JP6042777B2 - Qubit control method - Google Patents

Description

  The present invention relates to a qubit control method for realizing quantum computation using qubits.

  Quantum computing devices are expected to achieve parallelism on a scale that cannot be achieved with conventional computing devices by using quantum mechanical superposition, and many researches and developments have been made. In order to realize a quantum computer, it is essential to construct one-qubit gate operation and two-qubit gate operation.

  Here, when a qubit is constituted by a solid state element, an interaction between qubits is used to realize a gate between two qubits. However, the existence of such an interaction prevents the construction of a one-qubit operation gate. For this reason, in order to construct both the one-qubit gate and the two-qubit gate with high fidelity, a mechanism capable of freely turning on / off the interaction between the qubits is required.

  At present, for example, an auxiliary qubit is produced between qubits to be interacted with, and the above-mentioned interaction is controlled by irradiating the produced auxiliary qubit with a microwave pulse that causes unitary transformation. (See Non-Patent Documents 1 and 2). However, in these controls, it is difficult to increase the on / off ratio, and gate operation with a high fidelity enough to exceed the threshold necessary for the execution of quantum computation has not been realized yet.

  A method of turning on / off the interaction by changing the resonance energy between qubits is also used (see Non-Patent Documents 4 and 5). However, this technique has a problem that the on / off ratio cannot be made 100% even in an ideal situation without noise (Non-Patent Document 4). There is also a problem that it is easily affected by phase relaxation (Non-Patent Document 5).

  In fields such as NMR (Nuclear Magnetic Resonance), a method of controlling the on / off of an interaction by directly irradiating a microwave pulse to a qubit is used (see Non-Patent Document 6). However, this technique is not suitable for large-scale quantum computation because the number of necessary pulses increases exponentially as the number of qubits increases.

A. J. Kerman et al., "High-Fidelity Quantum Operations on Superconducting Qubits in the Presence of Noise", PHYSICAL REVIEW LETTERS, vol.101, 070501, 2008. K. Harrabi et al., "Engineered selection rules for tunable coupling in a superconducting quantum circuit", PHYSICAL REVIEW B, vol.79, 020507R, 2009. R. Raussendorf and H. J. Briegel, "A One-Way Quantum Computer", PHYSICAL REVIEW LETTERS, vol.86, no.22, pp.5188-5191, 2001. A. Blais et al., "Quantum-information processing with circuit quantum electrodynamics", PHYSICAL REVIEW A, vol.75, 032329, 2007. Y. Matsuzaki and H. Nakano1, "Enhanced energy relaxation process of quantum memory coupled with a superconducting qubit", Arxiv, 1105, 3798, 2011. L. M. K. Vandersypen et al., "Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance", NATURE. Vol.414, pp.883-887, 2001.

  As described above, the conventional technique has a problem that the gate operation necessary for the execution of the quantum calculation cannot be realized yet and a high on / off ratio cannot be obtained. In addition, the conventional technology is susceptible to phase relaxation and is not suitable for large-scale quantum computation.

  The present invention has been made in order to solve the above-described problems, is not easily affected by phase relaxation, and is highly applicable to large-scale quantum computation and has high interaction between two qubits. An object is to obtain an on / off ratio.

A qubit control method according to the present invention includes a first gate operation step in which an auxiliary qubit coupled to each of two qubits is multiplied by one qubit gate to set the auxiliary qubit to a state of | −1> A measurement step for measuring the quantum state of the auxiliary qubit after a predetermined time in which the auxiliary qubit is in a state of | -1> in one gate operation step, and a measurement result in the measurement step after measurement by the measurement step And a second gate operation step of multiplying the auxiliary qubit by one qubit gate to bring the auxiliary qubit into a state of | −1>. In the first gate operation step, one qubit gate is applied in the X direction determined by a Hamiltonian representing a system in which two qubits and auxiliary qubits are combined, and in the measurement step, auxiliary qubits are applied in the Y direction. Measure the quantum state of.

  In the qubit control method, the measurement step may be performed after π / g (g is the Hamiltonian of the auxiliary qubit) after the state of | −1> in the first gate operation step.

  In the qubit control method, the two qubits and the auxiliary qubit are composed of superconducting flux qubits, and in the first gate operation step and the second gate operation step, if the auxiliary qubit is irradiated with resonance microwaves, Good.

  As described above, according to the present invention, a high on / off ratio can be obtained in the interaction between two qubits in a state that is not easily affected by phase relaxation and is applicable to large-scale quantum computation. An excellent effect is obtained.

FIG. 1 is a flowchart for explaining a qubit control method according to an embodiment of the present invention. FIG. 2A is an explanatory diagram illustrating a state in the middle of an operation process by the qubit control method according to the embodiment of the present invention. FIG. 2B is an explanatory diagram illustrating a state in the middle of an operation process by the qubit control method according to the embodiment of the present invention. FIG. 2C is an explanatory diagram illustrating a state in the middle of an operation process by the qubit control method according to the embodiment of the present invention. FIG. 3 is a configuration diagram showing a configuration example of qubits for implementing the qubit control method according to the embodiment of the present invention. FIG. 4 is a configuration diagram showing another configuration example of a qubit for carrying out the qubit control method according to the embodiment of the present invention.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is a flowchart for explaining a qubit control method according to an embodiment of the present invention. In this qubit control method, first, in step S101, the auxiliary qubit coupled to each of the two qubits is multiplied by one qubit gate to bring the auxiliary qubit into a state of | −1> (first gate operation). Step). Here, one qubit gate is multiplied in the X direction determined by a Hamiltonian representing a system in which two qubits and auxiliary qubits are combined. For example, the auxiliary qubit may be irradiated with a microwave having a predetermined intensity. This operation turns on the interaction between the two qubits.

  Next, in step S102, the quantum state of the auxiliary qubit is measured after a predetermined time in which the auxiliary qubit is in the state of | -1> in the first gate operation step (measurement step). Here, the quantum state of the auxiliary qubit is measured in the Y direction determined by a Hamiltonian representing a system in which the two qubits and the auxiliary qubit are combined. This measurement may be performed by measuring the quantum state of the auxiliary qubit after π / g (g is the Hamiltonian of the auxiliary qubit) after the state of | -1> in the first gate operation step. After a time of π / g, a cluster state is generated by three qubits.

  Next, in step S103, based on the measurement result in the measurement in step S102, the auxiliary qubit is multiplied by one qubit gate to bring the auxiliary qubit into a state of | −1> (second gate operation step). For example, the auxiliary quantum bit may be irradiated with a microwave having a predetermined intensity based on the measurement result. The interaction between two qubits is turned off by the above-described measurement and the operation of applying one qubit gate based on the measurement result.

  Hereinafter, the above-described qubit control method will be described in more detail.

  In the present invention, unlike the conventional technique that uses unitary operation, non-unitary projection measurement is performed on the auxiliary qubit to control the interaction between the two qubits. There is a big feature. In the following, for the sake of simplicity, a case where all the interactions between qubits are equal will be described as an example.

  First, a Hamiltonian in a state where two qubits and three qubits of auxiliary qubits are combined can be configured as shown by the following equation (1).

Further, ω ₁ is a Hamiltonian of one qubit, ω ₂ is a Hamiltonian of an auxiliary qubit, and ω ₃ is a Hamiltonian of the other qubit. Further, g ₁₂ is a Hamiltonian for the interaction between one qubit and the auxiliary qubit, and g ₂₃ is a Hamiltonian for the interaction between the auxiliary qubit and the other qubit.

The Hamiltonian H represented by the equation (1) becomes the Hamiltonian H represented by the following equation (2) by corresponding to an appropriate rotating coordinate system. In the Hamiltonian H of the formula (2), g ₁₂ = g ₂₃ = g.

  At this time, it is considered that the interaction between one qubit and the other qubit is controlled by the auxiliary qubit. First, as shown in FIG. 2A, the auxiliary qubit 203 is arranged between the two qubits 201 and 202. In this configuration, if the auxiliary qubit 203 is polarized to a state of | −1> (the eigenvalue of the spin ½ Pauli operator in the auxiliary qubit 203 and the eigenvalue is 1), the Hamiltonian H is 0. Thus, the interaction between the qubit 201 and the qubit 202 is turned off.

  Next, one qubit gate is applied to the auxiliary qubit 203 by irradiating microwaves, for example, so that the auxiliary qubit 203 is in a state represented by the following expression (3). By this operation, as shown in FIG. 2B, the interaction between the qubit 201 and the qubit 202 is turned on.

  Further, when the interaction is turned on, entanglement is generated between the three qubits 201, the auxiliary qubits 203, and the qubits 202. In particular, when a time of t = π / g has elapsed since the operation of applying one qubit gate to the auxiliary qubit 203, a cluster is formed between the three qubits 201, the auxiliary qubit 203, and the qubit 202. A state is generated.

  As described above, after the interaction between the qubit 201 and the qubit 202 is turned on, the quantum state of the auxiliary qubit 203 is measured in the Y direction. Note that one qubit gate is multiplied in the X direction determined by a Hamiltonian representing a system in which two qubits 201, qubit 202 and auxiliary qubit 203 are coupled, and the quantum state of the auxiliary qubit is measured in the Y direction. To do. According to the measurement of the auxiliary qubit 203 in the Y direction described above, between the qubit 201 and the qubit 202, between the two qubits equivalent to the gate “controlled-Z gate” between the two quantum states necessary for the quantum calculation. The gate comes to be configured.

  Here, the measurement in the Y direction of the auxiliary qubit 203 is performed, for example, by using a phase gate S represented by the following formula (4) and an Adamard gate (Hadamard Gate) H represented by the following formula (5): After applying to the auxiliary qubit 203, the projection measurement in the Z direction may be performed. The Z direction is a direction determined by a Hamiltonian representing a system in which two qubits 201, qubits 202, and auxiliary qubits 203 are coupled, as in the X direction and the Y direction described above.

  As described above, after the auxiliary qubit 203 is measured in the Y direction, one qubit gate is applied to the auxiliary qubit 203 by, for example, microwave irradiation based on the measurement result in the measurement, and FIG. As shown, the auxiliary qubit 203 is returned to the state of | −1>. By these operations, as shown in FIG. 2C, the interaction between the qubit 201 and the qubit 202 is turned off.

  As described above, by combining microwave irradiation and measurement in the Y direction (projection measurement), the interaction between two qubits arranged with an auxiliary qubit sandwiched at any timing can be turned on. / Can be turned off.

In the above description, the case where the interaction between qubits is the same has been described. Next, the case where the interaction between qubits is different will be described. In the following description, g ₁₂ > g ₂₃ is assumed. Even if g ₁₂ <g ₂₃ , the same operation is possible.

  First, as shown in FIG. 2A, the auxiliary qubit 203 is arranged between the two qubits 201 and 202. In this configuration, if the auxiliary qubit 203 is polarized to a state of | −1> (the eigenvalue of the spin ½ Pauli operator in the auxiliary qubit 203 and the eigenvalue is 1), the Hamiltonian H is 0. Thus, the interaction between the qubit 201 and the qubit 202 is turned off.

  Next, one qubit gate is applied to the auxiliary qubit 203 by irradiating microwaves, for example, so that the auxiliary qubit 203 is in a state represented by the following expression (6). By this operation, as shown in FIG. 2B, the interaction between the qubit 201 and the qubit 202 is turned on.

  As described above, after the interaction is turned on, after the time indicated by the following expression (7) has elapsed, for example, a spin echo is generated by applying a π pulse by microwave irradiation to the qubit 201. .

  Next, when the time indicated by the following equation (8) has elapsed, the quantum state of the auxiliary qubit 203 is measured in the Y direction. Thereby, a gate between two qubits equivalent to “controlled-Z gate” is configured between the qubit 201 and the qubit 202.

  After measuring the above-described auxiliary qubit 203 in the Y direction, based on the measurement result in the measurement, the auxiliary qubit 203 is multiplied by one qubit gate by, for example, microwave irradiation, and as shown in FIG. The qubit 203 is returned to the state of | −1>. By these operations, as shown in FIG. 2C, the interaction between the qubit 201 and the qubit 202 is turned off.

  As described above, even when the interaction between qubits is different, the interaction can be switched on / off by combining the spin echo of either qubit with the measurement to the auxiliary qubit. Become.

  In the prior art, the method of changing the resonance condition of the qubit to turn on / off the interaction only incompletely, or the number of necessary π pulses increases exponentially as the number of qubits increases. Methods have been used. On the other hand, in the present invention, the number of necessary operations is about the same as the number of qubits, and in principle, the interaction can be completely turned on / off, which is different from the conventional technique. . Also, in the prior art, the interaction is turned on / off using unitary conversion, whereas in the present invention, the interaction is turned on / off using measurement, which is a non-unitary process. Has major features.

  By the way, the qubit may be composed of a superconducting flux qubit as shown in FIG. One qubit 301 composed of a superconducting flux qubit and an auxiliary qubit 303 composed of a superconducting flux qubit, and the auxiliary qubit 303 and the other auxiliary qubit 302 composed of a superconducting flux qubit are connected via a capacitance. Can be combined. In the figure, the Josephson junction is indicated by “x”. FIG. 3 shows a basic configuration. Actually, for example, a qubit is connected to the right side of the qubit 302 via an auxiliary qubit, and a qubit 301 is connected to the left side of the qubit 301 via an auxiliary qubit. By connecting qubits and repeating these, it is possible to construct a set of a plurality of qubits. The same configuration can be made above and below each qubit.

  Further, the detection of the quantum state of the auxiliary qubit 203 can be performed by using Josephson branch amplification (not shown) composed of SQUIDs. For example, the SQUID for Josephson branch amplification may be coupled to the superconducting magnetic flux qubit that becomes the auxiliary qubit 203. In addition, it is only necessary to apply one qubit gate to the auxiliary qubit 203 by irradiating resonance microwaves with a control line (not shown) provided in the vicinity of the auxiliary qubit 203. The control line may be arranged three-dimensionally immediately above or directly below the plane on which each qubit is arranged. The measuring means for detecting the quantum state may be arranged three-dimensionally immediately above or immediately below the plane where each quantum bit is arranged.

  Note that, for example, in the case of such direct coupling, the coupling becomes large (several tens of MHz or more) compared with the case of using a microwave resonator, so that it is necessary in a short time (tens of nanoseconds or less). A gate operation between two qubits is possible.

Here, the Hamiltonian of the superconducting magnetic flux qubit can be expressed by the following equation (9). Here, σ _Z is expressed by Expression (10).

| L> represents a state in which the superconducting permanent current flows counterclockwise, and | R> represents a state in which the superconducting permanent conduction flows clockwise. Since σ _x represents tunneling between these two states, it can be expressed by the following equation (11). When ε is 0, the lifetime of the qubit is maximized. Therefore, a case where ε is 0 is considered here.

  Further, when the Hamiltonian is diagonalized, it can be expressed by Expression (12).

  At this time, a Hamiltonian representing a microwave for applying one qubit gate can be expressed by the following equation (13).

Here, λ _t represents the strength of the microwave, and φ represents the phase of the microwave. When the qubit is not rotated, λ _{t is set} to 0. When rotating the qubit, the value of λ _t is set to a value (several times to several tens of times) sufficiently larger than both the difference frequency Δ−ω and the coupling constant g. Rotation can be controlled.

  When riding on the rotating coordinate system, the Hamiltonian can be rewritten as the following equation (14). The qubits 301, qubits 302, and auxiliary qubits 303 composed of such superconducting magnetic flux qubits may be arranged as shown in FIG.

  Here, the interaction represented by the following equation (15) is applied between adjacent qubits such as between the qubit 301 and the auxiliary qubit 303 or between the auxiliary qubit 303 and the qubit 302. To do.

  Such a Hamiltonian can be configured by, for example, controlling ε to 0 by controlling an external magnetic field and coupling the superconducting flux qubits via a capacitance. Alternatively, if the value of Δ is sufficiently smaller than ε, a similar Hamiltonian can be configured even when the superconducting flux qubits are magnetically coupled.

  By interposing a superconducting flux qubit serving as an auxiliary qubit between superconducting flux qubits used in quantum computation, it becomes possible to control the interaction between the superconducting flux qubits.

  Specifically, when the interaction is not applied, the state of the auxiliary qubit is polarized to | −1>. When an interaction is to be applied between two qubits, the auxiliary qubit between the two qubits is first irradiated with a resonance microwave to generate a state of | +>. Thereafter, as described above, a π pulse that causes a spin echo is applied to one of the two qubits, and then the quantum state of the auxiliary qubit is measured in the Y direction. Thereafter, the interaction between the two qubits can be turned off again by returning the quantum state of the auxiliary qubits to | −1> by microwave irradiation based on the measurement results.

  As described above, a gate between two qubits equivalent to “controlled-Z gate” can be configured. If such a “controlled-phase” gate can be configured on a two-dimensional arrangement, an arbitrary quantum algorithm can be executed by a method called “one-way quantum computer” (see Non-Patent Document 3).

  For example, as shown in the plan view of FIG. 4, two qubits 401, qubits 402, and auxiliary qubits 403 made of superconducting flux qubits are arranged in a matrix and adjacent qubits are arranged. May be combined. In FIG. 4, the Josephson junction is indicated by “x”.

  As described above, in the present invention, the auxiliary qubit coupled to each of the two qubits is used, the operation of applying one qubit gate to the auxiliary qubit, and the state of the auxiliary qubit in the Y direction. The interaction between the two qubits is turned on / off by the measurement operation and the operation of applying one qubit gate to the auxiliary qubit based on the measurement result. In a state that is difficult to receive and applicable to large-scale quantum computation, a high on / off ratio can be obtained in the interaction between two qubits.

  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.

  201, 202 ... qubits, 203 ... auxiliary qubits.

Claims (3)

A first gate operation step of multiplying an auxiliary qubit coupled to each of the two qubits by one qubit gate to place the auxiliary qubit in a state of | −1>;
A measurement step of measuring a quantum state of the auxiliary qubit after a predetermined time in which the auxiliary qubit is in a state of | -1> in the first gate operation step;
After the measurement in the measurement step, a second gate operation step in which a single qubit gate is applied to the auxiliary qubit based on the measurement result in the measurement step so that the auxiliary qubit is in a state of | −1>. With
In the first gate operation step, one qubit gate is applied in the X direction determined by a Hamiltonian representing a system in which the two qubits and the auxiliary qubit are combined, and in the measurement step, the qubit is operated in the Y direction. A method of controlling a qubit characterized by measuring a quantum state of an auxiliary qubit. The qubit control method according to claim 1,
The qubit control method is characterized in that the measurement step is performed after π / g (g is a Hamiltonian of the auxiliary qubit) after the state of | -1> in the first gate operation step. The qubit control method according to claim 1 or 2,
The two qubits and the auxiliary qubit are composed of superconducting flux qubits,
In the first gate operation step and the second gate operation step, the auxiliary qubit is irradiated with a resonance microwave.

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