JP6130314B2 - Ising type interaction generator - Google Patents

Description

  The present invention relates to an Ising interaction generator that generates an Ising interaction between qubits.

  Quantum computing devices are expected to achieve parallelism on a scale that cannot be achieved by conventional computing devices by using quantum mechanical superposition (entanglement), and many researches and developments have been made. Entanglement used in quantum computation is a special correlation between qubits. For example, when each of a plurality of qubits having entanglement is measured, a strong correlation appears between the measured values. By using these correlations, quantum computation can be performed at a speed faster than classical computation.

  In quantum computation, there are various types of entanglement that enables high-speed operation. Among them, entanglement that has attracted attention in recent years is called a cluster state (see Non-Patent Document 1). It is known that if this entanglement can be generated, quantum computation that is extremely robust against errors can be performed.

  In order to generate the cluster state described above, a type of interaction called an Ising type is used (see Non-Patent Document 1). Usually, an interaction occurs through energy exchange between qubits. On the other hand, in the case of the Ising type, interaction is generated not by energy but by phase exchange between qubits.

  Conventionally, a method of generating an Ising type interaction between qubits by coupling a plurality of superconducting flux qubits inductively (electromagnetic induction) is known (see Non-Patent Documents 2 and 3). The generation of Ising-type interaction of a conventional superconducting flux qubit will be described with reference to FIG. FIG. 3 is an explanatory diagram for explaining the occurrence of interaction. FIG. 3 illustrates the case of two superconducting rings 301 and 302 as to the occurrence of interaction. In FIG. 3, the Josephson junction is indicated by “x”.

  In addition, a magnetic flux 311 penetrating the superconducting ring 301 and a magnetic flux 312 penetrating the superconducting ring 302 are applied by an external magnetic field (not shown), and a superconducting flux qubit is generated for each. Note that the number of superconducting rings is not limited to two, and three or more superconducting rings may be arranged.

  As shown in FIG. 3, the superconducting ring 301 and the superconducting ring 302 are arranged close to each other. For example, an induced magnetic field generated from the superconducting ring 301 induces further induced current in the superconducting ring 302. As a result, the superconducting flux qubit of the superconducting ring 301 and the superconducting flux qubit of the superconducting ring 302 are coupled inductively. When the external magnetic field is changed to a predetermined condition in such an inductively coupled state, an Ising type interaction can be generated between the two superconducting flux qubits described above.

The above-described interaction will be described using mathematical expressions. The Hamiltonian H of the superconducting flux qubit in the state where the interaction with one superconducting flux qubit does not work is expressed by the following equation using Josephson junction energy E _j , Josephson junction capacitance C _j , and gate capacitance C _g. It is represented by

V _e ⁽ⁱ⁾ is a voltage applied to the island i between the Josephson junctions via the gate capacitor C _{g (i)} . V _i is the voltage of the island i applied to the island i between the Josephson junctions via the gate capacitor C _{g (i)} . Φ ₀ represents the magnetic flux quantum. “Island” refers to a region on the superconducting ring having the same potential and continuous.

The phase difference ψ _i through the Josephson junction placed on the same superconducting ring is subject to the following constraint based on the applied magnetic flux fΦ ₀ into the superconducting ring.

Next, the derivation of Hamiltonian H _AB in a state where two superconducting qubits A and B are coupled inductively will be described.

When the superconducting qubit A and the superconducting qubit B are coupled inductively, the applied magnetic fluxes f ^A and f ^B applied to each are effectively expressed by the following equations (5) and ( 6). Here, I _A and I ^B are currents flowing through the superconducting qubit A and the superconducting qubit B, and M is a mutual inductance. Further, the new combined Hamiltonian H _AB is represented by the following formula (7).

Here, ε represents the energy dispersion with respect to the external magnetic field (or can be regarded as the difference in the minimum energy of the double well potential formed by the qubit), and Δ represents the strong coupling due to the tunnel effect between the double wells. Represents Σ _x and σ _z both represent a Pauli matrix. In Equation (7), the effective Hamiltonian of the interaction acting between the superconducting qubit A and the superconducting qubit B can be expressed as the following equation.

In this way, two types of interaction, σ _z σ _z and σ _x σ _z , are working, and the interaction strength κ _i is about 0.01 times Josephson energy.

  By changing the external magnetic flux, ε can be changed, and the Hamiltonian of the system can be changed accordingly. Therefore, by changing the external magnetic flux to be in the region of ε >> Δ, the second term and the fourth term of Equation (7) can be ignored, so that the superconducting qubit A, the superconducting qubit The Hamiltonian of B can be approximated as:

Furthermore, in the equation (8), the σ _x σ _z type interaction does not satisfy the energy conservation law, and therefore is approximately eliminated, and only the σ _z σ _z type interaction can be left. As a result, the Hamiltonian of the system with the Ising type interaction using the coupling between the superconducting flux qubits by the external magnetic field is finally expressed as follows. Here, g represents a coupling constant.

R. Raussendorf and H. J. Briegel, "A One-Way Quantum Computer", PHYSICAL REVIEW LETTERS, vol.86, no.22, pp.5188-5191, 2001. J. E. Mooij et al., "Josephson Persistent-Current Qubit", SCIENCE, vol.285, pp.1036-1039, 1999. T. P. Orlando et al., "Superconducting persistent-current qubit", PHYSICAL REVIEW B, vol.60, no.22, pp.15398-15413, 1999.

  As described above, conventionally, in an apparatus that generates an Ising-type interaction between superconducting flux qubits, a plurality of superconducting rings that generate superconducting flux qubits are arranged in close proximity to each other. Inductive (electromagnetic induction) coupled state, the external magnetic field applied to each superconducting ring is changed to the “ε >> Δ” state, and an Ising-type interaction is generated between qubits. I was letting.

  However, in a state where “ε >> Δ”, the superconducting magnetic flux qubit becomes vulnerable to magnetic flux noise, and as a result, the lifetime of the qubit is shortened. There is a problem in that an Ising-type interaction can be generated only under conditions that shorten the lifetime.

  The present invention has been made to solve the above-described problems, and an object of the present invention is to enable Ising-type interaction to occur without shortening the lifetime of a qubit.

  An Ising-type interaction generator according to the present invention includes a capacitor that couples a first superconducting ring having a Josephson junction and a second superconducting ring having a Josephson junction, and the first superconducting ring includes: The second superconducting ring is connected via a capacitor and generates an Ising interaction between the first qubit by the first superconducting ring and the second qubit by the second superconducting ring.

  In the Ising-type interaction generator, a first magnetic field applying unit that applies a magnetic field to the first superconducting ring, a second magnetic field applying unit that applies a magnetic field to the second superconducting ring, and an electric field applied to the first superconducting ring. And a second electric field applying means for applying an electric field to the second superconducting ring, wherein the first magnetic field applying means sets the energy dispersion of the first qubit to 0 to the applied magnetic field. The second magnetic field applying unit approaches the energy dispersion of the second qubit with respect to the applied magnetic field close to zero.

  In the Ising-type interaction generator, the first magnetic field applying means changes the magnetic field penetrating the first superconducting ring to bring the energy dispersion of the first qubit with respect to the magnetic field closer to 0, and the second magnetic field applying means 2 Change the magnetic field penetrating the superconducting ring to bring the energy dispersion of the second qubit to the magnetic field closer to zero.

  In the Ising-type interaction generator, Ising is performed between the first qubit and the second qubit by controlling the electric field applied by the first electric field applying unit and the electric field applied by the second electric field applying unit, respectively. Generate type interaction.

  As described above, according to the present invention, since the first superconducting ring and the second superconducting ring are coupled (connected) by the capacitor, the Ising type can be realized without shortening the lifetime of the qubit. An excellent effect that interaction can occur is obtained.

FIG. 1 is a configuration diagram showing a configuration of an Ising type interaction generator according to an embodiment of the present invention. FIG. 2 shows the coupling constant g ′ and the coupling strength Δ due to the tunnel effect between the double wells when the gate voltages V _E1 and V _E2 are applied in the Ising type interaction generator according to the embodiment of the present invention. It is a characteristic view which shows the result. FIG. 3 is an explanatory diagram for explaining the generation of Ising-type interaction of a conventional superconducting flux qubit.

  Hereinafter, an embodiment of the present invention will be described with reference to FIG. FIG. 1 is a configuration diagram showing a configuration of an Ising type interaction generator according to an embodiment of the present invention.

  The device includes a capacitor 103 that couples a first superconducting ring 101 with a Josephson junction and a second superconducting ring 102 with a Josephson junction. The first superconducting ring 101 and the second superconducting ring 102 are connected via a capacitor 103. The Ising interaction generator generates an Ising interaction between a first qubit formed by the first superconducting ring 101 and a second qubit formed by the second superconducting ring 102. In FIG. 1, reference numerals 111, 112, 113, 114, 121, 122, 123, and 124 are Josephson junctions. In the embodiment, each superconducting ring has four Josephson junctions. Is illustrated.

  The apparatus also includes a first magnetic field application unit 104, a second magnetic field application unit 105, a first electric field application unit 106, and a second electric field application unit 107.

  The first magnetic field application unit 104 applies the magnetic flux f <b> 1 to the first superconducting ring 101. By controlling the magnetic flux f1 to be applied, the energy dispersion of the first qubit with respect to the magnetic flux f2 is brought close to zero. The second magnetic field application unit 105 applies the magnetic flux f <b> 2 to the second superconducting ring 102. By controlling the magnetic flux f2 to be applied, the energy dispersion of the second qubit with respect to the magnetic flux f2 is brought close to zero. The magnetic flux f1 is a magnetic field penetrating the first superconducting ring 101, and the magnetic flux f2 is a magnetic field penetrating the second superconducting ring 102.

  The first electric field application unit 106 applies an electric field to the first superconducting ring 101, and the second electric field application unit 107 applies an electric field to the second superconducting ring 102. By controlling the electric field applied by the first electric field applying unit 106 and the electric field applied by the second electric field applying unit 107, an Ising interaction is generated between the first qubit and the second qubit. Hereinafter, the application of the electric field is referred to as application of a gate voltage.

  As described above, the superconducting flux qubit can adjust the energy of the qubit by applying a gate voltage (applying an electric field) through the capacitance. In the present invention, the characteristics of this superconducting flux qubit are used. Hereinafter, this will be described using mathematical expressions.

  First, consider a system in which a qubit is initialized to | +> in a superconducting flux qubit coupled via a capacitance. The Hamiltonian H of this system can be expressed by the following equation.

The final term of equation (12) represents an interaction due to capacitive coupling of qubits. Φ ₀ represents the magnetic flux quantum, ψ _i represents the phase of each Josephson junction, C _{J (i)} represents the capacitance of each Josephson junction, and E _{J (i)} represents the energy of each Josephson junction. Further, the charge energy Ec _{(i) of} each Josephson junction is calculated by “Ec _(i) = e ² / 2C _{J (i)} ”.

By changing the external magnetic flux, ε can be changed, and the Hamiltonian of the system can be changed accordingly. Therefore, the Hamiltonian is derived when the external magnetic flux is changed to be in the region of ε = 0. When the Hamiltonian of the above formulas (11) to (13) is developed under the condition of ε = 0 in the same manner as the formula expansion described in the prior art section of this specification, the Hamiltonian H of the entire system is expressed by the following formula. Is done.

  It can be seen that the equations (15) and (10) are similar, and both form an Ising type interaction.

  Hereinafter, the Ising type interaction generator in the embodiment shown in FIG. 1 will be described in more detail. The first superconducting ring 101 includes four Josephson junctions 111, 112, 113, and 114, which constitute a first qubit. The second superconducting ring 102 includes four Josephson junctions 121, 122, 123, and 124, which constitute a second qubit.

In the embodiment, the first electric field application unit 106 includes a capacitor having a capacitance Cg1 and a power source that supplies the gate voltage V _E1 , and the second electric field application unit 107 uses the capacitor having the capacitance Cg2 and the gate voltage V _E2 . It consists of a power supply to supply. The capacitance of the capacitor 103 is Cc.

  VI1 is the potential of the island formed by the Josephson junction 112, the Josephson junction 113, the capacitor of the first power supply unit 106, and the capacitor 103, and VI2 is the Josephson junction 122, the Josephson junction 123, the second power supply unit. This is the potential of an island composed of 107 capacitors and capacitor 103. Moreover, the magnetic flux f1 and the magnetic flux f2 are normalized by the magnetic flux quantum. Each superconducting ring only needs to be provided with at least one Josephson junction. Further, the position where the Josephson junction is provided may be any place in the superconducting ring.

In the capacitive coupling of the first qubit and the second qubit by the capacitor 103 described above, the magnetic flux (external magnetic flux) generated by the first magnetic field application unit 104 and the second magnetic field application unit 105 is changed to be in the vicinity of ε = 0. Let Thereafter, by applying the gate voltage V _E1 and the gate voltage V _E2 simultaneously, an Ising type interaction can be configured.

  If the individual superconducting rings and gate capacitors in the Ising interaction generator have the same configuration and parameters, the applied gate voltages can be made equal. On the other hand, if these configurations and parameters are different, a gate voltage that can change the energy of each qubit equally may be applied.

FIG. 2 shows the coupling constant g ′ and the coupling due to the tunnel effect between the double wells with respect to the application of the gate voltages V _E1 and V _E2 in the Ising type interaction generator according to the embodiment, using the equation (14). It is the result of calculating the strength Δ. Various parameters used in the calculation are as follows.

Since the superconducting ring and the gate capacitor have the same configuration and parameters, the gate voltages V _E1 and V _E2 are applied with the same voltage.

As shown in FIG. 2, it can be seen that by increasing V _E1 and V _E2 simultaneously from 0 V to 0.005 V, Δ ′ / 2 decreases and the coupling constant g ′ increases. This means that in equation (14), the energy “½σ _x Δ ′” of each qubit decreases, and the σ _x σ _x- type interaction between qubits increases. Yes. In addition, there is no σ _z σ _z type or σ _x σ _z type interaction that is not commutative with the energy of the qubit.

  Unlike the inductive coupling between qubits used in the conventional Ising type interaction generator between superconducting flux qubits, the present invention couples a plurality of qubits capacitively using capacitors (capacitors 103). Unlike the conventional method, it is characterized in that the Ising-type interaction is generated under such a condition that the lifetime of the qubit is increased.

The present invention generates an Ising type interaction consisting only of σ _x σ _x type between superconducting flux qubits at the optimum operating point (near ε = 0) where flux noise resistance of superconducting flux qubits is maximized. it can. That is, an Ising type interaction generator between superconducting flux qubits having a long qubit lifetime can be realized. Also, the Ising interaction is useful for quantum computation.

  The present invention is not limited to the embodiment described above, and many modifications and combinations can be implemented by those having ordinary knowledge in the art within the technical idea of the present invention. It is obvious.

  DESCRIPTION OF SYMBOLS 101 ... 1st superconducting ring, 102 ... 2nd superconducting ring, 103 ... Capacitor, 104 ... 1st magnetic field application part, 105 ... 2nd magnetic field application part, 106 ... 1st electric field application part, 107 ... 2nd electric field application Part, 111, 112, 113, 114, 121, 122, 123, 124 ... Josephson junction.

Claims (3)

A capacitor coupling the first superconducting ring with the Josephson junction and the second superconducting ring with the Josephson junction ;
First magnetic field applying means for applying a magnetic field to the first superconducting ring;
Second magnetic field applying means for applying a magnetic field to the second superconducting ring;
First electric field applying means for applying an electric field to the first superconducting ring;
Second electric field applying means for applying an electric field to the second superconducting ring ,
The first superconducting ring and the second superconducting ring are connected via the capacitor,
The first magnetic field application means approaches the energy dispersion of the first qubit with respect to the applied magnetic field to 0,
The second magnetic field applying means approaches the energy dispersion of the second qubit with respect to the applied magnetic field close to 0,
An Ising interaction generator that generates an Ising interaction between a first qubit formed by the first superconducting ring and a second qubit formed by the second superconducting ring. In the Ising type interaction generator according to claim 1 ,
The first magnetic field applying means changes the magnetic field penetrating the first superconducting ring to bring the energy dispersion of the first qubit with respect to the magnetic field closer to 0,
The Ising-type interaction generator, wherein the second magnetic field applying means changes the magnetic field penetrating the second superconducting ring to bring the energy dispersion of the second qubit to the magnetic field close to zero. In the Ising type interaction generator according to claim 1 or 2 ,
An Ising interaction is generated between the first qubit and the second qubit by controlling the electric field applied by the first electric field applying unit and the electric field applied by the second electric field applying unit, respectively. An Ising type interaction generator characterized by causing

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