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Quantum Computer
Qubit solid-state device: Demonstration of a C-NOT circuit
Ok, now that we understand these basic operation principles, I would like to introduce the results of our experiment. Experimental data is shown in the following figures. The vertical axis of these graphs shows the value of output current flowing through the probe electrode used for observation. Higher values of current mean that a qubit is closer to the 1 state in which a Cooper-pair exists in the Cooper-pair box. The horizontal axis represents change made in degree of superposition in control-bit input, from the pure 0 state on the left, to the increasing weight of a1 state when moving to the right.
Experimental Results 1: This graph demonstrates what happens when fixing target-bit input to the 0 state and gradually changing control-bit input from 0 to 1. The output of the target bit changes from 1 to 0 in accordance with that change.
Experimental Results 2: This graph, in contrast, demonstrates what happens when fixing target-bit input to the 1 state and gradually changing control-bit input from 0 to 1. In this case, the output of the target bit changes from 0 to 1 in accordance with that change.
For both experimental results 1 and 2, the table shown below each graph is called a "truth table" that expresses the logical operation expected of a C-NOT operation in a quantum computer. The above experimental results demonstrated that the correct results as those shown in the truth tables were obtained. Specifically, the state of the target bit flips when the control bit is in the 0 state and remains unchanged when the control bit is in the 1 state. In the two output graphs shown, the data inside the green bars at both ends of each graph reflects these results. This, by itself, however, cannot be said to constitute the logical operation of a quantum computer. Of particular importance is the fact that the data at both ends of each graph are connected in a continuous manner as can be seen in the area enclosed by the ellipse at the center. This shows that input of a quantum-mechanical superposition state results in the output of the expected superposition state, which is very different from existing computers.
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In this experiment, we successfully performed a 2-bit logical operation using solid-state qubits, a world’s first. In general, a circuit performing a logical operation is called a "gate," and a gate or set of gates that can perform any logical operation needed by a computer by an appropriate combination of that gate or gate set is called a "universal gate." In existing computers, a set of AND and NOT gates or a NAND gate corresponds to a universal gate. In a quantum computer, the gate set consisting of a gate for controlling superposition in one qubit and a C-NOT gate for 2 qubits corresponds to a universal gate. We have therefore successfully constructed a universal gate for a quantum computer using a solid-state device.
Reading computational expressions
The notation "| >" in the expression α|0> + β|1> is a means of expressing states in quantum mechanics. In the input figures shown, the expression α|0> + β|1> indicates a 1-bit superposition state while α|01> + β|10> indicates a 2-bit entangled state.
