Please note that JavaScript and style sheet are used in this website,
Due to unadaptability of the style sheet with the browser used in your computer, pages may not look as original.
Even in such a case, however, the contents can be used safely.

Quantum Computer

Quantum computer operation mechanism

We then proceeded to study a method for performing a quantum logic operation with two qubits, which is the other condition that must be satisfied for achieving quantum computing. As a first step in this direction, we succeeded in placing two qubits in an entangled state in February 2003. --> Press Release

The entangled state is indispensable for manifesting the ultra-high-speed properties of a quantum computer. To begin with, the entangled state makes it possible to handle 2N states as desired. In the case of two qubits, for example, we know that the four values 00, 01, 10, and 11 can be simultaneously expressed in a superposition state, but a quantum computer must also be able to deal with any combination of those values. Consider the combination of the values 00 and 11. Here, if the state of one of the qubits is decided, the state of the other qubit is likewise decided, giving these qubits a very strange form of correlation. This is called an entangled state. --> What is the difference between "entanglement" and "superposition"?

At that stage of our research in February of that year, however, we were not able to manipulate this correlation as we wanted despite the fact that we clarified its existence. To be able to say that "a logical operation was achieved," it was absolutely necessary that we be able to manipulate that correlation as desired, and to that end, we accelerated our research efforts.

solid state device

The device used in the experiment for this research (right figure) was basically the same as that of the February experiment demonstrating the entangled state.

The overall size of the device was slightly more than 1 micron while the size of a Cooper-pair box here was about 0.9 micron × 0.05 micron. The device consisted of aluminum thin film and fabricated using advanced nano-fabrication techniques.

This experiment, however, differed from the February experiment in two ways. First, we changed the structure of the device so that each of the two coupled qubits could be controlled independently as needed. Second, we contrived a new pulse-signal sequence for performing a logical operation. That is, discovering the voltage pulse conditions for enabling a logical operation was a key to our success in freely creating an entangled state.

I will now describe the mechanism of a logical operation on this device using simplified conceptual diagrams. We first consider the case with the control bit in the 0 state.

There is no excess Cooper-pair in the Cooper-pair box of the control bit at this time. If we now apply a voltage pulse having appropriate height and length, a Cooper-pair can be made to tunnel into the Cooper-pair box of the target bit. That is to say, the state of the target bit can be made to flip from 0 to 1.

Let’s now consider the case with the control bit in the 1 state.

This time, an excess Cooper-pair exists in the Cooper-pair box of the control bit. The existence here of only two electrons is enough to change the energy state of the target bit via the coupling capacitor. As a result, the tunnel becomes blocked and the target bit remains unchanged even if a target pulse the same as before were to be applied to the target bit. In this way, the response of the target bit to the applied voltage pulse depends on the state of the control bit. In particular, the state of the target bit will flip from 0 to 1 only when the control bit is in the 0 state. This is a Controlled-NOT (C-NOT) logical operation in the sense that NOT logic controlled by the value of the control bit acts on the target bit.

In the above description, I have assumed that the state of the control bit and that of the target bit are clearly 0 or 1. But for this device to work as a quantum computer circuit, correct operation must be ensured even if these qubits are in a superposition state, such as when the control bit is in a superposition state of the 0 and 1 state.

What is the difference between "entanglement" and "superposition"?

Another way of saying "entangled state" would be "non-separable state." Here, "separable" itself means the separation of a state composed of multiple qubits into the individual states of those qubits.
Let’s consider the states of two qubits (qubit A and qubit B). If qubit A is in the 0 state (denoted as |0>A) and qubit B in the 1 state (|1>B), the total state of these two qubits can be written as follows:
|0>A|1>B=|01>
Let’s now assume a state denoted as α|00>+β|01>. This indicates that the state |00> and the state |01> are in a superposition state. On closer examination, however, we can see that qubit A in this superposition state is always in the 0 state. The above state can therefore be rewritten as follows: α|00>+β|01>=|0>(α|0>+β|1>) This tells us that the states of these two qubits can be separated. (Incidentally, qubit B at this time takes on a superposition state denoted as α|0>+β|1>.) In other words, this is not an entangled state. But what about the state denoted as α|00>+β|11>? This too is a superposition state, but in this case, the state cannot be separated into the states of individual qubits. This, as a result, is an entangled state. As shown by these two examples, an entangled state is necessarily a superposition state but a superposition state is not necessarily an entangled state. An entangled state only can be achieved when some interaction exists between two qubits.