Client: IBM

Figure 1 shows an exemplary embodiment of a quantum mechanical computer radio frequency (RF) signaling system 100. The quantum mechanical computer radio frequency (RF) signaling system 100 may include a transmission lines 102, a plurality of networks of reactive electrical components a 106-112 coupled to the transmission lines 102, a plurality of switch units 114-120 respectively coupled to the plurality of networks of reactive electrical components a 106-112, a plurality of output-stage networks of reactive electrical components 122-128 respectively coupled to the plurality of switch units 114-120, and a plurality of substantially identical qubits 130-136 respectively coupled to the output-stage networks of reactive electrical components 122-128. The quantum mechanical computer radio frequency (RF) signaling system 100 may also include a control logic unit 112 having respective control outputs 138-144 for controlling the actuation of the switches within switch units 114-120. The control logic unit 112 may be implemented in hardware, firmware, software, or any combination thereof. For illustrative brevity only four (4) qubits 130-136 are depicted in Figure 1. 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 and controllable switch units. 

The quantum mechanical computer radio frequency (RF) signaling system 100 may be maintained at cryogenic temperatures below one hundred (100) millikelvins (mK) in order to maintain the signaling system 100 at superconducting temperatures. For example, the quantum mechanical computer radio frequency (RF) signaling system 100 may be cooled in a cryostat to a temperature of about 30 mK. 

In operation, a radio frequency (RF) pulse signal is applied to the transmission lines 102. The transmission lines 102 is terminated by an impedance matching resistor 146 in order to mitigate RF signal reflections associated with the radio frequency (RF) pulse signal propagating along the transmission lines 102. Referring to Figure 7, an example of a radio frequency (RF) pulse signal 700 that is applied to the transmission lines 102 (Figure 1) is depicted, whereby a 4 Ghz RF signal is generated over a 20 nanosecond (ns) pulse period (T.sub.pulse) at 1 microsecond (.mu.s) intervals (T.sub.int). Alternatively, according to other non-limiting examples, the radio frequency (RF) pulse signal 700 may include an RF signal in the range of about 1-10 Ghz that is generated over a pulse period (T.sub.pulse) of about 10-500 ns at intervals (T.sub.int) in the order of microseconds (.mu.s), milliseconds (ms) or seconds (s). 

Referring back to Figure 1, the radio frequency (RF) pulse signal 700 (Figure 7) may be tapped off the transmission lines 102 and propagate in the direction of arrow A.sub.1. As depicted, the radio frequency (RF) pulse signal 700 propagates in the direction of arrow A.sub.1 and is input to the network of reactive electrical components a 106. The network of reactive electrical components a 106 attenuates the amplitude of the radio frequency (RF) pulse signal 700 by a factor of about 10-100. The attenuated radio frequency (RF) pulse signal 700 may then be received by switch unit a 114, whereby depending on the configuration of switches R.sub.1 and R.sub.2, qubit a 130 undergoes either a predefined change in the linear combination of at least two quantummechanical eigenstates, or maintains its current quantum mechanical eigenstate. Specifically, using control output a 138, if switch R.sub.1 of switch unit a 114 is actuated to a closed position while switch R.sub.2 of switch unit a 114 is actuated to an open position, the attenuated radio frequency (RF) pulse signal 700 passes through switch R.sub.1 and is applied to qubit a 130. By selecting the frequency of the attenuated radio frequency (RF) pulse signal 700 to substantially match the resonance of the qubit a 130, the qubit a 130 undergoes a predetermined rotation based on the amplitude of the attenuated radio frequency (RF) pulse signal 700. 

In some implementations, the output-stage network of reactive electrical components a 122 may be optionally omitted such that the attenuated radio frequency (RF) pulse signal 700 (Figure 7) passes through switch R.sub.1 to qubit a 130. In other implementations, the output-stage network of reactive electrical components a 122 may be included such that the attenuated radio frequency (RF) pulse signal 700 passes through switch R.sub.1 to qubit a 130 via the output-stage network of reactive electrical components a 122. As depicted in Figure 6, the output-stage network of reactive electrical components 600 may be substantially identical to that of the network of reactive electrical components a 106. However, in some implementations, the output-stage network of reactive electrical components 600 may be different to that of the network of reactive electrical components a 106. Moreover, each of the output-stage network of reactive electrical components 600 and the network of reactive electrical components a 106 may include a mix of different reactive components (e.g., capacitors and inductors). The output-stage network of reactive electrical components 600 further attenuates the radio frequency (RF) pulse signal 700 that passes through switch R.sub.1 to qubit a 130. Additionally, the reactive components of the output-stage network of reactive electrical components 600 isolate the qubit a 130 from the resistive characteristics of switches R.sub.1 and R.sub.2 within switch unit a 114. The resistive nature of switches R.sub.1 and R.sub.2 (e.g., Field Effecttransistor switches: FET switches) may accordingly cause the qubit a 130 to gradually loose its quantum eigenstate in the absence of such isolation.

Alternatively, as shown in Figure 1, using control output a 138, if switch R.sub.1 of switch unit a 114 is actuated to an open position while switch R.sub.2 of switch unit a 114 is actuated to a closed position, the qubit a 130 maintains its current eigenstate on the basis that it is isolated from the attenuated radio frequency (RF) pulse signal 700 (Figure 7) received from the network of reactive electrical components a 106. By closing switch R.subR.sub.2, the output terminal “o” of switch R.sub.1 is electrically coupled to ground via switch R.sub.2. Thus, any electrical leakage current across open-circuit switch R.subR.sub.1 (e.g., FET switch) may accordingly be diverted to ground via switch R.sub.2. By diverting this leakage current, potential quantum state changes associated with the qubit a 130 may be avoided. Thus, the qubit a 130 experiences longer coherence times. 

As further shown in Figure 1, the radio frequency (RF) pulse signal 700 (Figure 7) may be tapped off the transmission lines 102 and also propagate in the direction of arrow A.sub.2. As depicted, the radio frequency (RF) pulse signal 700 propagates in the direction of arrow A.sub.2 and is input to the network of reactive Electrical components b 108. The network of reactive Electrical components b 108 accordingly attenuates the amplitude of the radio frequency (RF) pulse signal 700 by a factor of about 10-100. The attenuated radio frequency (RF) pulse signal 700 (Figure 7) may then be received by switch unit b 116, whereby depending on the configuration of switches R.sub.1 and R.sub.2, qubit b 132 undergoes either a predefined change in the linear combination of at least two quantummechanical eigenstates, or maintains its current quantum mechanical eigenstate. Specifically, using control output b 140, if switch R.sub.1 of switch unit b 116 is actuated to a closed position while switch R.sub.2 of switch unit b 116 is actuated to an open position, the attenuated radio frequency (RF) pulse signal 700 passes through switch R.sub.1 and is applied to qubit b 132. Since the frequency of the attenuated radio frequency (RF) pulse signal 700 substantially matches the resonance of qubit b 132, as with qubit a 130, this qubit b 132 also undergoes the predetermined rotation based on the amplitude of the attenuated radio frequency (RF) pulse signal 700. 

In some implementations, the output-stage network of reactive electrical components b 124 may be optionally omitted such that the attenuated radio frequency (RF) pulse signal 700 (Figure 7) passes through switch R.sub.1 to qubit b 132. In other implementations, the output-stage network of reactive electrical components b 124 may be included such that the attenuated radio frequency (RF) pulse signal 700 passes through switch R.sub.1 to qubit b 132 via the output-stage network of reactive electrical components b 124. As depicted in Figure 6, output-stage network of reactive electrical components 600 may be substantially identical to that of the network of reactive Electrical components b 108. As such the output-stage network of reactive electrical components 600 further attenuates the radio frequency (RF) pulse signal 700 that passes through switch R.sub.1 to qubit b 132. Additionally, the reactive components of the output-stage network of reactive electrical components 600 isolate the qubit b 132 from the resistive characteristics of switches R.sub.1 and R.sub.2 within switch unit b 116. The resistive nature of switches R.sub.1 and R.sub.2 (e.g., Field Effecttransistor switches: FET switches) may accordingly cause the qubit b 132 to gradually loose its quantum eigenstate in the absence of such isolation. 

Alternatively, using control output b 140, if switch R.sub.1 of switch unit b 116 is actuated to an open position while switch R.sub.2 of switch unit b 116 is actuated to a closed position, the qubit b 132 maintains its current eigenstate on the basis that it is isolated from the attenuated radio frequency (RF) pulse signal 700 (Figure 7) received from the network of reactive Electrical components b 108. By closing switch R.subR.sub.2 of switch unit b 116, the output terminal “o” of switch R.sub.1 is electrically coupled to ground via switch R.sub.2. Thus, any electrical leakage current across the open-circuit switch R.subR.sub.1 (e.g., FET switch) of switch unit b 116 may accordingly be diverted to ground via switch R.sub.2. By diverting this leakage current, potential quantum state changes associated with the qubit b 132 may be avoided. Thus, the qubit b 132 experiences longer coherence times. 

Still referring to Figure 1, the radio frequency (RF) pulse signal 700 (Figure 7) may be tapped off the transmission lines 102 and further propagate in the direction of arrow A.sub.3. As depicted, the radio frequency (RF) pulse signal 700 propagates in the direction of arrow A.sub.3 and is input to the network of reactive Electrical components c 110. The network of reactive Electrical components c 110 accordingly attenuates the amplitude of the radio frequency (RF) pulse signal 700 by a factor of about 10-100. The attenuated radio frequency (RF) pulse signal 700 (Figure 7) may then be received by switch unit c 118, whereby depending on the configuration of switches R.sub.1 and R.sub.2, qubit c 134 undergoes either a predefined change in the linear combination of at least two quantummechanical eigenstates, or maintains its current quantum mechanical eigenstate. Specifically, using control output c 142, if switch R.sub.1 of switch unit c 118 is actuated to a closed position while switch R.sub.2 of switch unit c 118 is actuated to an open position, the attenuated radio frequency (RF) pulse signal 700 passes through switch R.sub.1 and is applied to qubit c 134. Since the frequency of the attenuated radio frequency (RF) pulse signal 700 substantially matches the resonance of qubit c 134, as with qubits 130-132, this qubit c 134 also undergoes the predetermined rotation based on the amplitude of the attenuated radio frequency (RF) pulse signal 700. 

In some implementations, the output-stage network of reactive electrical components c 126 may be optionally omitted such that the attenuated radio frequency (RF) pulse signal 700 (Figure 7) passes through switch R.sub.1 to qubit c 134. In other implementations, the output-stage network of reactive electrical components c 126 may be included such that the attenuated radio frequency (RF) pulse signal 700 passes through switch R.sub.1 to qubit c 134 via the output-stage network of reactive electrical components b 124. As depicted in Figure 6, output-stage network of reactive electrical components 600 may be substantially identical to that of the output-stage network of reactive electrical components c 110. As such the output-stage network of reactive electrical components 600 further attenuates the radio frequency (RF) pulse signal 700 that passes through switch R.sub.1 to qubit c 134. Additionally, the reactive components of the output-stage network of reactive electrical components 600 isolate the qubit c 134 from the resistive characteristics of switches R.sub.1 and R.sub.2 within switch unit c 118. The resistive nature of switches R.sub.1 and R.sub.2 (e.g., Field Effecttransistor switches: FET switches) may accordingly cause the qubit c 134 to gradually loose its quantum eigenstate in the absence of such isolation. 

Alternatively, using control output c 142, if switch R.sub.1 of switch unit c 118 is actuated to an open position while switch R.sub.2 of switch unit c 118 is actuated to a closed position, the qubit c 134 maintains its current eigenstate on the basis that it is isolated from the attenuated radio frequency (RF) pulse signal 700 (Figure 7) received from the network of reactive Electrical components c 110. By closing switch R.subR.sub.2 of switch unit c 118, the output terminal “o” of switch R.sub.1 is electrically coupled to ground via switch R.sub.2. Thus, any electrical leakage current across the open-circuit switch R.subR.sub.1 (e.g., FET switch) of switch unit c 118 may accordingly be diverted to ground via switch R.sub.2. By diverting this leakage current, potential quantum state changes associated with the qubit c 134 may be avoided. Thus, the qubit c 134 experiences longer coherence times. 

Still referring to Figure 1, the radio frequency (RF) pulse signal 700 (Figure 7) may be tapped off the transmission lines 102 and further propagate in the direction of arrow A.sub.4. As depicted, the radio frequency (RF) pulse signal 700 also propagates in the direction of arrow A.sub.4 and is accordingly input to the network of reactive Electrical components d 112. The network of reactive Electrical components d 112 thus attenuates the amplitude of the radio frequency (RF) pulse signal 700 by a factor of about 10-100. The attenuated radio frequency (RF) pulse signal 700 may then be received by switch unit d 120, whereby depending on the configuration of switches R.sub.1 and R.sub.2, qubit d 136 undergoes either a predefined change in the linear combination of at least two quantummechanical eigenstates, or maintains its current quantum mechanical eigenstate. Specifically, using control output d 144, if switch R.sub.1 of switch unit d 120 is actuated to a closed position while switch R.sub.2 of switch unit d 120 is actuated to an open position, the attenuated radio frequency (RF) pulse signal 700 (Figure 7) passes through switch R.sub.1 and is applied to qubit d 136. Since the frequency of the attenuated radio frequency (RF) pulse signal 700 substantially matches the resonance of qubit d 136, as with qubits 130-134, this qubit d 136 also undergoes the predetermined rotation based on the amplitude of the attenuated radio frequency (RF) pulse signal 700. 

In some implementations, the output-stage network of reactive electrical components d 128 may be optionally omitted such that the attenuated radio frequency (RF) pulse signal 700 (Figure 7) passes through switch R.sub.1 to qubit d 136. In other implementations, the output-stage network of reactive electrical components d 128 may be included such that the attenuated radio frequency (RF) pulse signal 700 passes through switch R.sub.1 to qubit d 136 via the output-stage network of reactive electrical components d 128. As depicted in Figure 6, output-stage network of reactive electrical components 600 may be substantially identical to that of the network of reactive Electrical components d 112. As such the output-stage network of reactive electrical components 600 further attenuates the radio frequency (RF) pulse signal 700 that passes through switch R.sub.1 to qubit d 136. Additionally, the reactive components of the output-stage network of reactive electrical components 600 isolate the qubit d 136 from the resistive characteristics of switches R.sub.1 and R.sub.2 within switch unit d 120. The resistive nature of switches R.sub.1 and R.sub.2 (e.g., Field Effecttransistor switches: FET switches) may accordingly cause the qubit d 136 to gradually loose its quantum eigenstate in the absence of such isolation. 

Alternatively, using control output d 144, if switch R.sub.1 of switch unit d 120 is actuated to an open position while switch R.sub.2 of switch unit d 120 is actuated to a closed position, the qubit d 136 maintains its current eigenstate on the basis that it is isolated from the attenuated radio frequency (RF) pulse signal 700 (Figure 7) received from the network of reactive Electrical components d 112. By closing switch R.subR.sub.2 of switch unit d 120, the output terminal “o” of switch R.sub.1 is electrically coupled to ground via switch R.sub.2. Thus, any electrical leakage current across the open-circuit switch R.subR.sub.1 (e.g., FET switch) of switch unit d 120 may accordingly be diverted to ground via switch R.sub.2. By diverting this leakage current, potential quantum state changes associated with the qubit d 136 may be avoided. Thus, the qubit d 136 experiences longer coherence times. 

The attenuation of the radio frequency (RF) pulse signal 700 (Figure 7) by the networks of reactive electrical components a 106-112 allows individual signal amplitude adjustment and mitigates interactions between the qubits 130-136. Referring to Figure 5, an exemplary network of reactive electrical components 502 that may be used for networks 106-112 (Figure 1) is depicted. The network of reactive electrical components 502 may be described by its equivalent circuit 504. As shown, an inputRF pulse signal (i.e., RF.sub.1) is attenuated by the divider network of capacitors (i.e., reactive components) to provide an outputattenuated RF pulse signal (i.e., RF.sub.2). In particular, the relationship between the inputRF pulse signal (i.e., RF.sub.1) and the outputattenuated RF pulse signal (i.e., RF.sub.2) is given by: 

RF 2 = RF 1 ( C 1 C 1 + C 2 + C adj ) equation 1 ##EQU00001## 

Whereby C.sub.1 is an input capacitive reactive component having an input terminal coupled to the transmission lines 102 (Figure 1) and an output terminal coupled to parallel capacitive reactive components C.sub.adj and C.sub.2. Thus, the input capacitive reactive component C.sub.1 and the parallel configured capacitive reactive components C.sub.adj, C.sub.2 are in series. Based on equation 1, by increasing the capacitance value of variable capacitor C.sub.adj, the attenuation of the inputRF pulse signal (i.e., RF.sub.1) is also increased. Conversely, by decreasing the capacitance value of variable capacitor C.sub.adj, the attenuation of the inputRF pulse signal (i.e., RF.sub.1) is accordingly reduced. 

Referring to Figure 6, the depicted output-stage network of reactive electrical components 600 may be used for networks 122-128 of Figure 1. The output-stage network of reactive electrical components 600 may be described by its equivalent circuit 602. As shown, the attenuated RF pulse signal RF.sub.2 output from network 502 (Figure 5) is (optionally) further attenuated (i.e., RF pulse signal RF.sub.3) by the divider network of capacitors (i.e., reactive components) corresponding to output-stage network of reactive electrical components 600. In particular, the relationship between the inputted attenuated RF pulse signal RF.sub.2 and the outputted further attenuated RF pulse signal RF.sub.3 is given by: 

RF 3 = RF 2 ( C 1 ‘ C 1 ‘ + C 2 ‘ + C adj ‘ ) equation 2 ##EQU00002## 

Whereby C’.sub.1 is an input capacitive reactive component having an input terminal coupled to output terminal `o` (Figure 1) of a respective switch unit and an output terminal coupled to parallel capacitive reactive components C’.sub.adj and C’.sub.2. Thus, the input capacitive reactive component and the parallel configured capacitive reactive components C’.sub.adj, C’.sub.2 are in series. Based on equation 2, by increasing the capacitance value of variable capacitor C’.sub.adj, the attenuation of the attenuated input RF pulse signal (i.e., RF.sub.2) is also increased. Conversely, by decreasing the capacitance value of variable capacitor C’.sub.adj, the attenuation of the attenuated input RF pulse signal (i.e., RF.sub.2) is accordingly reduced. As previously described, the circuits depicted in both FIGS. 5 and 6 may be identical, thus applying the same attenuation to the received RF pulse signals. Moreover, the circuits depicted in both FIGS. 5 and 6 are utilized in both the plurality of networks of reactive electrical components a 106-112 (Figure 1) and the plurality of output-stage networks of reactive electrical components 122-128 (Figure 1), respectively. 

Referring to Figure 3, an exemplary controllable reactive component 302 used to implement a variable capacitor 904 is depicted. The exemplary controllable reactive component 302 represented by variable capacitor 904 may be used in both the plurality of networks of reactive electrical components a 106-112 (Figure 1: C.sub.adj) and the plurality of output-stage networks of reactive electrical components 122-128 (Figure 1; and Figure 6: C.sub.adj), respectively. As depicted, the controllable reactive component 302 may include a parallel configuration of multiple capacitors C.sub.adj1, C.sub.adj2, C.sub.adj3, and C.sub.adj4. Each of the capacitors C.sub.adj1, C.sub.adj2, C.sub.adj3, C.sub.adj4 are connected to ground via respective switches S.sub.adj1, S.sub.adj2, S.sub.adj3, and S.sub.adj4. In particular, one terminal of each of the capacitors C.sub.adj1, C.sub.adj2, C.sub.adj3, C.sub.adj4 is coupled together, while the other terminal of each of the capacitors C.sub.adj1, C.sub.adj2, C.sub.adj3, C.sub.adj4 is connected in series to respective switches S.sub.adj1, S.sub.adj2, S.sub.adj3, and S.sub.adj4. In operation, by actuating the switches S.sub.adj1, S.sub.adj2, S.sub.adj3, S.sub.adj4 to a closed position, the capacitors C.sub.adj1, C.sub.adj2, C.sub.adj3, C.sub.adj4 are coupled to ground and remain part of the parallel configuration of capacitors. Alternatively, by actuating the switches S.sub.adj1, S.sub.adj2, S.sub.adj3, S.sub.adj4 to an open position, the capacitors C.sub.adj1, C.sub.adj2, C.sub.adj3, C.sub.adj4 are not coupled to ground and are thus removed from the parallel configuration of capacitors. For example, by actuating switches S.sub.adj1 and S.sub.adj4 to a closed position and switches S.sub.adj2 and S.sub.adj3 to an open position, capacitors C.sub.adj1 and C.sub.adj4 are coupled to ground and in a parallel configuration, while capacitors C.sub.adj2 and C.sub.adj2 are not within the parallel configuration. The total capacitance is thus the sum of capacitors C.sub.adj1 and C.sub.adj4. By varying the switch positions, different capacitance values can therefore be obtained for altering the attenuation factors within the networks of reactive electrical components a 106-112 and the plurality of output-stage networks of reactive electrical components 122-128. For example, in order to increase the total capacitance given by the sum of capacitors C.sub.adj1 and C.sub.adj4, switch S.sub.adj3 may additionally be actuated to a closed position. The total capacitance is now the sum of capacitors C.sub.adj1, C.sub.adj3, and C.sub.adj4. Thus, the controllable reactive component 302 provides an exemplary adjustable reactance within the plurality of networks of reactive electrical components a 106-112 (Figure 1) and the plurality of output-stage networks of reactive electrical components 122-128 (Figure 1). Accordingly, varying this adjustable reactance in turn varies the attenuation provided by the plurality of networks of reactive electrical components a 106-112 (Figure 1) and the plurality of output-stage networks of reactive electrical components 122-128 (Figure 1). 

For illustrative brevity only four (4) parallel capacitors and switches are depicted in Figure 3. However, it may be appreciated that any number of parallel capacitors may be utilized in order to establish the requisite resolution of attenuation factor variation exhibited by any one of the plurality of networks of reactive electrical components a 106-112 (Figure 1) and the optionally provided plurality of output-stage networks of reactive electrical components 122-128 (Figure 1). The capacitors associated with the networks of reactive electrical components a 106-112 (Figure 1) and the plurality of output-stage networks of reactive electrical components 122-128 (Figure 1) may have capacitance values in the range of 0.1-10 femtofarads (fFs). However, greater or lesser values may be contemplated. 

Referring to Figure 2, the switches S.sub.adj1, S.sub.adj2, S.sub.adj3, S.sub.adj4 (Figure 3) used in the exemplary controllable reactive component 302 (Figure 3) may be implemented by a transistor device. Thus, switch 802 may be implemented by FET device 804. More specifically, by applying a control voltage to the gate G of the FET device 804, a closed electrical circuit connection may be established between the drain D and the Source S of the device 804. 

Referring to Figure 4, each of the qubits 130-136 shown in Figure 1 may, for example, include a transmon 402. As depicted, the transmon 402 may be characterized as a resonant circuit 404 having a capacitance C and a non-linear inductance LAO. Thus, when the transmon receives an RF pulse signal having a frequency that is substantially the same as (i.e., matches) its resonant frequency, the transmon may accordingly oscillate backwards and forwards between, for example, two (2) quantummechanical eigenstates. The oscillation frequency backwards and forwards between these two states occurs at a lower frequency that is proportional to the amplitude of the RF pulse signal. Therefore, as previously described, by controlling the amplitude of the RF pulse signal that is applied to the transmon 402, a desired quantum mechanical eigenstate may be achieved at the end of each pulse period. The transmon 402 may include a josephson junction formed by a metal-insulator-metal (MIM) layer of aluminum, aluminum oxide, and aluminum. 

Referring back to Figure 1, in operation, two or more of the substantially identical qubits 130-136 may require a predefined change in their respective quantum mechanical eigenstates (e.g., a .pi./2 rotation). Referring 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 the same for all of the substantially identical qubits 130-136 (Figure 1), adjustments to each individual qubit’s 130-136 (Figure 1) angular rotation is accomplished by varying the amplitude (V.sub.rf) of the radio frequency (RF) pulse signal 700 via the respective networks of reactive electrical components a 106-108 (Figure 1). Referring back to Figure 1, in particular, the respective networks of reactive electrical components a 106-108 provide such an adjustment by means of variable capacitor C.sub.adj. Also, as previously described, in embodiments that further include output-stage network of reactive electrical components a 122-108d, the amplitude V.sub.rf (Figure 7) of the radio frequency (RF) pulse signal 700 (Figure 7) may be further adjusted using variable capacitors C’.sub.adj (Figure 6). 

For example, the radio frequency (RF) pulse signal 700 (Figure 7) may be applied to qubit a 130 and qubit b 132 by configuring respective switch unit a 114 and switch unit b 116 accordingly. Since qubit a 130 and qubit b 132 are substantially identical and receive the same radio frequency (RF) pulse signal 700 that is tapped off the transmission lines 102, there may be an expectation that the qubit a 130, qubit b 132 underdo the same quantum mechanical rotation. This expectation may however be thwarted by a difference in reactive component tolerances between the network of reactive electrical components a 106 corresponding to qubit a 130 and the network of reactive Electrical components b 108 corresponding to qubit b 132. More specifically, although the capacitors (i.e., reactive components) within qubit a 130‘s network of reactive electrical components a 106 are manufactured to be the same as qubit b 132‘s network of reactive Electrical components b 108, the manufacturing process may cause slight variations in the capacitance values between the networks of reactive electrical components a 106, 108. For instance, although capacitor C.sub.2 within the qubit a 130‘s network of reactive electrical components a 106 is manufactured to have the same capacitance as capacitor C.sub.2 within qubit b 132‘s network of reactive Electrical components b 108, due to manufacturing tolerances, the C.sub.2 capacitor values in the networks of reactive electrical components a 106, 108 may slightly differ. This causes a slight difference in capacitive reactance value, which in turn contributes to differences in attenuation between network 106 and network 108. Thus, for the same applied RF pulse signal 700 (Figure 7), qubit a 130 and qubit b 132 undergo different rotations as a result of the RF pulse signal 700 being attenuated by slightly different amounts before being applied to the qubit a 130, qubit b 132. However, during calibration, each of the network of reactive electrical components a 106, 108 can be individually adjusted to compensate for such differences in attenuation resulting from reactive component tolerances. Thus, by making the appropriate adjustments, each of qubit a 130 and qubit b 132 receive an attenuated RF pulse signal having the same amplitude, which subsequently causes both qubits to undergo the same predetermined rotation (e.g., a .pi./2 rotation). More particularly, the C.sub.adj capacitance values of the network of reactive electrical components a 106, 108 may be adjusted to compensate for such differences in attenuation resulting from the reactive component tolerances associated with the network of reactive electrical components a 106, 108. 

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 quantummechanical 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 quantummechanical 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 quantummechanical 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 matchestheir 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. 

Figure 9 shows an exemplary two-dimensional array of qubits 900 receiving RF pulse signals, according to one embodiment. Each of the dark circles denoted by numbers 1-5 represent a qubit. As depicted, each of the qubits are weakly coupled (i.e., reactively) by quantum communication (QC) links QCL. The QC linkslinks QCL may include superconductive electrical links formed from, for example, Aluminum (Al) or Niobium (Nb), whereby each QC link QCL may be reactively coupled (e.g., capacitively) to a qubit at each end. The QC linkslinks QCL provide a means for enabling quantum entanglement conditions between the qubits in the array. As shown, qubits 1 are coupled to transmission line TL1 and are driven at a frequency F1, qubits 2 are coupled to transmission line TL2 and are driven at a frequency F2, qubits 3 are coupled to transmission line TL3 and are driven at a frequency F3, qubits 4 are coupled to transmission line TL4 and are driven at a frequency F4, qubits 5 are coupled to transmission line TL5 and are driven at a frequency F5, and qubits 1 are coupled to transmission line TL’1 and are also driven at frequency F1. In a serpentine connection approach, transmission lines that carry the same frequency to the qubits may be connected together. For example, transmission lines TL1 and TL’1 are both driven at the same frequency F1, and are thus connected together, as indicated by dashed lineconnection 908. Although for illustrative brevity, only transmission lines TL1 and TL’1 are shown, additional transmission lines coupled to other qubits 1 in the exemplary two-dimensional array of qubits 900 would also follow a serpentine pattern of connections. The same rationale may be applied to transmission lines TL2-TL5. 

Alternatively, connections such as connection 908 may be omitted in favor of, for example, inductively coupling a frequency source to transmission lines being driven by the same frequencypulse signal. For example, transmission lines TL1 and TL’1 are both driven at the same frequency F1. Therefore, the RF output signal from a single RF source 904 (i.e., signal generator) may be inductively coupled to each of the transmission lines TL1, TL’1 that are driven at the same frequency F1. In particular, inductive coupling device a 904couples the RF output signal from RF source 904 to transmission lines TL1, while inductive coupling device b 906couples the RF output signal from RF source 904 to transmission lines TL’1. The same rationale may be applied to transmission lines TL2-TL5. The qubits 1-5 depicted in exemplary two-dimensional array of qubits 900 may include the same or similar circuitry for receiving an attenuated RF pulse signal as those corresponding to system 100 of Figure 1. 

The above exemplary two-dimensional array of qubits 900 of qubits 1-5 may be utilized to form, among other things, a surface code method of error prevention/correction using a discrete number of frequencies, pulse shapes, and phases. For example, one approach may contemplate using five (5) different qubit frequencies (i.e., F1-F5), and six (6) or more different pulses (e.g., pulse period, pulse interval, etc.) associated with each frequency. It may be appreciated that the depicted 2D mesh is exemplary. Thus, different lattices with different interconnections of the qubits and a different numbers of frequencies can be utilized. 

The two-dimensional array of qubits 900 may be maintained at cryogenic temperatures below one hundred (100) millikelvins (mK) in order to maintain the array 900 at superconducting temperatures. For example, the two-dimensional array of qubits 900 may be cooled in a cryostat to a temperature of about 30 mK. 

Although the exemplary embodiments described in the foregoing include networks of reactive components having capacitor devices, other reactive components such as inductors may also be utilized in order to provide a divider network capable of attenuating the received RF pulse signals in a controlled manner.