Figure 8 shows a quantum mechanical computer radio frequency (RF) signaling system 800, according to another embodiment. In particular, the quantum mechanical computer radio frequency (RF) signaling system 800 enables quantum entanglement between reactively coupled qubits. As depicted, quantum mechanical computer radio frequency (RF) signaling system 800 includes transmission lines 102, a plurality of networks of reactive electrical components 802-804 coupled to the transmission lines 102, a switch control unit 812 having control outputs 138-144 that are coupled to the plurality of networks of reactive electrical components 802-804d, and a plurality of qubit x 806 and qubit y 808 coupled to the plurality of networks of reactive electrical components 802-804d. As further depicted, a reactive coupling element 810 may couple qubit x 806 and qubit y 808. The reactive coupling element 810 may include a network of reactive components, a single capacitor between points A and B, or a transmission line capacitively coupled to links 825 and 827. Using reactive coupling element 810, a quantum entanglement condition between qubit x 806 and qubit y 808 may be accomplished.
The switch control unit 812 includes respective control outputs 138-144 that, among other things, control the actuation of switches within the plurality of networks of reactive electrical components 802-804d. In particular, the plurality of networks of reactive electrical components 802-804d may be identical to those utilized in Figure 1. The actuation of such switches is depicted in Figure 3, whereby under the control of a reactive network switch control unit 906, different capacitance values and attenuation factors can be set. Switch control unit 812 may be identical to reactive network switch control unit 906, and thus controls the capacitance values and attenuation factors for the plurality of networks of reactive electrical components 802-804d. Although not depicted in Figure 8, as with Figure 1, a switch unit identical to or similar to switch unit a 114 ( Figure 1) may be utilized between networks of reactive electrical components 802 and 804b, and qubit x 806. Moreover, a switch unit identical to or similar to switch unit b 116 ( Figure 1) may be utilized between networks of reactive electrical components 804c and 804d, and qubit y 808. Thus, depending on the configuration of switches R.sub.1 and R.sub.2 within each of the switch unit a 114 and switch unit b 116 ( Figure 1), qubit x 806 and qubit y 808 undergo either a predefined change in the linear combination of at least two quantum mechanical eigenstates, or maintain their current quantum mechanical eigenstate. The switch control unit 812 may be implemented in hardware, firmware, software, or any combination thereof. For illustrative brevity only two (2) adjacent qubit x 806 and qubit y 808 are depicted in Figure 8. It may, however, be appreciated that any number of qubits (i.e., 1-N) can be coupled to the transmission lines 102, via corresponding networks of reactive electrical components.
In operation, radio frequency (RF) pulse signals f.sub.1 and f.sub.2 are applied to respective transmission lines 102. The transmission lines 102 are each terminated by an impedance matching resistor 146 R in order to mitigate RF signal reflections associated with the radio frequency (RF) pulse signals f.sub.1, f. Sub.2 propagating along each of the transmission lines 102. RF pulse signals f.sub.1 and f.sub.2 may be similar to the RF pulse signal illustrated in Figure 7. For example, RF pulse signals f.sub.1 may include a 5.00 Ghz RF signal that is generated over a 20 nanosecond (ns) pulse period (T.sub.pulse) at 1 microsecond (.mu.s) intervals (T.sub.int). Also, RF pulse signals f.sub.2 may include a 5.05 Ghz RF signal that is generated over a 20 nanosecond (ns) pulse period (T.sub.pulse) at 1 microsecond (.mu.s) intervals (T.sub.int).
In the embodiment of Figure 8, each of the qubit x 806 and qubit y 808 can be driven by one of two different RF pulse signals (f.sub.1 or f.sub.2) that are each attenuated by a network of reactive electrical components. Furthermore, adjacent qubit x 806 and qubit y 808 may be reactively coupled to each other via the reactive coupling element 810. Specifically, as depicted in Figure 8, an RF pulse signal f.sub.1 may be applied to, and propagate, along transmission lines 102. The RF pulse signal f.sub.1 is then tapped off the transmission lines 102 and attenuated by the network of reactive electrical components 802, whereby the attenuated RF pulse signal f.sub.1 is applied to qubit x 806. Another RF pulse signal f.sub.2 may be applied to, and propagate, along transmission line . The RF pulse signal f.sub.2 is then tapped off the transmission line and attenuated by the network of reactive electrical components 804b, whereby the attenuated RF pulse signal f.sub.2 is also applied to qubit x 806. Thus, qubit x 806 may be driven either by an attenuated version of RF pulse signal f.sub.1 or an attenuated version of RF pulse signal f.sub.2.
Similarly, as further depicted in Figure 8, RF pulse signal f.sub.1 is also tapped off transmission lines 102 and attenuated by the network of reactive electrical components 804c, whereby the attenuated RF pulse signal f.sub.1 is applied to qubit y 808. RF pulse signal f.sub.2 is also tapped off transmission line and attenuated by the network of reactive electrical components 804d, whereby the attenuated RF pulse signal f.sub.2 is also applied to qubit y 808. Thus, qubit y 808 may be driven either by an attenuated version of RF pulse signal f.sub.1 or an attenuated version of RF pulse signal f.sub.2.
As previously described in relation to Figure 7, a qubit's angular rotation is proportional to the product of the amplitude (V.sub.rf) and pulse period (T.sub.pulse) of the radio frequency (RF) pulse signal 700. Since the pulse period (T.sub.pulse) of the radio frequency (RF) pulse signal 700 is related to its frequency, which is set to the resonance frequency of the qubit x 806 and qubit y 808 ( Figure 8), adjustments to each individual qubit x 806 and qubit y 808 ( Figure 8) angular rotation is accomplished by varying the amplitude (V.sub.adj) of the radio frequency (RF) pulse signals f.sub.1, f.sub.2 via the respective networks of reactive electrical components 802-804b ( Figure 8).
Referring back to Figure 8, since the networks of reactive electrical components 802-804d each have an identical electrical configuration to the network depicted in Figure 5, the networks of reactive electrical components 802-804d accordingly provide such an adjustment by means of variable capacitor C.sub.adj. Thus, for each of the networks of reactive electrical components 802-804d, increasing the capacitance of the variable capacitor C.sub.adj increases the attenuation, while decreasing the capacitance of the variable capacitor C.sub.adj decreases the attenuation provided the network.
The embodiment of Figure 8 may operate in two modes, whereby the quantum mechanical rotation of each qubit x 806 and qubit y 808 is either controlled separately (mode 1) or undergoes quantum mechanical entanglement with the other qubit (mode 2). In mode 1, for example, qubit x 806 may receive RF pulse signal f.sub.1 (e.g., 5.00 Ghz), which is attenuated by the network of reactive electrical components 802. Since the frequency of RF pulse signal f.sub.1 substantially matches the resonance frequency of qubit x 806, the qubit x 806 undergoes a predefined change (e.g., .pi./2) in the linear combination of at least two quantum mechanical eigenstates. However, since qubit y 808 has a resonant frequency that substantially matches the frequency of RF pulse signal f.sub.2 (e.g., 5.05 Ghz), based upon receiving attenuated RF pulse signal f.sub.1 from network 804c, the quantum mechanical eigenstate of qubit y 808 may remain substantially unchanged. Also in mode 1, for example, qubit y 808 may receive RF pulse signal f.sub.2 that is attenuated by network of reactive electrical components 804d. Since the frequency of RF pulse signal f.sub.2 substantially matches the resonance frequency of qubit y 808, the qubit y 808 undergoes a predefined change (e.g., .pi./2) in the linear combination of at least two quantum mechanical eigenstates. However, since qubit x 806 has a resonant frequency that substantially matches the frequency of RF pulse signal f.sub.1, based upon receiving attenuated RF pulse signal f.sub.2 from network 804b, the quantum mechanical eigenstate of qubit x 806 may remain unchanged. Thus, by applying RF pulse signal f.sub.1 (e.g., 5.00 Ghz) to qubit x 806 and applying RF pulse signal f.sub.2 (e.g., 5.05 Ghz) to qubit y 808, each qubit x 806 and quit y 808 eigenstate is individually controlled via an RF pulse signal that matches their individual resonant frequency.
In mode 2, for example, qubit x 806 receives RF pulse signal f.sub.2 that is attenuated by network of reactive electrical components 804b. Qubit y 808 also receives RF pulse signal f.sub.2 that is attenuated by network of reactive electrical components 804d. Although received RF pulse signal f.sub.2 matches the resonant frequency of qubit y 808 and does not substantially match the resonance frequency of qubit x 806, if the amplitude of RF pulse signal f.sub.2 is sufficient, some quantum entanglement occurs between qubit x 806 and qubit y 808 via the reactive coupling element 810. In particular, the quantum mechanical eigenstate change experienced by qubit y 808 depends on the quantum mechanical eigenstate of qubit x 806. Thus, the qubit x 806 and qubit y 808 are entangled.
The quantum mechanical computer radio frequency (RF) signaling system 800 may be maintained at cryogenic temperatures below one hundred (100) millikelvins (mK) in order to maintain the quantum mechanical computer radio frequency (RF) signaling system 800 at superconducting temperatures. For example, the quantum mechanical computer radio frequency (RF) signaling system 800 may be cooled in a cryostat to a temperature of about 30 mK.