1. Field of the Invention
The present invention relates to a quantum gate method and apparatus for executing a quantum gate operation using a resonator mode.
2. Description of the Related Art
The state of the nuclear spin of each rare-earth ion in crystal has a coherence time specifically long as a solid (it is approx. 500 μs at 4 K, 80 ms when a magnetic field is applied, and 30 s when an rf pulse sequence is applied), can be controlled and read by applying light thereto, and is therefore extremely suitable for realizing a solid quantum information processing device. A frequency-domain quantum computer has been proposed, in which a resonator mode is used to couple quantum bits formed of states of nuclear spins in crystal, thereby increasing the number of usable quantum bits (see, for example, Opt. Commun. 196, 119 (2001)). In the conventional technique, however, it is difficult to set a coupling constant g to a value sufficient for a 2-qubit gate (or multi-qubit gate) between quantum bits, since use of an f-f transition having a very small oscillator strength is presupposed for coupling with the resonator mode.
The reason why the use of the f-f transition is considered is that it satisfies the following two conditions, presupposing that a quantum bit is represented by the state of the nuclear spin of an ion in the electron ground state, which state has a long coherence time: (1) To discriminate the states of a single ion (such as |0> and |1> representing the basis states of the quantum bit) using optical transition energy, the employed homogenous broadening for an optical transition must be not more than the split width (10 to 100 MHz) due to the nuclear spin of the ion; and (2) since quantum bits are discriminated using optical transition energy, the employed homogenous broadening for the optical transition must be not more than the difference between energy levels used for discriminating the quantum bits (when quantum bits are discriminated using an inhomogenous distribution of a hyperfine structure, the homogenous broadening must be not more than approx. several kHz, and when the discrimination is executed using an inhomogenous broadening for an optical transition, the homogenous broadening must be not more than approx. several GHz).
If an f-d transition inherently allowable can be used instead of an f-f transition only a little allowable in the field of crystal, this is much more advantageous in view of the coupling constant (approx. 1000 times advantageous). However, the f-d transition has a great homogenous broadening (approx. 30 THz or less), and any method for satisfying the above-mentioned conditions (1) and (2) while using the f-d transition is not yet known.