) [Reference 3] Martin Sandberg, CM Wilson, Fredrik Persson, Thilo Bauch, Goran Johansson, Vitaly Shumeiko, Tim Duty, Per Delsing, "Tuning the field in a microwave resonator faster than the photon lifetime", Appl. Phys. Lett. 92, 203501 (2008)

第三操作部53による超伝導量子ビット4の周波数の制御の詳細については、例えば参考文献4を参照のこと。 For details on controlling the frequency of the superconducting qubit 4 by the third operation unit 53, refer to, for example, Reference 4.

〔参考文献4〕R. Barends, J. Kelly, A. Megrant, D. Sank, E. Jeffrey, Y. Chen, Y. Yin, B. Chiaro, J. Mutus, C. Neill, P. O'Malley, P. Roushan, J. Wenner, T. C. White, A. N. Cleland, John M. Martinis, "Coherent Josephson qubit suitable for scalable quantum integrated circuits", Pysical Review Letters 111, 080502 (2013) [Reference 4] R. Barends, J. Kelly, A. Megrant, D. Sank, E. Jeffrey, Y. Chen, Y. Yin, B. Chiaro, J. Mutus, C. Neill, P. O'Malley , P. Roushan, J. Wenner, TC White, AN Cleland, John M. Martinis, "Coherent Josephson qubit suitable for scalable quantum integrated circuits", Pysical Review Letters 111, 080502 (2013)

第四操作部54による超伝導量子ビット4と共振器3の結合強度の制御の詳細については、例えば参考文献5を参照のこと。 For details of controlling the coupling strength between the superconducting qubit 4 and the resonator 3 by the fourth operation unit 54, refer to Reference 5, for example.

〔参考文献5〕Yu Chen, C. Neill, P. Roushan, N. Leung, M. Fang, R. Barends, J. Kelly, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, A. Megrant, J. Y. Mutus, P. J. J. O’Malley, C. M. Quintana, D. Sank, A. Vainsencher, J. Wenner, T. C. White, Michael R. Geller, A. N. Cleland, John M. Martinis, "Qubit Architecture with High Coherence and Fast Tunable Coupling", Pysical R eview Letters 113, 220502 (2014) [Reference 5] Yu Chen, C. Neill, P. Roushan, N. Leung, M. Fang, R. Barends, J. Kelly, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, A. Megrant, JY Mutus, PJJ O'Malley, CM Quintana, D. Sank, A. Vainsencher, J. Wenner, TC White, Michael R. Geller, AN Cleland, John M. Martinis, "Qubit Architecture with High" Coherence and Fast Tunable Coupling ", Pysical Review Letters 113, 220502 (2014)

後述するように、決定部9は、所望の量子ゲートに対応する係数ξ11(ω),ξ12(ω),ξ21(ω),ξ22(ω)を所与として、式(12)-(15)を満たす、マイクロ波ドライブ光の周波数をωd、マイクロ波ドライブ光の強度Ωd、共振器3の周波数ωr、超伝導量子ビット4の周波数ωa及び超伝導量子ビット4と共振器3の結合強度gの少なくとも1つの値を決定する。 As will be described later, the determination unit 9 gives Eq. (12) given the frequencies ξ 11 (ω), ξ 12 (ω), ξ 21 (ω), ξ 22 (ω) corresponding to the desired quantum gate. -The frequency of the microwave drive light that satisfies (15) is ω d , the intensity of the microwave drive light Ω d , the frequency ω r of the resonator 3, the frequency ω a of the superconducting quantum bit 4, and the superconducting quantum bit 4. At least one value of the coupling strength g of the resonator 3 is determined.

この際、決定部9は、マイクロ波ドライブ光の周波数をωd、マイクロ波ドライブ光の強度Ωd、共振器3の周波数ωr、超伝導量子ビット4の周波数ωa及び超伝導量子ビット4と共振器3の結合強度gの一部を更に所与として、マイクロ波ドライブ光の周波数ωd、マイクロ波ドライブ光の強度Ωd、共振器3の周波数ωr、超伝導量子ビット4の周波数ωa及び超伝導量子ビット4と共振器3の結合強度gの他部を決定してもよい。 At this time, the determination unit 9 sets the frequency of the microwave drive light to ω d , the intensity of the microwave drive light Ω d , the frequency ω r of the resonator 3, the frequency ω a of the superconducting quantum bit 4, and the superconducting quantum bit 4. And a part of the coupling strength g of the resonator 3 is further given, the frequency ω d of the microwave drive light, the intensity Ω d of the microwave drive light, the frequency ω r of the resonator 3, and the frequency of the superconducting quantum bit 4. Other parts of ω a and the coupling strength g of the superconducting quantum bit 4 and the resonator 3 may be determined.

[技術的背景]
超伝導量子ビット4と共振器3からなる系のハミルトニアンHarは、マイクロ波ドライブ光の振幅Ωd及び周波数ωdに応じて回転座標系において式(1)のようになる。
[Technical background]
The Hamiltonian Har of the system consisting of the superconducting qubit 4 and the resonator 3 becomes as shown in Eq. (1) in the rotating coordinate system according to the amplitude Ω d and the frequency ω d of the microwave drive light.

Figure 0006765656
Figure 0006765656

ここで、χ=g2/(ωra)は分散シフトである。ωrは共振器3の周波数であり、ωaは超伝導量子ビット4の周波数であり、超伝導量子ビット4と共振器3の結合強度gである。ここでは、ωra,gは予め定められた固定された値であるとする。aは超伝導量子ビット4の消滅演算子、σは共振器3の消滅演算子であり、†は転置共役を意味する。 Where χ = g 2 / (ω ra ) is the variance shift. ω r is the frequency of the resonator 3, ω a is the frequency of the superconducting qubit 4, and is the bond strength g between the superconducting qubit 4 and the resonator 3. Here, it is assumed that ω r , ω a , and g are predetermined fixed values. a is the annihilation operator of the superconducting qubit 4, σ is the annihilation operator of the resonator 3, and † means the transposed conjugate.

超伝導量子ビット4と共振器3からなる系の下から4つのエネルギー準位は、|g,0>,|e,0>,|g,1>,|e,1>であり、これらはドライブ場がオフのとき、言い換えればマイクロ波ドライブ光がないときの固有状態である。ωdをωa-2χ<ωdaと定めると、ωdの回転座標系において、エネルギー準位構造は、ω|g,0>|e,0>|e,1>|g,1>となる入れ子型となる。 The four energy levels from the bottom of the system consisting of the superconducting qubit 4 and the resonator 3 are | g, 0>, | e, 0>, | g, 1>, | e, 1>. This is the eigenstate when the drive field is off, in other words, when there is no microwave drive light. If ω d is defined as ω a -2χ <ω da , then in the rotating coordinate system of ω d , the energy level structure is ω | g, 0>| e, 0>| e, 1 >| g, 1> is a nested type.

これに対して、ドライブ場がオンのとき、言い換えればマイクロ波ドライブ光があるときこれらの状態は着衣状態となり、式(2)-(5)と書ける。 On the other hand, when the drive field is on, in other words, when there is microwave drive light, these states are in the clothes state, and can be written as equations (2)-(5).

Figure 0006765656
Figure 0006765656

ここで、θl及びθhは、式(5'),(5'')により定義される。 Here, θ l and θ h are defined by Eqs. (5'), (5'').

Figure 0006765656
Figure 0006765656

そして、上記の着衣状態の固有エネルギー~ω1,~ω2,~ω3,~ω4は式(6)-(7')となる。 Then, the intrinsic energies ~ ω 1 , ~ ω 2 , ~ ω 3 , ~ ω 4 of the above-mentioned clothes state are given by equations (6)-(7').

Figure 0006765656
Figure 0006765656

この4レベルの系においては、|~3>,|~4>から|~1>,|~2>にエネルギー緩和がされ、そのとき光子を第一導波路1に発する。共振器3と超伝導量子ビット4からなる着衣状態の緩和レート~κ31,~κ32,~κ41,~κ42は式(8),(9)となる。i=3,4, j=1,2として、~κijは、|~i>から|~j>への緩和レートを意味する。θtlhである。κは、共振器3そのものの緩和レートであり所定の定数である。 In this 4-level system, energy relaxation is performed from | ~ 3>, | ~ 4> to | ~ 1>, | ~ 2>, and photons are then emitted to the first waveguide 1. The relaxation rate of the clothing state, which consists of the resonator 3 and the superconducting qubit 4, ~ κ 31 , ~ κ 32 , ~ κ 41 , ~ κ 42 is given by Eqs. (8) and (9). With i = 3,4, j = 1,2, ~ κ ij means the relaxation rate from | ~ i> to | ~ j>. θ t = θ l + θ h . κ is the relaxation rate of the resonator 3 itself and is a predetermined constant.

Figure 0006765656
Figure 0006765656

伝播するマイクロ波光子とこの着衣状態の系は式(10),(11)のような変換を行う。ωは、マイクロ波光子の周波数であり、ω=ωlhである。Δω=ωhlである。ωlhの定義は後述する。 The propagating microwave photon and this clothed system perform transformations as shown in equations (10) and (11). ω is the frequency of microwave photons, and ω = ω l , ω h . Δω = ω hl . The definitions of ω l and ω h will be described later.

Figure 0006765656
Figure 0006765656

これが、量子ゲートに相当する。|~1>,|~2>が超伝導量子ビット4の2状態系、言い換えればマイクロ波ドライブ光の影響を受けた超伝導量子ビット4及び共振器3が構成する着衣状態の中のエネルギー準位が低い2個の着衣状態に対応し、マイクロ波光子の基底は|ωl>,|ωh>であり、(ωlh)=(~ω32,~ω31)又は(~ω42,~ω41)である。ここで、例えば、~ω32=~ω3-~ω2であり、~ω31=~ω3-~ω1であり、~ω42=~ω4-~ω2であり、~ω41=~ω4-~ω1である。 This corresponds to a quantum gate. | ~ 1>, | ~ 2> are the two-state system of the superconducting qubit 4, in other words, the energy level in the clothing state composed of the superconducting qubit 4 and the resonator 3 influenced by the microwave drive light. Corresponding to two low-ranked clothing states, the base of microwave photons is | ω l >, | ω h >, and (ω l , ω h ) = (~ ω 32 , ~ ω 31 ) or (~ ω 42 , ~ ω 41 ). Here, for example, ~ ω 32 = ~ ω 3 - a ~ ω 2, ~ ω 31 = ~ ω 3 - a ~ ω 1, ~ ω 42 = ~ ω 4 - a ~ ω 2, ~ ω 41 = ~ ω 4 - is ~ ω 1.

ここで、緩和レートが~κ31=~κ32となるとき(すなわち、θt=π/4のとき、このときωdとωdの条件は式(17)となる)に着目すると、式(12)-(15)は、(ωlh)=(~ω32,~ω31)のときξ11l)=ξ21l)=1, ξ12l)=ξ22l)=0, ξ11h)=ξ21h)=0, ξ12h)=ξ22h)=1となる。これは、緩和レートが~κ41=~κ42となるときかつ(ωlh)=(~ω42,~ω41)となるときも同様である。すなわち、マイクロ波光子・原子の変換式は式(16)のようなSWAPゲートとなる。 Here, focusing on the case where the relaxation rate is ~ κ 31 = ~ κ 32 (that is, when θ t = π / 4, the conditions of ω d and ω d are equation (17)). (12)-(15) is ξ 11l ) = ξ 21l ) = 1, ξ 12l ) when (ω l , ω h ) = (~ ω 32 , ~ ω 31 ) = ξ 22l ) = 0, ξ 11h ) = ξ 21h ) = 0, ξ 12h ) = ξ 22h ) = 1. This is also the case when the relaxation rate is ~ κ 41 = ~ κ 42 and when (ω l , ω h ) = (~ ω 42 , ~ ω 41 ). That is, the conversion formula for microwave photons and atoms is a SWAP gate as shown in equation (16).

Figure 0006765656
Figure 0006765656

また、入出力の光子の周波数基底を固定するためには、Δω=ωhl=式(18)が定数となる必要がある。 In addition, in order to fix the frequency basis of input / output photons, Δω = ω hl = equation (18) must be a constant.

Figure 0006765656
Figure 0006765656

Δωを以後定数とするとSWAPゲートのときのωd及びΩdであるωd sw及びΩd swは、式(19),(20)となる。 A omega d and Omega d when subsequent When constant SWAP gates [Delta] [omega omega d sw and Omega d sw is the formula (19) and (20).

Figure 0006765656
Figure 0006765656

このとき、マイクロ波光子の周波数基底は式(21),(22)となる。 At this time, the frequency basis of the microwave photon is given by Eqs. (21) and (22).

Figure 0006765656
Figure 0006765656

以後、この周波数基底を用いるとする。次に、√SWAPゲートについて説明する。 Hereinafter, this frequency basis will be used. Next, the √SWAP gate will be described.

√SWAPゲートを構成するために、決定部9は、ξ11l)=1,ξ12l)=0,ξ21l)=(1+i)/2,ξ22l)=(1-i)/2,ξ11h)=(1-i)/2,ξ12h)=(1+i)/2,ξ21h)=0,ξ22h)=1又はξ11l)=1,ξ12l)=0,ξ21l)=(1-i)/2,ξ22l)=(1+i)/2,ξ11h)=(1+i)/2,ξ12h)=(1-i)/2,ξ21h)=0,ξ22h)=1となるようなωd及びΩdを選ぶ。この際、許されるエラー範囲程度は値がずれてもよい。このとき、マイクロ波光子の周波数基底は式(21),(22)となるように選ぶと、SWAPゲートと√SWAPゲートの基底は等しくなる。 √ To construct the SWAP gate, the decision unit 9 determines ξ 11l ) = 1, ξ 12l ) = 0, ξ 21l ) = (1 + i) / 2, ξ 22 ( ω l ) = (1-i) / 2,ξ 11h ) = (1-i) / 2,ξ 12h ) = (1 + i) / 2,ξ 21h ) = 0 , ξ 22h ) = 1 or ξ 11l ) = 1, ξ 12l ) = 0, ξ 21l ) = (1-i) / 2, ξ 22l ) = (1 + i) / 2,ξ 11h ) = (1 + i) / 2,ξ 12h ) = (1-i) / 2,ξ 21h ) = 0,ξ 22 ( Select ω d and Ω d such that ω h ) = 1. At this time, the value may deviate within the allowable error range. At this time, if the frequency bases of the microwave photons are selected to be in equations (21) and (22), the bases of the SWAP gate and the √SWAP gate are equal.

なお、上記の説明では、決定部9が、ωra,gを予め定められた値に固定して、所望の量子ゲートに対応するξ11l),ξ12l),ξ21l),ξ22l),ξ11h),ξ12h),ξ21h),ξ22h)が得られるように、Ωddを決定していたが、これは一例に過ぎない。 In the above description, the determination unit 9 fixes ω r , ω a , g to predetermined values and corresponds to the desired quantum gate ξ 11l ), ξ 12l ). Ω d so that, ξ 21l ), ξ 22l ), ξ 11h ), ξ 12h ), ξ 21h ), ξ 22h ) can be obtained. , Ω d was decided, but this is just an example.

決定部9は、ωra,g,Ωddの一部を固定して、所望の量子ゲートに対応するξ11l),ξ12l),ξ21l),ξ22l),ξ11h),ξ12h),ξ21h),ξ22h)が得られるように、ωra,g,Ωddの他部を決定してもよい。例えば、決定部9は、Ωddを固定して、所望の量子ゲートに対応するξ11l),ξ12l),ξ21l),ξ22l),ξ11h),ξ12h),ξ21h),ξ22h)が得られるように、ωra,gを決定してもよい。 The determination unit 9 fixes a part of ω r , ω a , g, Ω d , ω d and corresponds to the desired quantum gate ξ 11l ), ξ 12l ), ξ 21 ( ω l), ξ 22 (ω l), ξ 11 (ω h), ξ 12 (ω h), ξ 21 (ω h), as ξ 22h) is obtained, ω r, ω a, Other parts of g, Ω d , ω d may be determined. For example, the determination unit 9 fixes Ω d and ω d and corresponds to the desired quantum gate ξ 11l ), ξ 12l ), ξ 21l ), ξ 22l ). ), Ξ 11h ), ξ 12h ), ξ 21h ), ξ 22h ) may be determined so that ω r , ω a , g can be obtained.

なお、これまでの説明では、共振器3の周波数ωr及び超伝導量子ビット4の周波数ωaを予め定められた値としていたため、共振器3の周波数ωr及び超伝導量子ビット4の周波数ωaのシフトには言及していなかったが、共振器3の周波数ωr及び超伝導量子ビット4の周波数ωaを動かす場合には、このシフトを考慮する必要がある。シフトを考慮した場合には、上記の説明において、共振器3の周波数を-ωrとし、超伝導量子ビット4の周波数を-ωaとし、χ=g2/(-ωr--ωa)とし、ωr=-ωr+χ、ωa=-ωa-χとすればよい。 Incidentally, so far in the description of, because it was a predetermined value a frequency omega a frequency omega r and superconducting quantum bit 4 of the resonator 3, the frequency of the frequency omega r and superconducting quantum bit 4 of the resonator 3 the shift of the omega a did not mention, when moving the frequency omega a frequency omega r and superconducting quantum bit 4 of the resonator 3, it is necessary to consider the shift. In consideration of the shift, in the above description, the frequency of the resonator 3 - and omega r, the frequency of the superconducting qubit 4 - and ω a, χ = g 2 / (- ω r - - ω a ) and, ω r = - ω r + χ, ω a = - may be used as the ω a -χ.

決定部9が、所望の量子ゲートに対応するξ11l),ξ12l),ξ21l),ξ22l),ξ11h),ξ12h),ξ21h),ξ22h)に対応するωra,g,Ωddの値を決定し、操作部5が決定された値となるように、ωra,g,Ωddを制御することで、SWAPゲート以外の量子計算を行うことができる量子ゲート装置を構成することができる。 The determination unit 9 corresponds to the desired quantum gate, ξ 11l ), ξ 12l ), ξ 21l ), ξ 22l ), ξ 11h ), ξ 12 ( Determine the values of ω r , ω a , g, Ω d , ω d corresponding to ω h ), ξ 21h ), ξ 22h ) so that the operation unit 5 becomes the determined value. In addition, by controlling ω r , ω a , g, Ω d , and ω d , it is possible to configure a quantum gate device capable of performing quantum calculations other than the SWAP gate.

また、上記の量子ゲート装置により、量子もつれを生成することができる。 In addition, quantum entanglement can be generated by the above-mentioned quantum gate device.

[変形例]
上記の実施形態は一例に過ぎず、この発明の趣旨を逸脱しない範囲で適宜変更が可能であることはいうまでもない。
[Modification example]
It goes without saying that the above embodiment is only an example and can be appropriately changed without departing from the spirit of the present invention.

例えば、量子ゲート装置は、サーキュレータ7を備えていなくてもよい。この場合、例えば、量子ゲート装置は、入力部6から出射されるマイクロ波光子を第一導波路1に入射し、共振器3から第一導波路1に戻ったマイクロ波光子を出力部8に入射するスイッチをサーキュレータ7の代わりに備えていてもよい。 For example, the quantum gate device may not include the circulator 7. In this case, for example, in the quantum gate device, the microwave photon emitted from the input unit 6 is incident on the first waveguide 1, and the microwave photon returned from the resonator 3 to the first waveguide 1 is sent to the output unit 8. An incident switch may be provided instead of the circulator 7.

また、上記の説明では、マイクロ波光子の周波数基底として式(21),(22)で定義される周波数基底を用いたが、マイクロ波光子の周波数基底は式(21),(22)で定義される周波数基底に限定されない。マイクロ波光子の周波数基底として、式(21),(22)で定義される周波数基底以外の周波数基底を用いてもよい。 Further, in the above description, the frequency basis defined by Eqs. (21) and (22) was used as the frequency basis of the microwave photon, but the frequency basis of the microwave photon is defined by Eqs. (21) and (22). It is not limited to the frequency basis to be used. As the frequency basis of the microwave photon, a frequency basis other than the frequency basis defined by Eqs. (21) and (22) may be used.

1 第一導波路
2 第二導波路
3 共振器
4 超伝導量子ビット
5 操作部
6 入力部
7 サーキュレータ
8 出力部
9 決定部
1 1st waveguide 2 2nd waveguide 3 Resonator 4 Superconducting qubit 5 Operation unit 6 Input unit 7 Circulator 8 Output unit 9 Decision unit

Claims (3)

共振器に結合している超伝導量子ビットと、
上記共振器に結合しており、マイクロ波光子が入射される第一導波路と、
上記超伝導量子ビットに結合しており、マイクロ波ドライブ光が入射される第二導波路と、
上記マイクロ波ドライブ光の周波数、上記マイクロ波ドライブ光の強度、上記共振器の周波数、上記超伝導量子ビットの周波数及び上記超伝導量子ビットと上記共振器の結合強度の少なくとも1つを制御可能な操作部と、
を含み、
所望の量子ゲートに対応するように、上記マイクロ波ドライブ光の周波数、上記マイクロ波ドライブ光の強度、上記共振器の周波数、上記超伝導量子ビットの周波数及び上記超伝導量子ビットと上記共振器の結合強度の少なくとも1つの値を決定する決定部を更に含み、
上記操作部は、上記決定された値となるように、上記マイクロ波ドライブ光の周波数、上記マイクロ波ドライブ光の強度、上記共振器の周波数、上記超伝導量子ビットの周波数及び上記超伝導量子ビットと上記共振器の結合強度の少なくとも1つを制御する、
量子ゲート装置。
Superconducting qubits coupled to the resonator,
The first waveguide, which is coupled to the resonator and in which microwave photons are incident,
A second waveguide that is coupled to the above superconducting qubit and in which microwave drive light is incident,
At least one of the frequency of the microwave drive light, the intensity of the microwave drive light, the frequency of the resonator, the frequency of the superconducting quantum bit, and the coupling strength between the superconducting quantum bit and the resonator can be controlled. Operation unit and
Only including,
The frequency of the microwave drive light, the intensity of the microwave drive light, the frequency of the resonator, the frequency of the superconducting quantum bit, and the frequency of the superconducting quantum bit and the resonator so as to correspond to the desired quantum gate. It further includes a determinant that determines at least one value of bond strength.
The operation unit performs the frequency of the microwave drive light, the intensity of the microwave drive light, the frequency of the resonator, the frequency of the superconducting quantum bit, and the superconducting quantum bit so as to obtain the determined values. And control at least one of the coupling strengths of the resonator,
Quantum gate device.
請求項1の量子ゲート装置において、
上記操作部は、上記マイクロ波ドライブ光の周波数及び上記マイクロ波ドライブ光の強度を制御可能な第一操作部である、
量子ゲート装置。
In the quantum gate device of claim 1,
The operation unit is a first operation unit capable of controlling the frequency of the microwave drive light and the intensity of the microwave drive light.
Quantum gate device.
共振器に結合している超伝導量子ビットと、
上記共振器に結合しており、マイクロ波光子が入射される第一導波路と、
上記超伝導量子ビットに結合しており、マイクロ波ドライブ光が入射される第二導波路と、
上記マイクロ波ドライブ光の周波数、上記マイクロ波ドライブ光の強度、上記共振器の周波数、上記超伝導量子ビットの周波数及び上記超伝導量子ビットと上記共振器の結合強度の少なくとも1つを制御可能な操作部と、
を含む量子ゲート装置において、
上記マイクロ波ドライブ光の周波数をωdとし、上記マイクロ波ドライブ光の強度をΩdとし、上記共振器の周波数を-ωrとし、上記超伝導量子ビットの周波数を-ωaとし、χ=g2/(-ωr--ωa)とし、ωr=-ωr+χ、ωa=-ωa-χとし、上記超伝導量子ビットと上記共振器の結合強度をgとし、上記マイクロ波ドライブ光の影響を受けた超伝導量子ビット及び共振器が構成する着衣状態の中のエネルギー準位が低い2個の着衣状態を|~1>,|~2>とし、ωを上記マイクロ波光子の周波数とし、ω=ωlhとし、(ωlh)=(~ω32,~ω31)又は(~ω42,~ω41)とし、~ω32=~ω3-~ω2とし、~ω31=~ω3-~ω1とし、~ω42=~ω4-~ω2とし、~ω41=~ω4-~ω1とし、Δω=ωhlとし、~ω1,~ω2,~ω3,~ω4は式(6)-(7')により定義されるとし、量子ゲートは式(10),(11)の変換を行うとし、上記量子ゲートに対応する係数ξ11(ω),ξ12(ω),ξ21(ω),ξ22(ω)は式(12)-(15)で定義されるとし、κを所定の定数とし、θtlhとし、θlhは式(5'),(5'')により定義されるとして、
Figure 0006765656
上記量子ゲートに対応する係数ξ11(ω),ξ12(ω),ξ21(ω),ξ22(ω)を所与として、式(12)-(15)を満たす、上記マイクロ波ドライブ光の周波数ωd、上記マイクロ波ドライブ光の強度Ωd、上記共振器の周波数-ωr、上記超伝導量子ビットの周波数-ωa及び上記超伝導量子ビットと上記共振器の結合強度gの少なくとも1つの値を決定する決定部を更に含み、
上記操作部は、上記決定された値となるように、上記マイクロ波ドライブ光の周波数ωd、上記マイクロ波ドライブ光の強度Ωd、上記共振器の周波数-ωr、上記超伝導量子ビットの周波数-ωa及び上記超伝導量子ビットと上記共振器の結合強度gの少なくとも1つを制御する、
量子ゲート装置。
Superconducting qubits coupled to the resonator,
The first waveguide, which is coupled to the resonator and in which microwave photons are incident,
A second waveguide that is coupled to the above superconducting qubit and in which microwave drive light is incident,
At least one of the frequency of the microwave drive light, the intensity of the microwave drive light, the frequency of the resonator, the frequency of the superconducting quantum bit, and the coupling strength between the superconducting quantum bit and the resonator can be controlled. Operation unit and
Oite quantum gate equipment including,
The frequency of the microwave drive light is omega d, the intensity of the microwave drive light is Omega d, the frequency of the resonator - and omega r, the frequency of the superconducting qubits - and ω a, χ = g 2 / a (- - ω r - ω a ), ω r = - ω r + χ, ω a = - and ω a -χ, the bond strength of the superconducting qubit and the resonator and g, the The two clothing states with low energy levels in the clothing state composed of the superconducting quantum bit and the resonator affected by the microwave drive light are | ~ 1> and | ~ 2>, and ω is the above micro. Let the frequency of the wave photon be ω = ω l , ω h , (ω l , ω h ) = (~ ω 32 , ~ ω 31 ) or (~ ω 42 , ~ ω 41 ), and ~ ω 32 = ~ ω 3 - a ~ ω 2, ~ ω 31 = ~ ω 3 - and ~ ω 1, ~ ω 42 = ~ ω 4 - and ~ ω 2, ~ ω 41 = ~ ω 4 - and ~ ω 1, Δω = ω h and -ω l, ~ ω 1, ~ ω 2, ~ ω 3, ~ ω 4 of the formula (6) - (7 ') and is defined by, the quantum gate has the formula (10), conversion of (11) Assuming that the coefficients ξ 11 (ω), ξ 12 (ω), ξ 21 (ω), ξ 22 (ω) corresponding to the above quantum gate are defined by Eqs. (12)-(15), κ Is a predetermined constant, θ t = θ l + θ h, and θ l and θ h are defined by equations (5') and (5'').
Figure 0006765656
Given the frequencies ξ 11 (ω), ξ 12 (ω), ξ 21 (ω), ξ 22 (ω) corresponding to the quantum gate, the microwave drive satisfying equations (12)-(15). light frequency omega d, the microwave drive light intensity omega d, of the resonator frequency - omega r, said superconducting quantum bit frequency - omega a and the superconducting qubits and coupling strength g of the resonator Further includes a decision unit that determines at least one value
The operation unit has the frequency ω d of the microwave drive light, the intensity Ω d of the microwave drive light, the frequency - ω r of the resonator, and the superconducting quantum bit so as to obtain the determined values. Controls frequency - ω a and at least one of the coupling strength g of the superconducting quantum bit and the cavity .
Quantum gate device.
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