Quantum state display device and game

Abstract

The operation of quantum gates and the results of their execution are visually displayed on a Bloch sphere. [Solution] The quantum state display device 1, which displays a single quantum state on a spherical surface, comprises a spherical surface 11, a display unit 12 including a plurality of display points arranged on the spherical surface 11, an input unit 13, and a control unit 14 that controls the display unit 12. Each display point on the display unit 12 represents the quantum state of a qubit. The input unit 13 is configured to allow the user to input a desired single quantum gate. When a single quantum gate is input to the input unit 13, the control unit 14 controls the display unit 12 to display a display point corresponding to the result of executing the single quantum gate on the qubit.

Description

[Technical Field]

[0001] This invention relates to a quantum state display device and a game. [Background technology]

[0002] The Bloch sphere is known as a visual representation of quantum states. Figure 1 is a perspective view of the Bloch sphere. The Bloch sphere is a sphere with radius 1 centered at the origin, with its north pole (0,0,1) corresponding to the qubit |0> and its south pole (0,0,-1) corresponding to the qubit |1>.

[0003] Any quantum state |Ψ> of a single qubit is a superposition of two quantum states |0> and |1>. |Ψ>=α|0>+β|1> (1) It can be expressed as follows. However, as a standardization condition |α| 2 +|β| 2 =1 (2) Let's assume that. Furthermore, as a generalization of this,

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[0004] The basic operations performed on a quantum computer are called quantum gates. A single quantum gate for a single qubit can be thought of as a transformation that maps one point on the Bloch sphere to another.

[0005] As a method for representing qubits intuitively, a computer implementation method has been disclosed that determines a point on the Bloch sphere, that is, converts the above (θ, φ) values ​​into variables in the sensory output space (see, for example, Patent Document 1). [Prior art documents] [Patent Documents]

[0006] [Patent Document 1] Special Publication Special Publication No. 2022-544371 [Overview of the Initiative] [Problems that the invention aims to solve]

[0007] Conventionally, the state of a qubit has been represented by a vector (arrow) on a Bloch sphere plotted on a two-dimensional plane. In contrast, no technology has yet been disclosed that displays the state of a qubit by emitting light from a display point on the surface of a three-dimensional sphere.

[0008] Furthermore, even if the method disclosed in Patent Document 1 can intuitively represent a predetermined quantum state as a point on the Bloch sphere, it only statically represents a uniquely determined quantum state. In other words, this method cannot dynamically represent the operation of a quantum gate.

[0009] This invention was made in view of these problems, and its purpose is to visually display the operation of quantum gates and the results of their execution on a Bloch sphere. [Means for solving the problem]

[0010] To solve the above problems, a quantum state display device according to one aspect of the present invention is a quantum state display device that displays a single quantum state on a spherical surface. This device comprises a spherical surface, a display unit including a plurality of display points arranged on the spherical surface, an input unit, and a control unit that controls the display unit. Each display point on the display unit represents the quantum state of a qubit. The input unit is configured to allow a user to input a desired single quantum gate. When a single quantum gate is input to the input unit, the control unit controls the display unit to display a display point corresponding to the result of executing the single quantum gate on the qubit.

[0011] According to this embodiment, the operation of a single quantum gate and the result of its execution can be visually displayed on a Bloch sphere.

[0012] In one embodiment, the input unit may be configured to allow the user to input a desired quantum state. In this case, when a quantum state is input to the input unit, the control unit controls the display unit to display a display point corresponding to that quantum state of the qubit.

[0013] In one embodiment, the display unit may include at least two display points. In this case, these two display points lie on the same great circle of the aforementioned sphere and are symmetrical with respect to the center of the sphere. In this case, the single quantum gate input to the input unit may include a Pauli X gate, a Pauli Y gate, a Pauli Z gate, an S gate, or a T gate.

[0014] In one embodiment, the display unit may include at least four display points. In this case, these four display points lie on the same great circle of the aforementioned sphere and are symmetrical with respect to the center of the sphere. In this case, the single quantum gate input to the input unit may include a Pauli X gate, a Pauli Y gate, a Pauli Z gate, and a T gate.

[0015] In one embodiment, the display unit may include at least six display points. In this case, these six display points are located on two orthogonal great circles of the aforementioned sphere and are symmetrical with respect to the center of the sphere. In this case, the single quantum gate input to the input unit may include an Hadamard gate, a Pauli X gate, a Pauli Y gate, a Pauli Z gate, an S gate, or a T gate.

[0016] In one embodiment, the display point may represent a quantum state by emitting light.

[0017] In one embodiment, when a single-qubit gate is input to the input unit, the control unit may control the display unit to dynamically represent the operation state of the single-qubit gate by continuously displaying intermediate display points from the currently displayed display point to the display point corresponding to the result of executing the single-qubit gate.

[0018] The quantum state display device according to an embodiment may further include a phase factor display unit. In this case, when a single-qubit gate is input to the input unit, the phase factor display unit displays a phase factor or an eigenvalue obtained when the single-qubit gate is executed on a qubit.

[0019] Another aspect of the present invention is also a quantum state display device. This device is a quantum state display device that displays two quantum states on a spherical surface. This device includes a first spherical surface, a second spherical surface, a first display unit including a plurality of display points arranged on the first spherical surface, a second display unit including a plurality of display points arranged on the second spherical surface, an input unit, and a control unit that controls the first display unit and the second display unit. Each display point of the first display unit represents the quantum state of the first qubit. Each display point of the second display unit represents the quantum state of the second qubit. The input unit is configured to allow a user to input a desired two-qubit gate. When a two-qubit gate is input to the input unit, the control unit controls the first display unit and the second display unit to display the display points corresponding to the result of executing the two-qubit gate on the first qubit and the second qubit.

[0020] According to this aspect, the operation state of the two-qubit gate and the execution result of the two-qubit gate can be visually displayed on the Bloch sphere.

[0021] In one embodiment, the two-qubit gate input to the input unit may include a controlled-Z gate, a controlled-NOT gate, or a swap gate.

[0022] Another aspect of the present invention is also a quantum state display device. This device is a quantum state display device that displays a quantum entanglement state on a sphere. This device comprises a first sphere, a second sphere, a first display unit including a plurality of display points arranged on the first sphere, a second display unit including a plurality of display points arranged on the second sphere, an input unit, and a control unit that controls the first display unit and the second display unit. Each display point of the first display unit represents the quantum state of a first qubit. Each display point of the second display unit represents the quantum state of a second qubit. The input unit is configured to accept a quantum entanglement display command. When a quantum entanglement display is input to the input unit, the control unit controls the first display unit and the second display unit so that each display point of the first display unit and each display point of the second display unit represents the quantum entanglement state of a first qubit and a second qubit.

[0023] According to this embodiment, the quantum entanglement state between two qubits can be visually represented on a Bloch sphere.

[0024] In one embodiment, the input unit may be configured to allow the user to input a measurement command while quantum entanglement is being displayed. In this case, when a measurement command is input to the input unit, the control unit controls the first display unit and the second display unit to randomly display one of the possible states of the first qubit and the second qubit.

[0025] Another aspect of the present invention is also a quantum state display device. This device is a quantum state display device that displays three quantum states on a sphere, and comprises a first sphere, a second sphere, a third sphere, a first display unit including a plurality of display points arranged on the first sphere, a second display unit including a plurality of display points arranged on the second sphere, a third display unit including a plurality of display points arranged on the third sphere, an input unit, and a control unit that controls the first display unit, the second display unit, and the third display unit. Each display point of the first display unit represents the quantum state of a first qubit. Each display point of the second display unit represents the quantum state of a second qubit. Each display point of the third display unit represents the quantum state of a third qubit. The input unit is configured to allow a user to input a desired three quantum gates. When a 3-quantum gate is input to the input unit, the control unit controls the first display unit, the second display unit, and the third display unit to display display points corresponding to the result of executing the 3-quantum gate on the first qubit, the second qubit, and the third qubit.

[0026] According to this embodiment, the operation of the three quantum gates and the results of their execution can be visually displayed on a Bloch sphere.

[0027] In one embodiment, the three quantum gates input to the input section may include a Toffoli gate.

[0028] Another aspect of the present invention is also a quantum state display device. This device is a quantum state display device that displays quantum teleportation on a sphere. This device comprises a first sphere, a second sphere, a third sphere, a first display unit including a plurality of display points arranged on the first sphere, a second display unit including a plurality of display points arranged on the second sphere, a third display unit including a plurality of display points arranged on the third sphere, an input unit, and a control unit that controls the first display unit, the second display unit, and the third display unit. Each display point on the first display unit represents a quantum state to be transferred to the receiver. Each display point on the second display unit represents a quantum state owned by the sender. Each display point on the third display unit represents a quantum state owned by the receiver. The input unit is configured to allow a user to input a quantum teleportation operation. When a quantum teleportation operation is input to the input unit, the control unit controls the first display unit, the second display unit, and the third display unit to represent the state when the quantum teleportation is performed.

[0029] According to this embodiment, the process of performing quantum teleportation can be visually displayed on a Bloch sphere.

[0030] In one embodiment, the input unit is configured to accept inputs of the quantum state that the sender wants to transmit, a first quantum entanglement display command, a second quantum entanglement display command, a measurement command, and a quantum gate corresponding to the measurement result. The control unit is configured to accept inputs of: When the sender inputs a quantum state they wish to transmit, the first display unit displays the quantum state to be transmitted, the second display unit displays the state |0>, and the third display unit displays the state |0>, thereby controlling the first, second, and third display units. When the first quantum entanglement display command is input to the input section, the second and third display sections are controlled so that each display point in the second display section and each display point in the third display section represent the quantum entanglement state between the second and third qubits. When a second quantum entanglement display command is input to the input section, the first, second, and third display sections are controlled so that each display point of the first, second, and third display sections represents the quantum entanglement state between the first, second, and third qubits. When a measurement command is input to the input unit, the first display unit, the second display unit, and the third display unit are controlled to randomly display one of the possible states of the first qubit, the second qubit, and the third qubit. When a quantum gate corresponding to the measurement result is input to the input unit, the third display unit is controlled so that it displays the quantum state that the sender wanted to transmit.

[0031] In one embodiment, the quantum gate corresponding to the measurement result is • If the measurement results show that the quantum state of the first qubit is |0> and the quantum state of the second qubit is |0>, then it is the identity operator. • If the measurement results show that the quantum state of the first qubit is |0> and the quantum state of the second qubit is |1>, then it is a Pauli X gate. • If the measurement results show that the quantum state of the first qubit is |1> and the quantum state of the second qubit is |0>, then it is a Pauli Z gate. If the measurement results show that the quantum state of the first qubit is |1> and the quantum state of the second qubit is |1>, then it may be a Pauli Y gate.

[0032] In one embodiment, the display point may represent a quantum state through mechanical movement by a three-axis rotation mechanism.

[0033] Another aspect of the present invention is a game, comprising pieces for each player and items, each corresponding to a plurality of quantum gates. Each piece can take on a plurality of states corresponding to a quantum state represented as a point on a Bloch sphere, and when an item acts on a piece, it changes the state of the piece according to the operation rules of the quantum gates.

[0034] In this configuration, players can understand the operation of quantum gates and the results of their execution while enjoying the game.

[0035] Furthermore, any combination of the above components, as well as conversions of the expression of the present invention between devices, methods, systems, recording media, computer programs, etc., are also valid embodiments of the present invention. [Effects of the Invention]

[0036] According to the present invention, the operation of a quantum gate and the results of its execution can be visually displayed on a Bloch sphere. [Brief explanation of the drawing]

[0037] [Figure 1] This is a perspective view of the Bloch sphere. [Figure 2] This is a schematic diagram of a quantum state display device according to the first embodiment. [Figure 3] This is a diagram showing a typical single-quantum gate. [Figure 4] This is a schematic diagram of a quantum state display device whose display unit consists of two display points. [Figure 5] This is a schematic diagram of a quantum state display device whose display unit consists of four display points. [Figure 6] This is a schematic diagram of a quantum state display device whose display unit consists of six display points. [Figure 7] This diagram shows the display when a Pauli Y gate is input to the input terminal, with the currently displayed points being (0, 0, 1). [Figure 8] This diagram shows the display when an Adamard gate is input to the input field, with the currently displayed point being (0, 0, 1). [Figure 9] This diagram shows the display when an S gate is input to the input, with the currently displayed point being (1, 0, 0). [Figure 10] This is a schematic diagram of a quantum state display device equipped with a phase factor display unit. [Figure 11] This diagram shows the display unit and phase factor display unit when a Pauli Z gate is input to the input, with the currently displayed point being (0, 0, 1). [Figure 12] This diagram shows the display unit and phase factor display unit when a Pauli Z gate is input to the input terminal, with the currently displayed points being (0, 0, -1). [Figure 13] This diagram shows the display unit and phase factor display unit when a T gate is input to the input, with the currently displayed points being (0, 0, -1). [Figure 14] This figure shows the display unit and phase factor display unit 15 when a Pauli X gate is input to the input unit, with the currently displayed point being (0, 0, 1). [Figure 15] This diagram shows the display unit and phase factor display unit when a Pauli Y gate is input to the input terminal, with the currently displayed point being (0, 0, 1). [Figure 16] This figure shows the display unit 12 and the phase factor display unit 15 when an Adamard gate is input to the input unit, with the currently displayed point being (0, 1, 0). [Figure 17] This is a schematic diagram of a quantum state display device according to a second embodiment. [Figure 18] This diagram shows a typical two-quantum gate. [Figure 19] This diagram shows the state of the first and second display units when a controlled NOT gate is input to the input unit, with the currently displayed points of the first display unit being (0, 0, -1) and the second display unit being (0, 0, 1). [Figure 20] This diagram shows the state of the first and second display units when a replacement gate is input to the input unit, with the currently displayed point of the first display unit being (0, 0, -1) and the display point of the second display unit 24 being (0, 0, 1). [Figure 21] This diagram shows a quantum circuit that generates quantum entanglement. [Figure 22]This is a schematic diagram illustrating the sequence of operations of a quantum state display device in its initial state |00>. [Figure 23] This is a schematic diagram illustrating the sequence of operations of the quantum state display device in its initial state |01>. [Figure 24] This is a schematic diagram illustrating the sequence of operations of a quantum state display device in its initial state |10>. [Figure 25] This is a schematic diagram illustrating the sequence of operations of the quantum state display device in its initial state |11>. [Figure 26] This is a schematic diagram of a quantum state display device according to the fourth embodiment. [Figure 27] This diagram shows three typical quantum gates. [Figure 28] This diagram shows the state of the first, second, and third display units when a Toffoli gate is input to the input unit, with the currently displayed points of the first display unit being (0, 0, -1), the second display unit being (0, 0, -1), and the third display unit being (0, 0, 1). [Figure 29] This diagram shows a quantum circuit that enables quantum teleportation. [Figure 30] This is a flowchart showing the procedure for representing quantum teleportation using the quantum state display device of the fifth embodiment. [Figure 31] This figure shows the state of the first sphere, the second sphere, and the third sphere when the process in step S2 is executed. [Figure 32] This figure shows the state of the first sphere, the second sphere, and the third sphere when the process in step S4 is executed. [Figure 33] This figure shows the state of the first sphere, the second sphere, and the third sphere when the process in step S6 is executed. [Figure 34] This figure shows the state of the first sphere, the second sphere, and the third sphere when the process in step S8 is executed. [Figure 35] This figure shows the state of the first sphere, the second sphere, and the third sphere when the process in step S10 is executed. [Figure 36] This diagram shows which quantum gate should be executed on the third qubit, depending on the measurement result in step S7. [Figure 37] This is a schematic diagram of the game according to the sixth embodiment. [Figure 38] This diagram shows an image of the LED display that makes up a Bloch sphere. [Modes for carrying out the invention]

[0038] The present invention will be described below with reference to the drawings, based on preferred embodiments. The embodiments are illustrative and not limiting, and not all features or combinations thereof described in the embodiments are necessarily essential to the invention. The same or equivalent components, members, and processes shown in each drawing are denoted by the same reference numerals, and redundant explanations are omitted as appropriate. Furthermore, the scale and shape of each part shown in each drawing are set for convenience to facilitate explanation and are not to be interpreted restrictively unless otherwise specified. In addition, when terms such as "first," "second," etc. are used in this specification or claims, unless otherwise specified, these terms do not indicate any order or importance, but are merely for distinguishing one configuration from another. Furthermore, some components that are not important for explaining the embodiments are omitted from the drawings.

[0039] [First Embodiment] Figure 2 is a schematic diagram of a quantum state display device 1 according to the first embodiment. The quantum state display device 1 comprises a sphere 11, a display unit 12, an input unit 13, and a control unit 14.

[0040] As an example, sphere 11 is the Bloch sphere shown in Figure 1. That is, sphere 11 is a unit sphere with radius 1 centered at the origin. If we take a Cartesian coordinate system as shown in Figure 2, then each quantum state of a single qubit |0>, |1>, |+>, |->, |i>, and |-i> can be associated with each point on sphere 11, as follows. Quantum state |0> ⇔ point (0, 0, 1) Quantum state |1> ⇔ point (0, 0, -1) Quantum state |+> ⇔ point (1, 0, 0) Quantum state |-> ⇔ point (-1, 0, 0) Quantum state |i> ⇔ point (0, 1, 0) Quantum state |-i> ⇔ point (0, -1, 0)

[0041] The display unit 12 includes a plurality of display points arranged on the spherical surface 11. In the example shown in Figure 2, the display unit 12 includes six display points: display point 12a, display point 12b, display point 12c, display point 12d, display point 12e, and display point 12f. In this case, display point 12a is located at point (0, 0, 1), display point 12b at (0, 0, -1), display point 12c at (1, 0, 0), display point 12d at (-1, 0, 0), display point 12e at (0, 1, 0), and display point 12f at (0, -1, 0). In other words, display point 12a corresponds to the quantum state |0>, display point 12b to the quantum state |1>, display point 12c to the quantum state |+>, display point 12d to the quantum state |->, display point 12e to the quantum state |i>, and display point 12f to the quantum state |-i>.

[0042] Each display point on the display unit 12 represents the quantum state of a qubit. That is, when a qubit is in the quantum state corresponding to a certain display point, that display point visually represents it.

[0043] The display points 12a to 12f may be composed of LEDs, for example. In this case, each LED may represent a quantum state by being lit or blinking. For example, when the qubit is in the quantum state |0>, LED 12a lights up or blinks, and LEDs 12b to 12f are off. Or, when the qubit is in the quantum state |-i>, LED 12f lights up or blinks, and LEDs 12a to 12e are off, and so on.

[0044] The method of displaying the display points is not limited to illumination, blinking, or extinguishing; for example, the quantum state may be represented by changing the color, brightness, saturation, etc. Alternatively, the display method may not be by light emission, but rather by a physical entity such as a small sphere moving on the spherical surface 11, and the quantum state may be represented by the position where this physical entity remains. Thus, the method of displaying the display points can be any suitable method as long as it can visually represent which position on the spherical surface 11 corresponds to the quantum state of the qubit.

[0045] The input unit 13 accepts input from the user. That is, the input unit 13 is configured to allow the user to input a single quantum gate of their choice. Specifically, the input unit 13 may display a list of single quantum gates, such as the Hadamard gate, Pauli X gate, and Pauli Z gate, and the user may be able to select a desired single quantum gate from this list.

[0046] When the input unit 13 receives input from the user, it transmits the content of that input as an input signal to the control unit 14.

[0047] When the control unit 14 receives an input signal from the input unit 13, it transmits a control signal to the display unit 12. Using this control signal, the control unit 14 controls the display unit 12 to display a display point corresponding to the result of executing one quantum gate included in the input signal on the qubit of the quantum state currently displayed on the display unit 12.

[0048] For example, as shown in equation (4) below, when a Pauli X gate is executed on a qubit in the quantum state |0>, the quantum state changes to |1>. X|0>=|1> (4)

[0049] When this quantum gate operation is represented by the quantum state display device 1, if the display point 12a (position (0,0,1) on the sphere 11) is lit or blinking (corresponding to quantum state |0>), and the user inputs a Pauli X gate to the input unit 13, the display point 12a turns off, and instead the display point 12b (position (0,0,-1) on the sphere 11) lights up or blinks (corresponding to quantum state |1>).

[0050] This allows the user to visually understand that when a Pauli X gate is executed on a qubit in the quantum state |0>, the quantum state changes to |1>.

[0051] Figure 3 shows representative single-quantum gates. Specifically, Figure 3 shows the symbols and 2x2 matrix representations for six types of single-quantum gates: the Hadamard gate, Pauli X gate, Pauli Y gate, Pauli Z gate, S gate (also called a phase gate), and T gate (also called a π / 8 gate).

[0052] In this specification, following convention, the quantum states |0> and |1> are defined as the basis. These quantum states |0> and |1> are eigenstates of the Pauli Z gate, as follows. Z|0>=|0> (5) Z|1>=-|1> (6) In other words, when the Pauli Z gate is executed on the quantum state |0>, the quantum state remains |0> and an eigenvalue of 1 is obtained. Similarly, when the Pauli Z gate is executed on the quantum state |1>, the quantum state remains |1> and an eigenvalue of -1 is obtained.

[0053] Quantum states |+> and |-> are,

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[0054] The quantum states |i> and |-i> are,

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[0055] The results of applying the Hadamard gate (H) to each quantum state |0>, |1>, |+>, |->, |i>, and |-i> are as follows: H|0>=|+> (15) H|1>=|-> (16) H|+>=|0> (17) H|->=|1> (18) H|i>=e iπ / 4 |-i> (19) H|-i>=e -iπ / 4 |i> (20)

[0056] The results of applying the Pauli X gate (X) to each quantum state |0>, |1>, |+>, |->, |i>, and |-i> are as follows: X|0>=|1> (21) X|1>=|0> (22) X|+>=|+> (23) X|->=-|-> (24) X|i>=i|-i> (25) X|-i>=-i|i> (26)

[0057] The results of applying the Pauli Y gate (Y) to each quantum state |0>, |1>, |+>, |->, |i>, and |-i> are as follows: Y|0>=i|1> (27) Y|1>=-i|0> (28) Y|+>=-i|-> (29) Y|->=i|+> (30) Y|i>=|i> (31) Y|-i>=-|-i> (32)

[0058] The results of applying the Pauli Z gate (Z) to each quantum state |0>, |1>, |+>, |->, |i>, and |-i> are as follows: Z|0>=|0> (33) Z|1>=-|1> (34) Z|+>=|-> (35) Z|->=|+> (36) Z|i>=|-i> (37) Z|-i>=|i> (38)

[0059] The results of applying the S gate (S) to each quantum state |0>, |1>, |+>, |->, |i>, and |-i> are as follows: S|0>=|0> (39) S|1>=i|1> (40) S|+>=|i> (41) S|->=|-i> (42) S|i>=|+> (43) S|-i>=|-> (44)

[0060] The results of applying the T gate (T) to each quantum state |0>, |1>, |+>, |->, |i>, and |-i> are as follows: T|0>=|0> (45) T|1>=e iπ / 4|1> (46)

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[0061] One special quantum gate is the identity operator I. When the identity operator is applied to any quantum state |Ψ>, the quantum state remains unchanged as |Ψ>, and the eigenvalue 1 is obtained. I|Ψ>=|Ψ> In other words, the identity operator I is a quantum gate that "does nothing".

[0062] As an example of this embodiment, Figure 4 is a schematic diagram of a quantum state display device 1a in which the display unit 12 is composed of two display points 12a and 12b. However, to avoid complexity, the input unit and control unit are omitted from the illustration. The display points 12a and 12b are located at the points (0, 0, 1) and (0, 0, -1) on the sphere 11, respectively. That is, the display points 12a and 12b represent the quantum states |0> and |1>, respectively.

[0063] In the example in Figure 4, the display points 12a and 12b correspond to the North and South Poles of the sphere 11, respectively. That is, the two display points 12a and 12b are located on the same great circle (on a single meridian circle in the example in Figure 4) of the sphere 11, and are symmetrical with respect to the center O of the sphere.

[0064] The quantum state display device 1a can, for example, represent the operation of a single quantum gate that causes a transformation between quantum states |0> and |1>. As shown in equations (21), (22), (27), (28), (29), (33), (34), (39), (40), (45), and (46), such transformations are realized by Pauli X gates, Pauli Y gates, Pauli Z gates, S gates, or T gates. That is, the single quantum gate input to the input of the quantum state display device 1a may include Pauli X gates, Pauli Y gates, Pauli Z gates, S gates, or T gates.

[0065] According to this embodiment, the operation of one quantum gate and the result of the execution of one quantum gate can be visually displayed on the Bloch sphere using two display points.

[0066] As another example of this embodiment, Figure 5 is a schematic diagram of a quantum state display device 1b in which the display unit 12 is composed of four display points 12a, 12b, 12c, and 12d. However, to avoid complexity, the input unit and control unit are omitted from the illustration. The display points 12a, 12b, 12c, and 12d are located at the points (0, 0, 1), (0, 0, -1), (1, 0, 0), and (-1, 0, 0) on the sphere 11, respectively. That is, the display points 12a, 12b, 12c, and 12d represent the quantum states |0>, |1>, |+>, and |->, respectively.

[0067] In the example in Figure 5, the display points 12a, 12b, 12c, and 12d correspond to the North Pole, South Pole, point at 0 degrees longitude on the equator, and point at 180 degrees longitude on the equator, respectively, on the sphere 11. That is, the four display points 12a, 12b, 12c, and 12d are each located on the same great circle (on a single meridian circle in the example in Figure 4) of the sphere 11, and are symmetrical with respect to the center O of the sphere.

[0068] The quantum state display device 1b can, for example, represent the operation of a single quantum gate that causes a transformation between quantum states |0>, |1>, |+>, and |->. As shown in equations (15), (16), (17), (18), (21), (22), (23), (24), (27), (28), (29), (30), (33), (34), (35), (36), (45), (46), (47), and (48), such transformations are realized by Hadamard gates, Pauli X gates, Pauli Y gates, Pauli Z gates, or T gates. That is, the single quantum gate input to the input of the quantum state display device 1a may include Hadamard gates, Pauli X gates, Pauli Y gates, Pauli Z gates, or T gates.

[0069] According to this embodiment, the operation of one quantum gate and the result of executing one quantum gate can be visually displayed on the Bloch sphere using four display points.

[0070] As yet another example of this embodiment, Figure 6 is a schematic diagram of a quantum state display device 1c in which the display unit 12 is composed of six display points 12a, 12b, 12c, 12d, 12e, and 12f. However, to avoid complexity, the input unit and control unit are omitted from the illustration. The display points 12a, 12b, 12c, 12d, 12e, and 12f are located at the points (0, 0, 1), (0, 0, -1), (1, 0, 0), (-1, 0, 0), (0, 1, 0), and (0, -1, 0) on the sphere 11, respectively. That is, the display points 12a, 12b, 12c, and 12d represent the quantum states |0>, |1>, |+>, |->, |i>, and |-i>, respectively.

[0071] In the example in Figure 6, the display points 12a, 12b, 12c, 12d, 12e, and 12f correspond to the North Pole, South Pole, point at 0 degrees longitude on the equator, point at 180 degrees longitude on the equator, point at 90 degrees east longitude on the equator, and point at 90 degrees west longitude on the equator, respectively, on the sphere 11. That is, the six display points 12a, 12b, 12c, 12d, 12e, and 12f are located on two orthogonal great circles of the sphere 11 (on one meridian circle and on the equator in the example in Figure 4), and are symmetrical with respect to the center O of the sphere.

[0072] The quantum state display device 1c can, for example, represent the operation of a single quantum gate that causes a transformation between quantum states |0>, |1>, |+>, |->, |i>, and |-i>. As shown in equations (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49), (50), such transformations can be realized using Hadamard gates, Pauli X gates, Pauli Y gates, Pauli Z gates, S gates, or T gates. In other words, the single quantum gate input to the input section of the quantum state display device 1a may include an Adamard gate, a Pauli X gate, a Pauli Y gate, a Pauli Z gate, an S gate, or a T gate.

[0073] According to this embodiment, the operation of one quantum gate and the execution result of one quantum gate can be visually displayed on the Bloch sphere using six display points.

[0074] In the above embodiment, the input unit 13 was configured to accept a single quantum gate desired by the user as input from the user. The input unit 13 may also be configured to accept a desired quantum state as input. In this case, when a quantum state is input to the input unit 13, the control unit 14 may control the display unit 12 to display a display point corresponding to that quantum state of the qubit.

[0075] Since the input unit 13 is configured to accept a desired quantum state, the user can specify the initial state of their desired single quantum state and then visually understand how the quantum state changes when a single quantum gate is executed on it.

[0076] In another embodiment of this design, when a single quantum gate is input to the input unit 13, the control unit 14 may control the display unit to dynamically represent the operation of the single quantum gate by continuously illuminating intermediate display points from the currently displayed point to the display point corresponding to the result of executing the single quantum gate.

[0077] Figure 7 shows the state of the display unit 12 when a Pauli Y gate is input to the input unit 13, with the currently displayed display point 12a1 being (0, 0, 1) (i.e., the initial state being |0>). In this example, the display unit 12 is assumed to have multiple display points on the meridian around the y-axis.

[0078] The Pauli Y gate corresponds to rotating a point on the Bloch sphere by π about the y-axis. Therefore, when the Pauli Y gate is executed on the quantum state |0>, the quantum state changes to |1> (see equation (27)). This transition of quantum states can be represented on the spherical surface 11 of the quantum state display device 1 by moving from point (0,0,1) along the meridian about the y-axis to point (0,0,-1).

[0079] In the example shown in Figure 7, when a Pauli Y gate is input to the input unit 13, the control unit 14 controls the display unit 12 to illuminate the display points 12a2, 12a3, 12a4, and 12a5 in succession, starting from the currently displayed display point 12a1, and finally illuminating the display point 12a6 (i.e., point (0, 0, -1)). This allows the operation of the Pauli Y gate to be dynamically represented.

[0080] Figure 8 shows the state of the display unit 12 when an Adamard gate is input to the input unit 13, with the currently displayed display point 12b1 being (0, 0, 1) (i.e., the initial state being |0>). In this example, the display unit 12 is assumed to have multiple display points on a great circle around a rotation axis AX1 located midway between the x and z axes (i.e., the straight line (x, y, z) = t(1, 0, 1), where t is a parameter).

[0081] The Hadamard gate corresponds to rotating a point on the Bloch sphere by π around axis AX1. Therefore, when the Hadamard gate is applied to the quantum state |0>, the quantum state changes to |+> (see equation (15)). This transition of quantum states can be represented on the spherical surface 11 of the quantum state display device 1 by moving from point (0,0,1) along a great circle around the rotation axis AX1 to point (1,0,0).

[0082] In the example shown in Figure 8, when an Adamard gate is input to the input unit 13, the control unit 14 controls the display unit 12 to illuminate the display points 12b2, 12b3, 12b4, and 12b5 in succession, starting from the currently displayed display point 12b1, and finally illuminating the display point 12b6 (i.e., the point (1, 0, 0)). This allows the operation of the Adamard gate to be dynamically represented.

[0083] Figure 9 shows the state of the display unit 12 when an S gate is input to the input unit 13, with the currently displayed display point 12c1 being (1, 0, 0) (i.e., the initial state being |+>). In this example, the display unit 12 is assumed to have multiple display points on the equator (i.e., on a great circle around the z axis).

[0084] The S gate corresponds to rotating a point on the Bloch sphere around the z-axis by π / 2. Therefore, when the S gate is executed on the quantum state |+>, the quantum state changes to |i> (see equation (41)). This transition of quantum states can be represented on the spherical surface 11 of the quantum state display device 1 by moving from point (1, 0, 0) along the equator to point (0, 1, 0).

[0085] In the example shown in Figure 9, when an S gate is input to the input unit 13, the control unit 14 controls the display unit 12 to illuminate the display points 12c2, 12c3, 12c4, and 12c5 in succession, starting from the currently displayed display point 12c1, and finally illuminating the display point 12c6 (i.e., point (0, 1, 0)). This allows the operation of the S gate to be dynamically represented.

[0086] In yet another embodiment of this design, the quantum state display device may further include a phase factor display unit. In this case, when a single quantum gate is input to the input unit, the phase factor display unit displays the phase factor or eigenvalue obtained when the single quantum gate is executed on the qubit.

[0087] Figure 10 is a schematic diagram of a quantum state display device 2 equipped with a phase factor display unit 15. The quantum state display device 2 includes the phase factor display unit 15 in addition to the configuration of the quantum state display device 1 shown in Figure 2. The other configurations of the quantum state display device 2 are the same as those of the quantum state display device 1.

[0088] Figure 11 shows the display unit 12 and the phase factor display unit 15 when a Pauli Z gate is input to the input unit 13, with the currently displayed point being (0, 0, 1) (i.e., the initial state being |0>).

[0089] As shown in equation (33), the quantum state |0> is an eigenstate of the Pauli Z gate, and its eigenvalue is 1. Therefore, when the Pauli Z gate is executed on the initial state |0>, the quantum state remains unchanged as |0>, and the display point also remains (0, 0, 1). On the other hand, the phase factor display unit 15 displays the eigenvalue 1.

[0090] Figure 12 shows the display unit 12 and the phase factor display unit 15 when a Pauli Z gate is input to the input unit 13, with the currently displayed points being (0, 0, -1) (i.e., the initial state being |1>).

[0091] As shown in equation (34), the quantum state |1> is an eigenstate of the Pauli Z gate, and its eigenvalue is -1. Therefore, when the Pauli Z gate is executed on the initial state |1>, the quantum state remains unchanged as |1>, and the display point also remains (0, 0, -1). On the other hand, the phase factor display unit 15 displays the eigenvalue -1.

[0092] Figure 13 shows the display unit 12 and the phase factor display unit 15 when a T gate is input to the input unit 13, with the currently displayed points being (0, 0, -1) (i.e., the initial state being |1>).

[0093] As shown in equation (46), the quantum state |1> is an eigenstate of the T gate, and its eigenvalue is e iπ / 4 Therefore, when the T gate is executed on the initial state |1>, the quantum state remains unchanged as |1>, and the display point also remains (0, 0, -1). On the other hand, the phase factor display unit 15 shows the eigenvalue e iπ / 4 This will be displayed.

[0094] Figure 14 shows the display unit 12 and the phase factor display unit 15 when a Pauli X gate is input to the input unit 13, with the currently displayed point being (0, 0, 1) (i.e., the initial state being |0>).

[0095] As shown in equation (21), when a Pauli X gate is executed on the initial state |1>, the quantum state changes to |1>, and a phase factor of 1 is obtained. Therefore, the display point changes from (0, 0, 1) to (0, 0, -1). Meanwhile, the phase factor display unit 15 displays the phase factor of 1.

[0096] Figure 15 shows the display unit 12 and the phase factor display unit 15 when a Pauli Y gate is input to the input unit 13, with the currently displayed point being (0, 0, 1) (i.e., the initial state being |0>).

[0097] As shown in equation (27), when a Pauli Y gate is executed on the initial state |0>, the quantum state changes to |1>, and the phase factor i is obtained. Therefore, the display point changes from (0, 0, 1) to (0, 0, -1). Meanwhile, the phase factor display unit 15 displays the phase factor i.

[0098] Figure 16 shows the display unit 12 and the phase factor display unit 15 when an Adamard gate is input to the input unit 13, with the currently displayed point being (0, 1, 0) (i.e., the initial state being |i>).

[0099] As shown in Equation (19), when a Hadamard gate is applied to the initial state |i>, the quantum state changes to |-i>, and the phase factor e iπ / 4 is obtained. Accordingly, the display point changes from (0, 1, 0) to (0, -1, 0). On the other hand, the phase factor display unit 15 displays the phase factor e iπ / 4 .

[0100] As described above, according to this embodiment, in addition to visually displaying the operation state of the 1-qubit gate and the execution result of the 1-qubit gate on the Bloch sphere, the phase factor or eigenvalue obtained when the 1-qubit gate is executed can be displayed

[0101] [Second Embodiment] FIG. 17 is a schematic diagram of a quantum state display device 3 according to the second embodiment. The quantum state display device 3 includes a first spherical surface 21, a second spherical surface 22, a first display unit 23 including a plurality of display points arranged on the first spherical surface 21, a second display unit 24 including a plurality of display points arranged on the second spherical surface 22, an input unit 25, and a control unit 26.

[0102] As an example, the first spherical surface 21 and the second spherical surface 22 are the Bloch spheres shown in FIG. 1. That is, the first spherical surface 21 and the second spherical surface 22 are unit spheres with a radius of 1 centered at the origin.

[0103] A 2-qubit quantum state is a superposition of four states: |00>, |01>, |10>, and |11>. When an orthogonal coordinate system is adopted as shown in FIG. 17, each of the 2-qubit quantum states |00>, |01>, |10>, and |11> is associated with a combination of respective points on the first spherical surface 21 and the second spherical surface 22 as follows. Quantum state |00> ⇔ Point (0, 0, 1) on the first spherical surface 21 and point (0, 0, 1) on the second spherical surface 22 Quantum state |01> ⇔ Point (0, 0, 1) on the first spherical surface 21 and point (0, 0, -1) on the second spherical surface 22 Quantum state |10> ⇔ point (0, 0, -1) on the first sphere 21 and point (0, 0, 1) on the second sphere 22 Quantum state |11> ⇔ point (0, 0, -1) on the first sphere 21 and point (0, 0, -1) on the second sphere 22 Similarly, each quantum state |++>, |+->, |-+>, |-->, |ii>, |ii>, |-ii>, and |-ii> corresponds to the following, respectively. Quantum state |++> ⇔ Point (1, 0, 0) on the first sphere 21 and point (1, 0, 0) on the second sphere 22 Quantum state |+-> ⇔ Point (1, 0, 0) on the first sphere 21 and point (-1, 0, 0) on the second sphere 22 Quantum state |-+> ⇔ point (-1, 0, 0) on the first sphere 21 and point (1, 0, 0) on the second sphere 22 Quantum state |--> ⇔ Point (-1, 0, 0) on the first sphere 21 and point (-1, 0, 0) on the second sphere 22 Quantum state |ii> ⇔ point (0, 1, 0) on the first sphere 21 and point (0, 1, 0) on the second sphere 22 Quantum state |ii> ⇔ point (0, 1, 0) on the first sphere 21 and point (0, -1, 0) on the second sphere 22 Quantum state |-ii> ⇔ point (0, -1, 0) on the first sphere 21 and point (0, 1, 0) on the second sphere 22 Quantum state |-ii> ⇔ point (0, -1, 0) on the first sphere 21 and point (0, -1, 0) on the second sphere 22

[0104] The first display unit 23 includes a plurality of display points arranged on the first sphere 21. In the example of Figure 17, the first display unit 23 includes six display points: display point 23a, display point 23b, display point 23c, display point 23d, display point 23e, and display point 23f. In this case, display point 23a is located at point (0, 0, 1), display point 23b at (0, 0, -1), display point 23c at (1, 0, 0), display point 23d at (-1, 0, 0), display point 23e at (0, 1, 0), and display point 23f at (0, -1, 0). In other words, display point 23a corresponds to the quantum state |0>, display point 23b to the quantum state |1>, display point 23c to the quantum state |+>, display point 23d to the quantum state |->, display point 23e to the quantum state |i>, and display point 23f to the quantum state |-i>.

[0105] The second display unit 24 includes a plurality of display points arranged on the second sphere 22. In the example of Figure 17, the second display unit 24 includes six display points: display point 24a, display point 24b, display point 24c, display point 24d, display point 24e, and display point 24f. In this case, display point 24a is located at point (0, 0, 1), display point 24b at (0, 0, -1), display point 24c at (1, 0, 0), display point 24d at (-1, 0, 0), display point 24e at (0, 1, 0), and display point 24f at (0, -1, 0). In other words, display point 24a corresponds to the quantum state |0>, display point 24b to the quantum state |1>, display point 24c to the quantum state |+>, display point 24d to the quantum state |->, display point 24e to the quantum state |i>, and display point 24f to the quantum state |-i>.

[0106] Each display point in the first display unit 23 and the second display unit 24 represents the quantum state of a qubit. That is, when a qubit is in the quantum state corresponding to a display point, this display point visually indicates it. Display points 23a to 23f and display points 24a to 24f may be composed of LEDs, for example. In this case, each LED may represent the quantum state by being lit or blinking. For example, when the qubit is in the quantum state |00>, LEDs 23a and 24a are lit or blinking, and LEDs 23b to 23f and LEDs 24b to 24f are off. Or, when the qubit is in the quantum state |-ii>, LEDs 23f and 24f are lit or blinking, and LEDs 23a to 23e and LEDs 24a to 24e are off, and so on.

[0107] The method of displaying the display points is not limited to illumination, blinking, or extinguishing; for example, the quantum state may be represented by changing the color, brightness, saturation, etc. Alternatively, the display method may not be by light emission, but rather by a physical entity, such as a small sphere, moving on the spherical surfaces 21 and 22, and the quantum state being represented by the position where this physical entity remains. Thus, the method of displaying the display points can be any suitable method as long as it can visually represent which position on the spherical surfaces 21 and 22 corresponds to the quantum state of the qubit.

[0108] The input unit 25 accepts input from the user. That is, the input unit 25 is configured to allow the user to input a desired two-quantum gate. Specifically, the input unit 13 may display a list of controlled Z gates, controlled NOT gates, exchange gates, etc., and the user may be able to select a desired two-quantum gate from this list.

[0109] When the input unit 25 receives input from the user, it transmits the content of that input as an input signal to the control unit 26.

[0110] When the control unit 26 receives an input signal from the input unit 25, it transmits control signals to the first display unit 23 and the second display unit 24. Using these control signals, the control unit 26 controls the first display unit 23 and the second display unit 24 to display a display point corresponding to the result of executing the two quantum gates included in the input signal for the qubits of the quantum state currently displayed on the first display unit 23 and the second display unit 24.

[0111] Figure 18 shows representative two-quantum gates. Specifically, Figure 18 shows the symbols and 4x4 matrix representations for three types of two-quantum gates: controlled Z gates (also called CZ gates), controlled NOT gates (also called CNOT gates), and exchange gates (also called SWAP gates).

[0112] The results of applying a controlled Z gate (CZ) to each quantum state |00>, |01>, |10>, and |11> are as follows. CZ|00>=|00> (51) CZ|01>=|01> (52) CZ|10>=|10> (53) CZ|11>=-|11> (54)

[0113] The results of applying a controlled NOT gate (CX) to each quantum state |00>, |01>, |10>, |11>, |++>, |+->, |-+>, and |--> are as follows. CX|00>=|00> (55) CX|01>=|01> (56) CX|10>=|11> (57) CX|11>=|10> (58) CX|++>=|++> (59) CX|+->=|--> (60) CX|-+>=|-+> (61) CX|-->=|+-> (62)

[0114] The results of applying an exchange gate (SWAP) to each quantum state |00>, |01>, |10>, and |11> are as follows: SWAP|00>=|00> (63) SWAP|01>=|10> (64) SWAP|10>=|01> (65) SWAP|11>=|11> (66)

[0115] For example, as shown in equation (57), when a controlled NOT gate (CX) is applied to a qubit in the quantum state |10>, the quantum state changes to |11>. CX|10>=|11> (57)

[0116] When this quantum gate operation is represented by the quantum state display device 3, the first display point 23a (position (0,0,-1) on the first sphere 21) and the second display point 24a (position (0,0,1) on the second sphere 22) are lit or blinking (corresponding to the quantum state |10>), and when the user inputs a controlled NOT gate to the input unit 25, the first display point 23a continues to be lit or blinking. On the other hand, the second display point 24a turns off, and instead the second display point 24b (position (0,0,-1) on the sphere 11) is lit or blinking (corresponding to the quantum state |11>).

[0117] Figure 19 shows the state of the first display unit 23 and the second display unit 24 when a controlled NOT gate is input to the input unit 25, with the currently displayed point 23a of the first display unit 23 being (0, 0, -1) and the display point 24a of the second display unit 24 being (0, 0, 1) (i.e., the initial state being |10>). However, to avoid complexity, the input unit 25 and the control unit 26 are omitted from the illustration. The upper part of Figure 19 is the first sphere 21, and the lower part is the second sphere 22. The left side of Figure 19 is before the controlled NOT gate is executed, and the right side is after the controlled NOT gate is executed.

[0118] In this embodiment, the user can visually understand that when a controlled NOT gate is executed on a qubit in two quantum states |10>, the quantum state changes to |11>.

[0119] For example, as shown in equation (65), when a swap gate (SWAP) is executed on a qubit in the quantum state |10>, the quantum state changes to |01>. SWAP|10>=|01> (65)

[0120] When this quantum gate operation is represented by the quantum state display device 3, the first display point 23c (position (0,0,-1) on the first sphere 21) and the second display point 24c (position (0,0,1) on the second sphere 22) are lit or blinking (corresponding to quantum state |10>), and when the user inputs an exchange gate to the input unit 25, the first display point 23c turns off, and instead the first display point 23d (position (0,0,1) on the sphere 11) turns on or blinks. On the other hand, the second display point 24c turns off, and instead the second display point 24d (position (0,0,-1) on the sphere 11) turns on or blinks (corresponding to quantum state |01>).

[0121] Figure 20 shows the state of the first display unit 23 and the second display unit 24 when the display point 23c of the first display unit 23 is (0, 0, -1) and the display point 24c of the second display unit 24 is (0, 0, 1) (i.e., the initial state is |10>), and an exchange gate is input to the input unit 25. However, to avoid complexity, the input unit 25 and the control unit 26 are omitted from the illustration. The upper part of Figure 20 is the first sphere 21, and the lower part is the second sphere 22. The left side of Figure 20 is before the exchange gate is executed, and the right side is after the exchange gate is executed.

[0122] In this embodiment, the user can visually understand that when an exchange gate is executed on a qubit with two quantum states |10>, the quantum state changes to |01>.

[0123] [Third Embodiment] The third embodiment is a quantum state display device that displays quantum entanglement states on a spherical surface. The configuration of this quantum state display device is the same as the configuration of the quantum state display device 3 in Figure 17.

[0124] The quantum state display device 4 of this embodiment will be described below with reference to Figure 17. In this embodiment, the input unit 25 is configured to allow the user to input a quantum entanglement display command. In the following description, the quantum state display device 3 in Figure 17 will be read as the quantum state display device 4.

[0125] The first display unit 23 includes a plurality of display points arranged on the first sphere 21. In the example of Figure 17, the first display unit 23 includes six display points: display point 23a, display point 23b, display point 23c, display point 23d, display point 23e, and display point 23f. In this case, display point 23a is located at point (0, 0, 1), display point 23b at (0, 0, -1), display point 23c at (1, 0, 0), display point 23d at (-1, 0, 0), display point 23e at (0, 1, 0), and display point 23f at (0, -1, 0). In other words, display point 23a corresponds to the quantum state |0>, display point 23b to the quantum state |1>, display point 23c to the quantum state |+>, display point 23d to the quantum state |->, display point 23e to the quantum state |i>, and display point 23f to the quantum state |-i>.

[0126] The second display unit 24 includes a plurality of display points arranged on the second sphere 22. In the example of Figure 17, the second display unit 24 includes six display points: display point 24a, display point 24b, display point 24c, display point 24d, display point 24e, and display point 24f. In this case, display point 24a is located at point (0, 0, 1), display point 24b at (0, 0, -1), display point 24c at (1, 0, 0), display point 24d at (-1, 0, 0), display point 24e at (0, 1, 0), and display point 24f at (0, -1, 0). In other words, display point 24a corresponds to the quantum state |0>, display point 24b to the quantum state |1>, display point 24c to the quantum state |+>, display point 24d to the quantum state |->, display point 24e to the quantum state |i>, and display point 24f to the quantum state |-i>.

[0127] Each display point in the first display unit 23 and the second display unit 24 represents the quantum state of a qubit. That is, when a qubit is in the quantum state corresponding to a display point, this display point visually indicates it. Display points 23a to 23f and display points 24a to 24f may be composed of LEDs, for example. In this case, each LED may represent the quantum state by being lit or blinking. For example, when the qubit is in the quantum state |00>, LEDs 23a and 24a are lit or blinking, and LEDs 23b to 23f and LEDs 24b to 24f are off. Or, when the qubit is in the quantum state |-ii>, LEDs 23f and 24f are lit or blinking, and LEDs 23a to 23e and LEDs 24a to 24e are off, and so on.

[0128] The method of displaying the display points is not limited to illumination, blinking, or extinguishing; for example, the quantum state may be represented by changing the color, brightness, saturation, etc. Alternatively, the display method may not be by light emission, but rather by a physical entity, such as a small sphere, moving on the spherical surfaces 21 and 22, and the quantum state being represented by the position where this physical entity remains. Thus, the method of displaying the display points can be any suitable method as long as it can visually represent which position on the spherical surfaces 21 and 22 corresponds to the quantum state of the qubit.

[0129] When a quantum entanglement display command is input to the input unit 25, the control unit 26 controls the first display unit 23 and the second display unit 24 so that each display point of the first display unit 23 and each display point of the second display unit 24 represent the quantum entanglement state between the first qubit and the second qubit.

[0130] Figure 21 shows a quantum circuit 70 that generates quantum entanglement. The upper part of the quantum circuit 70 is the first qubit, and the lower part is the second qubit. The quantum circuit 70 consists of an Hadamard gate 71 for the first qubit, followed by controlled NOT gates 72 for the first and second qubits.

[0131] |a>, |b>, |c>, and |d> each represent a 1-qubit state. The two on the left are inputs, and the two on the right are outputs. The upper row corresponds to the first qubit, and the lower row corresponds to the second qubit. The following describes the case where |ab>=|00> is input as the initial state to quantum circuit 70.

[0132] When the initial state of the first qubit is |0>, the two quantum states after executing the Hadamard gate 71 (the dashed lines in the diagram) are:

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[0133] Similarly, the initial state |01> is determined by the quantum circuit 70.

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[0134] The following four pairs of quantum states are all quantum entangled states and are called Bell states.

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[0135] To display the quantum entanglement state using the quantum state display device 4, for example, all display points of the first display unit 23 and the second display unit 24 may be lit or blinked. This method allows for an intuitive understanding that the quantum entanglement state is, for example, a superposition state of two quantum states |00> and two quantum states |11>.

[0136] Another way to display the entangled quantum state using the quantum state display device 4 is to alternately light up or blink a display point corresponding to two quantum states |00> and a display point corresponding to two quantum states |11>. This method also allows for an intuitive understanding that the entangled quantum state is a superposition state of two quantum states |00> and two quantum states |11>.

[0137] In one embodiment of this design, the input unit 25 may be configured to allow the user to input a measurement command while quantum entanglement is being displayed. In this case, when a measurement command is input to the input unit 25, the control unit 26 controls the first display unit 23 and the second display unit 24 to randomly display one of the possible states of the first qubit and the second qubit.

[0138] Two qubits, for example

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[0139] Figure 22 schematically shows a series of operations of the quantum state display device 4 when the initial state is |00>. In the initial state |00>, the first display unit 23 has a dot (0, 0, 1) that is lit or blinking, and the second display unit 24 has a dot (0, 0, 1) that is lit or blinking.

[0140] When a quantum entanglement display command is input to the input unit 25, all display points on the first display unit 23 and the second display unit 24 light up or blink. This occurs after an Adamard gate is executed on the first qubit, causing the system state to become |+0>, followed by the execution of a controlled NOT gate, resulting in the system state becoming quantum entangled.

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[0141] Alternatively, the system may be in a quantum entangled state.

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[0142] Next, when a measurement command is input to the input unit 25, the display points corresponding to either state |00> or |11> that the first and second qubits can take will light up or blink randomly.

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[0143] Figure 23 schematically shows a series of operations of the quantum state display device 4 when the initial state is |01>. In the initial state |01>, the first display unit 23 is lit or blinking with the dot (0, 0, 1), and the second display unit 24 is lit or blinking with the dot (0, 0, -1).

[0144] When a quantum entanglement display command is input to the input unit 25, all display points on the first display unit 23 and the second display unit 24 light up or blink. This occurs after an Adamard gate is executed on the first qubit, changing the system state to |+1>, followed by the execution of a controlled NOT gate, resulting in a quantum entangled state.

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[0145] Alternatively, the system may be in a quantum entangled state.

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[0146] Next, when a measurement command is input to the input unit 25, the display points corresponding to either state |01> or |01> that the first and second qubits can take will light up or blink randomly.

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[0147] Figure 24 schematically shows a series of operations of the quantum state display device 4 when the initial state is |10>. In the initial state |10>, the first display unit 23 has a dot (0, 0, -1) that is lit or blinking, and the second display unit 24 has a dot (0, 0, 1) that is lit or blinking.

[0148] When a quantum entanglement display command is input to the input unit 25, all display points on the first display unit 23 and the second display unit 24 light up or blink. This occurs after an Adamard gate is executed on the first qubit, causing the system state to become |-0>, followed by the execution of a controlled NOT gate, resulting in the system being in a quantum entangled state.

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[0149] Alternatively, the system may be in a quantum entangled state.

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[0150] Next, when a measurement command is input to the input unit 25, the display points corresponding to either state |00> or |11> that the first and second qubits can take will light up or blink randomly.

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[0151] Figure 25 schematically shows a series of operations of the quantum state display device 4 when the initial state is |11>. In the initial state |11>, the first display unit 23 has a dot (0, 0, -1) that is lit or blinking, and the second display unit 24 has a dot (0, 0, -1) that is lit or blinking.

[0152] When a quantum entanglement display command is input to the input unit 25, all display points on the first display unit 23 and the second display unit 24 light up or blink. This occurs after an Adamard gate is executed on the first qubit, causing the system state to become |-1>, followed by the execution of a controlled NOT gate, resulting in the system being in a quantum entangled state.

number

[0153] Alternatively, the system may be in a quantum entangled state.

number

[0154] Next, when a measurement command is input to the input unit 25, the display points corresponding to either state |01> or |10> that the first and second qubits can take will light up or blink randomly.

number

[0155] After the quantum state display device 4 illuminates or flashes all the display points of the first display unit 23 and the second display unit 24 to display the quantum entanglement state, the first sphere 21 and the second sphere 22 may be separated, causing the two spheres to move away from each other. At this time, all the display points of the first display unit 23 and the second display unit 24 continue to illuminate or flash. By including this operation, it can be intuitively understood that the quantum entanglement state is maintained even when the locations are spatially separated.

[0156] As described above, according to this embodiment, the quantum entanglement state between two qubits, and the state when a measurement is performed on the quantum entanglement state, can be visually displayed on a Bloch sphere.

[0157] [Fourth Embodiment] Figure 26 is a schematic diagram of a quantum state display device 5 according to a fourth embodiment. The quantum state display device 5 comprises a first sphere 31, a second sphere 32, a third sphere 33, a first display unit 34 including a plurality of display points arranged on the first sphere 31, a second display unit 35 including a plurality of display points arranged on the second sphere 32, a third display unit 36 ​​including a plurality of display points arranged on the third sphere 33, an input unit 37, and a control unit 38.

[0158] As an example, the first sphere 31, the second sphere 32, and the third sphere 33 are Bloch spheres as shown in Figure 1. That is, the first sphere 31, the second sphere 32, and the third sphere 33 are unit spheres with radius 1 centered at the origin.

[0159] The quantum state of the 3 qubits is a superposition of eight states: |000>, |001>, |010>, |011>, |100>, |101>, |110>, and |111>. Taking a Cartesian coordinate system as shown in Figure 26, each quantum state of the 3 qubits, |000>, |001>, |010>, |011>, |100>, |101>, |110>, and |111>, corresponds to a combination of points on the first sphere 31, the second sphere 32, and the third sphere 33, respectively. Quantum state |000> ⇔ point (0,0,1) on the first sphere 31, point (0,0,1) on the second sphere 32, and point (0,0,1) on the third sphere 33. Quantum state |001> ⇔ point (0,0,1) on the first sphere 31, point (0,0,1) on the second sphere 32, and point (0,0,-1) on the third sphere 33. Quantum state |010> ⇔ point (0,0,1) on the first sphere 31, point (0,0,-1) on the second sphere 32, and point (0,0,1) on the third sphere 33. Quantum state |011> ⇔ point (0,0,1) on the first sphere 31, point (0,0,-1) on the second sphere 32, and point (0,0,-1) on the third sphere 33. Quantum state |100> ⇔ point (0, 0, -1) on the first sphere 31, point (0, 0, 1) on the second sphere 32, and point (0, 0, 1) on the third sphere 33. Quantum state |10¹> ⇔ point (0, 0, -1) on the first sphere 31, point (0, 0, 1) on the second sphere 32, and point (0, 0, -1) on the third sphere 33. Quantum state |110> ⇔ point (0, 0, -1) on the first sphere 31, point (0, 0, -1) on the second sphere 32, and point (0, 0, 1) on the third sphere 33. Quantum state |111> ⇔ point (0, 0, -1) on the first sphere 31, point (0, 0, -1) on the second sphere 32, and point (0, 0, -1) on the third sphere 33.

[0160] Each quantum state |+++>~|--->, |iii>~|-iii> can be mapped to a point on the first sphere 31, the second sphere 32, and the third sphere 33 using the same rules, so a detailed explanation is omitted.

[0161] The first display unit 34 includes a plurality of display points arranged on the first sphere 31. In the example of Figure 26, the first display unit 34 includes six display points: display point 34a, display point 34b, display point 34c, display point 34d, display point 34e, and display point 34f. In this case, display point 34a is located at point (0, 0, 1), display point 34b at (0, 0, -1), display point 34c at (1, 0, 0), display point 34d at (-1, 0, 0), display point 34e at (0, 1, 0), and display point 34f at (0, -1, 0). In other words, display point 34a corresponds to the quantum state |0>, display point 34b to the quantum state |1>, display point 34c to the quantum state |+>, display point 34d to the quantum state |->, display point 34e to the quantum state |i>, and display point 34f to the quantum state |-i>.

[0162] The second display unit 35 includes a plurality of display points arranged on the second sphere 32. In the example of Figure 26, the second display unit 35 includes six display points: display point 35a, display point 35b, display point 35c, display point 35d, display point 35e, and display point 35f. In this case, display point 35a is located at point (0, 0, 1), display point 35b at (0, 0, -1), display point 35c at (1, 0, 0), display point 35d at (-1, 0, 0), display point 35e at (0, 1, 0), and display point 35f at (0, -1, 0). In other words, display point 35a corresponds to the quantum state |0>, display point 35b to the quantum state |1>, display point 35c to the quantum state |+>, display point 35d to the quantum state |->, display point 35e to the quantum state |i>, and display point 35f to the quantum state |-i>.

[0163] The third display unit 36 ​​includes a plurality of display points arranged on the third sphere 33. In the example of Figure 26, the third display unit 36 ​​includes six display points: display point 36a, display point 36b, display point 36c, display point 36d, display point 36e, and display point 36f. In this case, display point 36a is located at point (0, 0, 1), display point 36b at (0, 0, -1), display point 36c at (1, 0, 0), display point 36d at (-1, 0, 0), display point 36e at (0, 1, 0), and display point 36f at (0, -1, 0). In other words, display point 36a corresponds to the quantum state |0>, display point 36b to the quantum state |1>, display point 36c to the quantum state |+>, display point 36d to the quantum state |->, display point 36e to the quantum state |i>, and display point 36f to the quantum state |-i>.

[0164] Each display point in the first display unit 34, the second display unit 35, and the third display unit 36 ​​represents the quantum state of a qubit. That is, when a qubit is in the quantum state corresponding to a display point, this display point visually indicates it. Display points 34a to 34f, 35a to 35f, and 36a to 36f may be composed of LEDs, for example. In this case, each LED may represent the quantum state by being lit or blinking. For example, when the qubit is in the quantum state |000>, LEDs 34a, 35a, and 36a are lit or blinking, and LEDs 34b to 34f, 35b to 35f, and LEDs 36b to 36f are off. Or, when the qubit is in the quantum state |-ii>, LEDs 34f, 35f, and 36f are lit or blinking, and LEDs 34a to 34e, 35a to 35e, and LEDs 36a to 36e are off, and so on.

[0165] The method of displaying the points is not limited to illumination, blinking, or extinguishing; for example, the quantum state may be represented by changing the color, brightness, saturation, etc. Alternatively, the display method may not be by light emission, but rather by a physical entity, such as a small sphere, moving on the spherical surfaces 31, 32, and 33, and the quantum state being represented by the position where this physical entity remains. Thus, the method of displaying the points can be any suitable method, as long as it can visually represent which position on the spherical surfaces 31, 32, and 33 corresponds to the quantum state of the qubit.

[0166] The input unit 37 accepts input from the user. That is, the input unit 37 is configured to allow the user to input three quantum gates of their choice. Specifically, the input unit 37 may display a list of controlled Z gates, controlled NOT gates, exchange gates, etc., and the user may be able to select the desired three quantum gates from this list.

[0167] When the input unit 37 receives input from the user, it transmits the content of that input as an input signal to the control unit 38.

[0168] When the control unit 38 receives an input signal from the input unit 37, it transmits control signals to the first display unit 34, the second display unit 35, and the third display unit 36. Based on these control signals, the control unit 38 controls the first display unit 34, the second display unit 35, and the third display unit 36 ​​to display a display point corresponding to the result of executing the three quantum gates included in the input signal for the quantum state qubits currently displayed on the first display unit 34, the second display unit 35, and the third display unit 36.

[0169] Figure 27 shows the Toffoli gate (also known as the CCNOT gate) as a representative example of the three quantum gates. Specifically, Figure 18 shows the notation and 8x8 matrix representation of the Toffoli gate.

[0170] The results of applying a controlled Z gate (CCNOT) to each quantum state |000>, |001>, |010>, |011>, |100>, |101>, |110>, and |111> are as follows. CCNOT|000>=|000> (69) CCNOT|001>=|001> (70) CCNOT|010>=|010> (71) CCNOT|011>=|011> (72) CCNOT|100>=|100> (73) CCNOT|101>=|101> (74) CCNOT|110>=|111> (75) CCNOT|111>=|110> (76)

[0171] For example, as shown in equation (75), when a Toffoli gate (CCNOT) is applied to a qubit in the quantum state |110>, the quantum state changes to |111>. CCNOT|110>=|111> (75)

[0172] When this quantum gate operation is represented by the quantum state display device 5, the first display point 34b (position on the first sphere 31 (0,0,-1)), the second display point 35b (position on the second sphere 32 (0,0,-1)), and the third display point 36a (position on the third sphere 33 (0,0,1)) are lit or blinking (corresponding to the quantum state |110>). When the user inputs a Toffoli gate to the input unit 37, the first display point 34b and the second display point 35b continue to be lit or blinking. On the other hand, the third display point 36a turns off, and instead the third display point 36b (position on the sphere 11 (0,0,-1)) lights up or blinks (corresponding to the quantum state |111>).

[0173] FIG. 28 shows states of the first display unit 34, the second display unit 35, and the third display unit 36 when a Toffoli gate is input to the input unit 37, where the currently displayed display point 34b of the first display unit 34 is at (0, 0, -1), the display point 35b of the second display unit 35 is at (0, 0, -1), and the display point 36a of the third display unit 36 is at (0, 0, 1) (that is, when the initial state is |110>). Note that illustration of the input unit 37 and the control unit 38 is omitted to avoid complication. The upper part of FIG. 28 is the first spherical surface 31, the middle part is the second spherical surface 32, and the lower part is the third spherical surface 33. The left side of FIG. 28 is before execution of the Toffoli gate, and the right side is after execution of the controlled Toffoli gate.

[0174] According to this example, a user can visually understand that when a Toffoli gate is executed on a qubit in the 3-qubit state |110>, the quantum state changes to |111>.

[0175] [Fifth Embodiment] The fifth embodiment is a quantum state display device that displays quantum teleportation on a spherical surface. The configuration of this quantum state display device is common to the configuration of the quantum state display device 5 in FIG. 26.

[0176] Hereinafter, the quantum state display device 6 of the present embodiment will be described with reference to FIG. 26. In the present embodiment, the input unit 37 is configured such that a user can input an operation for quantum teleportation. In the following description, the quantum state display device 5 in FIG. 26 is read as the quantum state display device 6.

[0177] The first display unit 34 includes a plurality of display points arranged on the first sphere 31. In the example of Figure 26, the first display unit 34 includes six display points: display point 34a, display point 34b, display point 34c, display point 34d, display point 34e, and display point 34f. In this case, display point 34a is located at point (0, 0, 1), display point 34b at (0, 0, -1), display point 34c at (1, 0, 0), display point 34d at (-1, 0, 0), display point 34e at (0, 1, 0), and display point 34f at (0, -1, 0). In other words, display point 34a corresponds to the quantum state |0>, display point 34b to the quantum state |1>, display point 34c to the quantum state |+>, display point 34d to the quantum state |->, display point 34e to the quantum state |i>, and display point 34f to the quantum state |-i>.

[0178] The second display unit 35 includes a plurality of display points arranged on the second sphere 32. In the example of Figure 26, the second display unit 35 includes six display points: display point 35a, display point 35b, display point 35c, display point 35d, display point 35e, and display point 35f. In this case, display point 35a is located at point (0, 0, 1), display point 35b at (0, 0, -1), display point 35c at (1, 0, 0), display point 35d at (-1, 0, 0), display point 35e at (0, 1, 0), and display point 35f at (0, -1, 0). In other words, display point 35a corresponds to the quantum state |0>, display point 35b to the quantum state |1>, display point 35c to the quantum state |+>, display point 35d to the quantum state |->, display point 35e to the quantum state |i>, and display point 35f to the quantum state |-i>.

[0179] The third display unit 36 ​​includes a plurality of display points arranged on the third sphere 33. In the example of Figure 26, the third display unit 36 ​​includes six display points: display point 36a, display point 36b, display point 36c, display point 36d, display point 36e, and display point 36f. In this case, display point 36a is located at point (0, 0, 1), display point 36b at (0, 0, -1), display point 36c at (1, 0, 0), display point 36d at (-1, 0, 0), display point 36e at (0, 1, 0), and display point 36f at (0, -1, 0). In other words, display point 36a corresponds to the quantum state |0>, display point 36b to the quantum state |1>, display point 36c to the quantum state |+>, display point 36d to the quantum state |->, display point 36e to the quantum state |i>, and display point 36f to the quantum state |-i>.

[0180] Each display point in the first display unit 34, the second display unit 35, and the third display unit 36 ​​represents the quantum state of a qubit. That is, when a qubit is in the quantum state corresponding to a display point, this display point visually indicates it. Display points 34a to 34f, 35a to 35f, and 36a to 36f may be composed of LEDs, for example. In this case, each LED may represent the quantum state by being lit or blinking. For example, when the qubit is in the quantum state |000>, LEDs 34a, 35a, and 36a are lit or blinking, and LEDs 34b to 34f, 35b to 35f, and LEDs 36b to 36f are off. Or, when the qubit is in the quantum state |-ii>, LEDs 34f, 35f, and 36f are lit or blinking, and LEDs 34a to 34e, 35a to 35e, and LEDs 36a to 36e are off, and so on.

[0181] The method of displaying the points is not limited to illumination, blinking, or extinguishing; for example, the quantum state may be represented by changing the color, brightness, saturation, etc. Alternatively, the display method may not be by light emission, but rather by a physical entity, such as a small sphere, moving on the spherical surfaces 31, 32, and 33, and the quantum state being represented by the position where this physical entity remains. Thus, the method of displaying the points can be any suitable method, as long as it can visually represent which position on the spherical surfaces 31, 32, and 33 corresponds to the quantum state of the qubit.

[0182] Figure 29 shows a quantum circuit 80 that realizes quantum teleportation. The upper part of the quantum circuit 80 is the first qubit, the middle part is the second qubit, and the lower part is the third qubit. The quantum circuit 80 consists of an Adamard gate 81 for the second qubit, followed by a controlled NOT gate 82 for the second and third qubits, followed by a controlled NOT gate 83 for the first and second qubits, and followed by an Adamard gate 84 for the first qubit.

[0183] The principle of quantum teleportation is explained below. Let the state of the first qubit be |Ψ1>, the state of the second qubit be |Ψ2>, and the state of the third qubit be |Ψ3>. Following convention, the sender will be called Alice and the receiver Bob. Alice performs the following operations to send information represented by quantum states to Bob.

[0184] First, Alice sets the quantum state |φ>=α|0>+β|1> that she wants to send to Bob as the first qubit. Then, Alice initializes the second and third qubits to |0>. That is, the state at this point (initial state) is as follows: |Ψ1>=|φ>=α|0>+β|1> (77) |Ψ2>=|0> (78) |Ψ3>=|0> (79)

[0185] Alice inputs this state into quantum circuit 80. The following describes the actions performed within quantum circuit 80.

[0186] First, the Hadamard gate 81 is executed on the second qubit |0>. Then, the state of the second qubit changes to |+>. That is, at the point of the dashed line (1), the states of each qubit are as follows: |Ψ1>=|φ> (80) |Ψ2>=|+> (81) |Ψ3>=|0> (82)

[0187] Next, controlled NOT gates are executed on the second and third qubits. As a result, the second and third qubits become entangled. That is, at the point indicated by the dashed line (2), the states of the second and third qubits are as follows:

number

[0188] Here, one of the entangled quantum states, |Ψ2>, is sent to Alice, and the other entangled quantum state, |Ψ3>, is sent to Bob.

[0189] Next, a controlled NOT gate 83 is executed on the first and second qubits. As a result, all three qubits—the first, second, and third—become entangled. That is, at the point indicated by the dashed line (3), the states of the first, second, and third qubits are as follows:

number

[0190] Here, Alice performs measurements on the first qubit and the second qubit. Then, as can be seen from Equation (81), the states |Ψ1>|Ψ2> of the first qubit and the second qubit are necessarily observed as any one of |0>|0>, |0>|1>, |1>|0>, and |1>|1>. The following can be understood from Equation (81).

[0191] If the measurement result |Ψ1>|Ψ2>=|0>|0> is observed, |Ψ3>=α|0>+β|1> (85) is determined. Since this is the state desired to be transmitted that was initially set to the first qubit (Equation (77)), the information desired to be transmitted is conveyed to Bob without any operation performed as it is (that is, without executing any gate operation on |Ψ3>).

[0192] If the measurement result |Ψ1>|Ψ2>=|0>|1> is observed, the state of the third qubit (the state held by Bob) is |Ψ3>=β|0>+α|1> (86) is determined. This is different from the state α|0>+β|1> desired to be transmitted. To convert this state into the desired transmission state α|0>+β|1>, Bob only needs to execute a Pauli X gate on |Ψ3>.

[0193] If the measurement result |Ψ1>|Ψ2>=|1>|0> is observed, the state of the third qubit (the state held by Bob) is |Ψ3>=α|0>-β|1> (87) is determined. This is different from the state α|0>+β|1> desired to be transmitted. To convert this state into the desired transmission state α|0>+β|1>, Bob only needs to execute a Pauli Z gate on |Ψ3>.

[0194] If the measurement result |Ψ1>|Ψ2>=|1>|1> is observed, the state of the third qubit (the state held by Bob) is |Ψ3>=-β|0>+α|1> (88) This is confirmed. This is different from the desired state α|0>+β|1>. To convert this state to the desired state α|0>+β|1>, Bob can execute a Pauli Y gate on |Ψ3>.

[0195] Based on the above principles, the procedure for representing quantum teleportation using the quantum state display device 6 will be explained. Figure 30 is a flowchart showing the procedure for representing quantum teleportation using the quantum state display device 6.

[0196] In step S1, the user inputs the quantum state they wish to transmit into the input unit 37. Specifically, for example, the input unit 37 may be configured to allow the user to select one of the following six quantum states they wish to transmit: |0>, |1>, |+>, |->, |i>, and |-i>.

[0197] In step S2, the control unit 38 controls the first display unit 34, the second display unit 35, and the third display unit 36 ​​to display the initial state of the first qubit as input by the user in step S1 on the first sphere 31, the initial state of the second qubit |0> on the second sphere 32, and the initial state of the third qubit |0> on the third sphere 33.

[0198] In step S3, the user inputs the first quantum entanglement command to the input unit 37. This corresponds to executing the Hadamard gate 81 and the controlled NOT gate 82 in the quantum circuit 80 shown in Figure 29.

[0199] In step S4, the control unit 38 controls the second display unit 35 and the third display unit 36 ​​so that all display points on the second sphere 32 and the third sphere 33 are displayed. This represents that the second qubit and the third qubit are in a quantum entangled state in the quantum circuit 80 of Figure 29.

[0200] In step S5, the user inputs a second quantum entanglement command to the input unit 37. This corresponds to executing a controlled NOT gate 83 and an Adamard gate 84 in the quantum circuit 80 shown in Figure 29.

[0201] In step S6, the control unit 38 controls the first display unit 34, the second display unit 35, and the third display unit 36 ​​so that all display points on the first sphere 31, the second sphere 32, and the third sphere 33 are displayed. This represents that the first qubit, the second qubit, and the third qubit are in a quantum entangled state in the quantum circuit 80 of Figure 29.

[0202] In step S7, the user inputs a measurement command into the input unit 37. This corresponds to performing a measurement on the first and second qubits at the point indicated by the dashed line (3) in the quantum circuit 80 of Figure 29.

[0203] In step S8, the control unit 38 controls the second display unit 35 and the third display unit 36 ​​to display the state of the first qubit determined by the measurement result on the first sphere 31, the state of the second qubit determined by the measurement result on the second sphere 32, and the state of the third qubit determined by the measurement result on the third sphere 33. When the quantum entanglement state of the first, second, and third qubits is actually measured, it is probabilistic which of the possible states will be observed and cannot be known until the measurement is performed. Conversely, at the moment of measurement, the state of the system is determined to be one of the possible states. To reflect this fact, the control unit 38 controls the first display unit 34, the second display unit 35, and the third display unit 36 ​​to display one of the possible states of the first, second, and third qubits "randomly".

[0204] In step S9, the user inputs a quantum gate to the input unit 37 according to the measurement result. Specifically, if the measurement result is |0> for the first qubit and |0> for the second qubit, the user inputs the identity operator (I) to the input unit 37 (i.e., "does nothing" for the third qubit). If the measurement result is |0> for the first qubit and |1> for the second qubit, the user inputs a Pauli X gate (X) to the input unit 37. If the measurement result is |1> for the first qubit and |0> for the second qubit, the user inputs a Pauli Z gate (Z) to the input unit 37. If the measurement result is |1> for the first qubit and |1> for the second qubit, the user inputs a Pauli Y gate (Y) to the input unit 37.

[0205] The user may be informed in advance, as a rule, of which quantum gate to input to the input unit 37 depending on the measurement results. Alternatively, the quantum state display device 6 may be equipped with an input operator input unit, and this input operator input unit may indicate to the user which quantum gate should be input to the input unit 37.

[0206] In step S10, the control unit 38 controls the third display unit 36 ​​to display the quantum state that the user input to the input unit 37 in step S1 (i.e., the quantum state that the user initially wanted to transmit) on the third sphere 33.

[0207] The following describes the first, second, and third quantum states displayed on the first sphere 31, the second sphere 32, and the third sphere 33, respectively, at each stage of the above flow, using as an example the case where the user inputs the quantum state |+> to the input unit 37 in step S1, and the measurement result in step S7 shows that the first qubit is |1> and the second qubit is |0>.

[0208] Figure 31 shows the state of the first sphere 31, the second sphere 32, and the third sphere 33 after the processing in step S2 has been performed. The quantum state |+> that the user has input to the input unit 37 and wants to transmit is displayed on the first sphere 31. The initial state |0> is displayed on the second sphere 32 and the third sphere 33, respectively.

[0209] Figure 32 shows the state of the first sphere 31, the second sphere 32, and the third sphere 33 after the processing in step S4 has been performed. On the first sphere 31, the quantum state |+> that the user inputs to the input unit 37 and wants to transmit is displayed as is. On the second sphere 32 and the third sphere 33, all display points are shown as the quantum entanglement state of the second qubit and the third qubit, respectively.

[0210] Figure 33 shows the state of the first sphere 31, the second sphere 32, and the third sphere 33 after the process in step S6 has been performed. On the first sphere 31, the second sphere 32, and the third sphere 33, all display points are shown as quantum entanglement states of the first, second, and third qubits, respectively.

[0211] Figure 34 shows the state of the first sphere 31, the second sphere 32, and the third sphere 33 after the process in step S8 has been performed. As a result of the measurement in step S7, the first qubit was |1> and the second qubit was |0>, so these results are displayed on the first sphere 31 and the second sphere 32. Also, as a result of the measurement in step S7, the state of the third qubit is determined to be |->, so this result is displayed on the third sphere 33.

[0212] Figure 35 shows the state of the first sphere 31, the second sphere 32, and the third sphere 33 after the processing in step S10. The measurement results from step S7 continue to be displayed on the first sphere 31 and the second sphere 32. In step S9, a Pauli Z gate is executed on the third qubit, and the state of the third qubit changes to |1> (i.e., the quantum state that the user initially wanted to send). The result is displayed on the third sphere 33.

[0213] Figure 36 summarizes which quantum gate should be executed on the third qubit depending on the measurement results in step S7.

[0214] As described above, according to this embodiment, the state in which quantum teleportation is performed can be visually displayed on a Bloch sphere.

[0215] [Sixth Embodiment] Figure 37 schematically shows Game 90 according to the sixth embodiment. Game 90 is a game similar to, for example, "Sugoroku" (a Japanese board game). That is, players move their pieces according to the results of dice or a roulette wheel, aiming to reach the goal as quickly as possible. The following describes how Game 90 is played by three people.

[0216] This game consists of pieces that each player possesses, and items that correspond to multiple quantum gates. Each piece can take on multiple states corresponding to quantum states represented as points on the Bloch sphere, and when an item acts on a piece, it changes the state of the piece according to the operation rules of the quantum gate.

[0217] In the example shown in Figure 37, game 90 comprises pieces 91a, 91b, and 91c, each player possessing, as well as items 92, 93, and 94.

[0218] Pieces 91a, 91b, and 91c can each take on one of four states corresponding to a single quantum state: |0>, |1>, |+>, and |->.

[0219] The movement of the pieces is basically determined by the outcome of a dice or roulette spin, but it also varies depending on the one of the four states the piece is in.

[0220] Item 92 corresponds to the Adamar Gate. Item 93 corresponds to the Pauli X Gate. Item 94 corresponds to the Pauli Z Gate.

[0221] When items 92, 93, and 94 act on pieces 91a, 91b, and 91c, they change the state of each piece according to the operation rules of a single quantum gate.

[0222] Players move their pieces while changing the state of their own or their opponent's pieces by using items 92, 93, and 94 as appropriate.

[0223] In the example above, pieces 91a, 91b, and 91c each took on four states corresponding to one quantum state: |0>, |1>, |+>, and |―>. However, the game is not limited to this; for example, pieces 91a, 91b, and 91c could take on six states corresponding to one quantum state: |0>, |1>, |+>, |―>, |i>, and |―i>. Furthermore, the game is not limited to items 92 and 93 corresponding to the Hadamard gate, and item 94 corresponding to the Pauli X gate; the game may also include items corresponding to the Pauli Y gate, Pauli Z gate, S gate, T gate, etc.

[0224] Game 90 may be a board game in which actual pieces are moved on a board, or it may be a computer game such as an online game or a game in a virtual space.

[0225] According to this embodiment, players can understand how quantum gates perform calculations and the results of their execution while enjoying the game. This allows beginners and elementary and junior high school students who are unfamiliar with quantum mechanics theory to learn the basics of quantum computing through the game.

[0226] The present invention has been described above 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.

[0227] [Modified examples of the embodiment] [Example 1] In the above explanation, the display point represented the quantum state by the illumination or flashing of an LED or similar device. However, it is not limited to this; the display point may also represent the quantum state through mechanical movement by a three-axis rotation mechanism. In this case, the display point is composed of a physical entity such as a small sphere, which moves on the Bloch sphere. The small sphere is rotatable around three mutually orthogonal axes (x, y, and z axes) passing through the center of the Bloch sphere. The position where the small sphere remains on the Bloch sphere corresponds to the quantum state.

[0228] [Differentiation 2] A Bloch sphere may be, for example, a spherical LED display. Figure 38 shows an image of the LED display that constitutes such a Bloch sphere.

[0229] In understanding the technical concept abstracted from the embodiments and modifications, that technical concept should not be interpreted restrictively 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. [Industrial applicability]

[0230] The technology disclosed herein can be widely used in the education industry, such as schools and cram schools; the toy and game industry, such as educational equipment, scientific instruments, and games; the entertainment industry, such as amusement parks and theme parks; the broadcasting and media industry, such as educational programs and scientific content; and indoor or outdoor displays, such as interior lighting and digital signage. [Explanation of Symbols]

[0231] 1. Quantum state display device 1a...Quantum state display device 1b...Quantum state display device 1c...Quantum state display device 11...spherical surface 12...Display section 13. Input section 14. Control Unit 15...Phase factor display area 12a...Display point 12b...Display point 12c...Display point 12d...Display point 12e...Display point 12f...Display point 12a1...Display point 12a2...Display point 12a3...Display point 12a4...Display point 12a5...Display point 12a6...Display point 12b1...Display point 12b2...Display point 12b3...Display point 12b4...Display point 12b5...Display point 12b6...Display point 12c1...Display point 12c2...Display point 12c3...Display point 12c4...Display point 12c5...Display point 12c6...Display point 21. The first sphere 22. The second sphere 23. First display unit 23a ··First display point 23b ··First display point 23c ··First display point 23d ··First display point 23e ··First display point 23f ··First display point 24. Second display section 24a ··Second display point 24b. Second display point 24c ··Second display point 24d ··Second display point 24e ··Second display point 24f ··Second display point 25. Input section 26. Control Unit 31. The first sphere 32. The second sphere 33. The Third Spheric Surface 34. First display unit 34a ··First display point 34b ··First display point 34c ··First display point 34d ··First display point 34e ··First display point 34f ··First display point 35. Second display section 35a ··Second display point 35b · Second display point 35c ··Second display point 35d ··Second display point 35e ··Second display point 35f ··Second display point 36. Third display section 36a ··Third display point 36b · Third display point 36c ··Third display point 36d ··Third display point 36e ··Third display point 36f ··Third display point 37. Input section 38. Control Unit 70...Quantum circuit 71. Adamard Gate 72. Control NOT gate 80...Quantum circuit 81. Adamar Gate 82. Control NOT gate 83. Control NOT Gate 84. Adamar Gate 90 Game 91a ·· Piece 91b... Piece 91c··piece 92 items 93 items 94 items AX1... Rotating shaft O···Center of the sphere S1... A step in which the user inputs the quantum state they want to send into the input unit. Step S2: Display the state the user wants to send on the first sphere, display the initial state |0> on the second sphere, and display the initial state |0> on the third sphere. S3... The user enters the first quantum entanglement display command into the input section. S4... A step to display all display points on the second and third spheres. S5... The user enters the second quantum entanglement display command into the input section. S6... A step to display all display points on the first sphere, the second sphere, and the third sphere. S7... The user enters a measurement command into the input section. S8... A step to display the measurement results on the second and third spheres. S9... A step in which the user inputs a quantum gate corresponding to the measurement result into the input unit. S10... A step to display the state that was initially intended to be sent on the third sphere.

Claims

1. A quantum state display device that displays one quantum state on a spherical surface, A sphere and, A display unit including a plurality of display points arranged on the spherical surface, Input section, A control unit that controls the display unit, Equipped with, Each display point on the aforementioned display unit represents the quantum state of a qubit, The input unit is configured to allow the user to input a desired single quantum gate. A quantum state display device characterized in that, when a quantum gate is input to the input unit, the control unit controls the display unit to display a display point corresponding to the result of executing the quantum gate on the qubit.

2. The input unit is further configured to allow the user to input a desired quantum state. The quantum state display device according to claim 1, characterized in that when a quantum state is input to the input unit, the control unit controls the display unit to display a display point corresponding to the quantum state of the qubit.

3. The display unit includes at least two display points, The quantum state display device according to claim 1, characterized in that the two display points are located on the same great circle of the sphere and are symmetrical with respect to the center of the sphere.

4. The display unit includes at least four display points, The quantum state display device according to claim 1, characterized in that the four display points are located on the same great circle of the sphere and are symmetrical with respect to the center of the sphere.

5. The display unit includes at least six display points, The quantum state display device according to claim 1, characterized in that the six display points are located on two orthogonal great circles of the sphere and are symmetrical with respect to the center of the sphere.

6. The quantum state display device according to claim 3, characterized in that the one quantum gate input to the input unit includes a Pauli X gate, a Pauli Y gate, a Pauli Z gate, an S gate, and a T gate.

7. The quantum state display device according to claim 4, characterized in that the one quantum gate input to the input unit includes a Hadamard gate, a Pauli X gate, a Pauli Y gate, a Pauli Z gate, and a T gate.

8. The quantum state display device according to claim 5, characterized in that the one quantum gate input to the input unit includes a Hadamard gate, a Pauli X gate, a Pauli Y gate, a Pauli Z gate, an S gate, and a T gate.

9. The quantum state display device according to claim 1, characterized in that the display point represents a quantum state by emitting light.

10. The quantum state display device according to claim 9, characterized in that when a quantum gate is input to the input unit, the control unit controls the display unit to dynamically represent the operation of the quantum gate by continuously illuminating intermediate display points from the currently displayed display point to the display point corresponding to the result of executing the quantum gate.

11. It further includes a phase factor display unit, The quantum state display device according to claim 1, characterized in that when a single quantum gate is input to the input unit, the phase factor display unit displays the phase factor or eigenvalue obtained when the single quantum gate is executed on the qubit.

12. A quantum state display device that displays two quantum states on a spherical surface, The first sphere and, The second sphere and, A first display unit including a plurality of display points arranged on the first spherical surface, A second display unit including a plurality of display points arranged on the second spherical surface, Input section, A control unit that controls the first display unit and the second display unit, Equipped with, Each display point on the first display unit represents the quantum state of the first qubit, Each display point on the second display unit represents the quantum state of the second qubit, The input unit is configured to allow the user to input a desired two-quantum gate. A quantum state display device characterized in that, when two quantum gates are input to the input unit, the control unit controls the first display unit and the second display unit to display display points corresponding to the result of executing the two quantum gates on the first qubit and the second qubit.

13. The quantum state display device according to claim 12, characterized in that the two quantum gates input to the input unit include a controlled NOT gate and an exchange gate.

14. A quantum state display device that displays quantum entanglement states on a spherical surface, The first sphere and, The second sphere and, A first display unit including a plurality of display points arranged on the first spherical surface, A second display unit including a plurality of display points arranged on the second spherical surface, Input section, A control unit that controls the first display unit and the second display unit, Equipped with, Each display point on the first display unit represents the quantum state of the first qubit, Each display point on the second display unit represents the quantum state of the second qubit, The aforementioned input unit is configured to allow the user to input a quantum entanglement display command. A quantum state display device characterized in that, when a quantum entanglement display is input to the input unit, the control unit controls the first display unit and the second display unit so that each display point of the first display unit and each display point of the second display unit represent the quantum entanglement state of the first qubit and the second qubit.

15. The aforementioned input unit is configured to allow the user to input measurement commands while quantum entanglement is being displayed. The quantum state display device according to claim 14, characterized in that when the measurement command is input to the input unit, the control unit controls the first display unit and the second display unit to randomly display any of the states that the first qubit and the second qubit can take.

16. A quantum state display device that displays three quantum states on a spherical surface, The first sphere and, The second sphere and, The third sphere and, A first display unit including a plurality of display points arranged on the first spherical surface, A second display unit including a plurality of display points arranged on the second spherical surface, A third display unit including a plurality of display points arranged on the third spherical surface, Input section, A control unit that controls the first display unit, the second display unit, and the third display unit, Equipped with, Each display point on the first display unit represents the quantum state of the first qubit, Each display point on the second display unit represents the quantum state of the second qubit, Each display point on the third display unit represents the quantum state of the third qubit, The input unit is configured to allow the user to input the desired three quantum gates. A quantum state display device characterized in that, when three quantum gates are input to the input unit, the control unit controls the first display unit, the second display unit, and the third display unit to display a display point corresponding to the result of executing the three quantum gates on the first qubit, the second qubit, and the third qubit.

17. The quantum state display device according to claim 16, characterized in that the three quantum gates input to the input unit include a Toffoli gate.

18. A quantum state display device that displays quantum teleportation on a spherical surface, The first sphere and, The second sphere and, The third sphere and, A first display unit including a plurality of display points arranged on the first spherical surface, A second display unit including a plurality of display points arranged on the second spherical surface, A third display unit including a plurality of display points arranged on the third spherical surface, Input section, A control unit that controls the first display unit, the second display unit, and the third display unit, Equipped with, Each display point on the first display unit represents a quantum state to be transmitted to the receiver, Each display point on the second display unit represents a quantum state owned by the transmitter. Each display point on the third display unit represents a quantum state owned by the receiver, The input unit is configured to allow the user to input the operation of quantum teleportation. A quantum state display device characterized in that, when a quantum teleportation operation is input to the input unit, the control unit controls the first display unit, the second display unit, and the third display unit to represent the state when the quantum teleportation is performed.

19. The input unit is configured to accept inputs of the quantum state that the sender wishes to transmit, a first quantum entanglement display command, a second quantum entanglement display command, a measurement command, and a quantum gate corresponding to the measurement result. The control unit, - When the quantum state that the sender wishes to transmit is input to the input unit, the first display unit displays the quantum state to be transmitted, the second display unit displays the state |0>, and the third display unit displays the state |0>, thereby controlling the first display unit, the second display unit, and the third display unit. - When the first quantum entanglement display command is input to the input unit, the second display unit and the third display unit are controlled so that each display point of the second display unit and each display point of the third display unit represent the quantum entanglement state of the second qubit and the third qubit. - When the second quantum entanglement display command is input to the input unit, the first display unit, the second display unit, and the third display unit are controlled so that each display point of the first display unit, each display point of the second display unit, and each display point of the third display unit represent the quantum entanglement state between the first qubit, the second qubit, and the third qubit. - When the measurement command is input to the input unit, the first display unit, the second display unit, and the third display unit are controlled to randomly display one of the possible states of the first qubit, the second qubit, and the third qubit. - When a quantum gate corresponding to the measurement result is input to the input unit, the third display unit is controlled so that it displays the quantum state that the sender wanted to transmit. The quantum state display device according to feature 18.

20. The quantum gate corresponding to the measurement results is, - If the measurement results show that the quantum state of the first qubit is |0> and the quantum state of the second qubit is |0>, then it is the identity operator. - If the measurement results show that the quantum state of the first qubit is |0> and the quantum state of the second qubit is |1>, then it is a Pauli X gate. - If the measurement results show that the quantum state of the first qubit is |1> and the quantum state of the second qubit is |0>, then it is a Pauli Z gate. - If the measurement results show that the quantum state of the first qubit is |1> and the quantum state of the second qubit is |1>, then it is a Pauli Y gate. The quantum state display device according to feature 19.

21. The quantum state display device according to claim 1, characterized in that the display point represents a quantum state by mechanical movement by a three-axis rotation mechanism.

22. Each player has pieces, Each item corresponds to multiple quantum gates, A game that has, Each of the aforementioned pieces can take on multiple states corresponding to quantum states represented as points on the Bloch sphere, The game is characterized in that when the aforementioned item is applied to the aforementioned piece, it changes the state of the piece according to the operation rules of the quantum gate.

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