Abstract:
A ferroelectric is used to switch a superconductor computer element. Part of the superconductor element can be a high temperature superconductor layer, doped to the vicinity of a superconductor insulator transition. The ferroelectric overlies the superconductor layer, forming a heterostructure. A voltage can be applied to polarize the ferroelectric. This polarization in turn generates an electric field for the superconductor layer, effectively changing its doping. For sufficiently large voltages the superconductor transitions into an insulating state. When included into a sensor, this heterostructure can function as a switch, used in relation to reading the state of qubits. When coupling two qubits, this heterostructure can be used to control the entanglement of the two qubits.

Description:
BACKGROUND  
         [0001]    1. Field of the Invention  
           [0002]    This invention relates to ferroelectric-superconductor heterostructures, and to high temperature solid state quantum computing devices.  
           [0003]    2. Description of Related Art  
           [0004]    A quantum bit (qubit) is an elementary component of a quantum computer or a quantum information device. The qubit is a bistable device capable of supporting the coherent evolution of its quantum states in a controlled fashion. Prime candidates for systems with two quantum states are superconducting devices, such as ring shaped Superconducting Quantum Interference Devices (“SQUIDs”).  
           [0005]    Matter in the superconducting state is capable of supporting currents with zero resistance, so-called supercurrents. This zero resistance flow is possible because electrons join in Cooper pairs, forming a superconducting condensate. Supercurrent carrying states consist of a macroscopic number of electrons, all in the same quantum state, and correspondingly the value of the current, a physical observable, has a very narrow distribution with a width inversely proportional to the number of the constituent electrons. The properties of such quantum states are easy to observe with very little uncertainty. Furthermore, tunneling between states with different supercurrents is possible, allowing for transitions between these quantum states. For these reasons, for example, left and right moving supercurrent carrying states in a SQUID are prime candidates for the quantum states of a qubit in a quantum computer.  
           [0006]    Proposals have been made and efforts are underway to fabricate qubits by patterning films of copper oxide superconductors as described, for example, by A. M. Zagoskin, “A scalable, tunable qubit, based on a clean DND or grain boundary D-D junction,” LANL, cond-mat/9903170 (March 1999, and the references therein, incorporated hereby in its entirety. During the fabrication it is necessary to mechanically, chemically or otherwise etch islands of these materials of various shapes and crystallographic orientations and connect them via weak links. Because of the nature of these materials and the need to fabricate islands of mesoscopic sizes, the techniques involved are complicated and costly. Furthermore, once the pattern is formed, it is generally difficult to change it. On the other hand, successful integration of the individual qubits into a practical quantum computer or other device requires these patterns to be flexible, in that one should be able to open and close connections between individual qubits reversibly. In particular it is essential for the operation of any quantum computing device that qubits are typically isolated from each other, but connected in a specific way when the qubits execute a computational step, for example, by entangling their quantum states. Finally, any increase in the operating temperature of these devices will make their applications easier. Thus, there is a need for reversible switching mechanisms for solid state quantum computing systems, capable of operating at high temperatures.  
           [0007]    An important characteristic of quantum computing systems is the tunneling rate of the qubit. The tunneling rate of the qubit, or the rate of quantum evolution is the frequency by which the state of the qubit tunnels from one of its quantum states to the other. The tunneling rate dictates the speed of operation of all the other components in the quantum computing system. For example, in order to read the state of a qubit, the qubit can be grounded, which collapses the wavefunction of the qubit into one of its quantum states. If the qubit could not be grounded at a frequency higher than its tunneling rate, then the qubit would change its state during the grounding procedure. Typically, the tunneling rate of a qubit is of the order of 10 GHz. The requirement to exceed this value places a stringent bound on the switching rate of any device that interfaces with the qubit, and the other parts of the quantum computing system.  
           [0008]    A single electron transistor (SET) is a switch that includes a superconducting mesoscopic island isolated by two Josephson tunnel junctions. Typically, the SET is controlled by a gate voltage, where the coupling between the gate and the SET is capacitive. By modulating the gate voltage the SET can be opened and closed, acting as a switch. The SET can perform switching functions for the transport of single electrons or Cooper pairs. The operation and behavior of SETs is known in the art, and is described in detail, for example, by P Joyez et al. In “Observation of Parity-Induced Supression of Josephson Tunneling in the Superconducting Single Electron Transistor,” Physical Review Letters, Vol. 72, No. 15, 11 April 1994, and the references therein.  
           [0009]    Coherence is present in a superconducting switch, if a supercurrent can pass through it. Coherent switches are important elements of the solid state quantum computing systems, particularly in supporting the entanglement of the quantum states of the qubits with minimal losses. Low temperature SETs, made of materials such as niobium or aluminum, have been shown to achieve coherence, see for example M. T. Tuominen, J. M. Hergenrother, T. S. Tighe, and M. Tinkham, “Experimental Evidence for Parity-Based  2   e  Periodicity in an Superconducting Single-Electron Transistor,” Phys. Rev. Lett. 69, 1997 (Sep. 28, 1992). However, current SETs made out of high temperature superconducting materials have not been shown to achieve coherence. This is in part due to the complications of working at higher temperatures.  
           [0010]    High-temperature copper-oxide superconductors (“cuprates”) are layered perovskite materials in which superconductivity depends strongly on the doping concentration. For example, in the compound GdBa 2 Cu 3 O 7-x  the doping of the system is achieved by changing the oxygen concentration x. As can be seen in the typical phase diagram of cuprates in FIG. 1, varying the doping x in the vicinity of the superconductor-insulator transition point, x c , at low temperatures, one can induce a transition from the superconducting phase to the insulating phase and vice versa.  
           [0011]    The doping of a bulk material is typically determined by its chemical composition, such as the oxygen concentration x. However, as recently demonstrated by C. H. Ahn, S. Garigli, P. Paruch, T. Tybell, L. Antognazza, J.-M. Triscone, “Electrostatic Modulation of Superconductivity in Ultrathin GdBa2Cu3O7-x Films,” Science 284, 1152 (May 14, 1999), in very thin films, with thickness not exceeding the Thomas-Fermi screeening length, doping can be substantially modified by applying an electric field. Such an electric field can be provided by, for example, a nearby ferroelectric material.  
           [0012]    The utility of the ferroelectric field effect for forming devices with high-T c , superconductors has been described before in U.S. Pat. No. 5,274,249. The operating temperature of the device is chosen to be around the critical temperature of the superconducting material. The device consists of a thin superconducting film, two superconducting electrodes, of greater thickness than the film, a ferroelectric layer over the thin film superconductor, and a gate electrode over the ferroelectric. If the ferroelectric is not polarized, the thin film is superconducting, and thus it is capable of supporting a supercurrent, in effect closing the switch. Whereas if there is a sufficient voltage applied at the gate, the ferroelectric becomes polarized and generates an electric field. This electric field in turn reduces the carrier density of the thin film superconductor such that it becomes an insulator. This prevents the flow of the supercurrents, in effect opening the switch.  
           [0013]    The use of the ferroelectric effect in quantum information processing has been proposed by Jeremy Levy. See, for example, J. Levy, “Quantum Information Processing with Ferroelectrically Coupled Quantum Dots”, LANL preprint, quant-ph/0101026 (2001), and the references therein, wherein a quantum information processor is proposed using ferroelectrically coupled quantum dots. The semi-conducting dots are coupled directly by a ferroelectric material, which is manipulated by laser energy. The proposal does not involve the use of superconductors, and applying voltage to the ferroelectric. The feasibility of the proposal is questionable as the proposed proximity of the ferroelectric material to the quantum dots can destroy the coherence required for the quantum bit operations. The proposed method addresses a different approach to the development of quantum computers which has limited scalability, and, therefore, practicality of the method is drastically limiting as well.  
           [0014]    Fabrication of the ferroelectric-superconductor heterostructures is known in the art. It is described, for example, in R. Ramesh, A. Inam, W. K. Chan, F. Tillerot, B. Wilkens, C. C. Chang, T. Sands, J. M. Tarascon, V. G. Keramidas, “Ferroelectric PbZr 0.2 Ti 0.8 O 3  thin films on epitaxial Y—Ba—Cu—O,” Appl. Phys. Lett. 59, 3542 (Dec. 30, 1991), and in R. Ramesh, A. Inam, B. Wilkens, W. K. Chan, T. Sands, J. M. Tarascon D. K. Fork, T. H. Geballe, J. Evans, J. Bullington. “Ferroelectric bismuth titanate/superconductor (Y—Ba—Cu—O) thin-film heterostructures on silicon.” Appl. Phys. Lett. 59, 1782 (Sep. 20, 1991). These devices include a substrate, a thin film of a high temperature superconductor, a thin film of a ferroelectric material, and electrodes.  
           [0015]    The ferroelectric field effect is strong, if the superconducting film is ultra-thin, typically a couple mono-layers. It is typically formed on a substrate, such as SrTiO 3 , with a buffer layer of PrBa 2 Cu 3 O (PBCO) deposited on top of it. The thickness of the buffer is typically 6 monolayers, or about 7.2 nm. Next, the superconductor is deposited on the buffer with a thickness of a couple of monolayers, or approximately 2.4 nm. Methods for fabricating ultra-thin films of YBCO are known in the art, as described in, for example, T. Terashima, K. Shimura, Y. Bando, Y. Matsuda, A. Fujiyama, and S. Komiyama, “Superconductivity of One-Unit-Cell Thick YBa 2 Cu 3 O 7  Thin Film,” Phys. Rev. Lett. 67, 1362 (Sep. 2, 1991).  
           [0016]    In summary, coherent switching between the quantum states of qubits, such as different supercurrent carrying states of SQUIDs, has not been achieved yet in high temperature superconductors. Thus, a mechanism for coherent switching between supercurrent carrying states in solid state quantum computing systems is needed. The coherent switch should operate reversibly, at a high frequency, and should have a reasonably simple structure for integration.  
         SUMMARY OF THE INVENTION  
         [0017]    In accordance with the present invention a ferroelectric-superconductor heterostructure is presented, which is operable in quantum computing systems. The heterostructure can be utilized for switching and other purposes.  
           [0018]    In accordance with an embodiment of the invention, a high speed, coherent, nonvolatile switch in a solid state quantum computing system includes a substrate layer, a superconductor layer, such as, for example, high temperature superconductor, overlying the substrate layer, a ferroelectric layer, such as Pb(Zr x Ti 2 −x)O 3  overlying the superconductor, and a metallic layer over the ferroelectric layer, acting as an electrode.  
           [0019]    The superconductor can have a thickness of several monolayers of the superconducting material. A buffer layer can be deposited between the superconducting material and the ferroelectric material. When no voltage is applied to the electrode, the ferroelectric is unpolarized, therefore the superconductor beneath the ferroelectric material is in its superconducting state. Thus, the switch is closed. When a voltage is applied to the electrode, the ferroelectric polarizes, generating an electric field. This electric field changes the chemical potential of the dopants in the superconductor, in effect pulling charge carriers out of the superconductor, leaving the region underlying the ferroelectric insulating. The change of state of the superconductor can occur faster than the tunneling rate between the quantum states, thus satisfying the speed requirement for the appropriate operations of a qubit.  
           [0020]    In accordance with another embodiment of the invention, a tuneable Josephson junction includes a layer of ferroelectric, such as Pb(Zr x Ti 2 −x)O 3 , overlying a superconductor, a plurality of electrodes deposited across the width of said ferroelectric. In operation, when a voltage is applied to one of the electrodes, the corresponding part of the ferroelectric polarizes, in effect pulling the charges off the superconductor beneath it, making the underlying superconductor material insulating. Thus, by applying different voltages to the electrodes separately, sections of the underlying superconductor can be made insulating, leaving the other sections superconducting.  
           [0021]    As outlined above, coherent switches are employed in solid state quantum computing systems. The process of quantum computing includes entanglement of the quantum states of qubits during the execution of quantum algorithms. In order to accomplish the entanglement, the qubits can be directly connected by superconducting links without disturbing the sensitive wavefunctions of the qubits. It is necessary only for portions of the overall algorithm to have the quantum states of the qubits directly entangled. For the remaining time the qubits can be disconnected. A coherent switch can be employed to control the connection between the qubits.  
           [0022]    In another embodiment of the invention an outer dc-SQUID surrounds an inner superconducting loop that includes at least one Josephson junction. Since the supercurrents of the quantum states of the inner loop are directly related to the supercurrents of the outer dc-SQUID, the outer dc-SQUID can be used to read the quantum states of the inner loop, which is serving as a qubit. However, in order to perform quantum computations, the inner loop should be decoupled from the outer dc-SQUID. This has been accomplished previously by breaking the outer dc-SQUID so that supercurrents could not flow in it. An application of the present invention would provide a mechanism for decoupling the inner loop by including a coherent switch into the outer dc-SQUID. When the switch is closed, supercurrents can flow in the outer dc-SQUID, and thus the superconducting loops are coupled. When the switch is open, no supercurrent flows in the outer dc-SQUID, thus the SQUIDs are decoupled. This architecture therefore provides a reversible mechanism for reading the quantum state of the inner loop. 
       
    
    
     DESCRIPTION OF THE FIGURES  
       [0023]    [0023]FIG. 1 illustrates a phase diagram on the doping—temperature plane of cuprate superconductors.  
         [0024]    [0024]FIGS. 2 a  through  2   e  illustrate the fabrication of embodiments of the invention.  
         [0025]    [0025]FIGS. 3 a  and  3   b  illustrate the operation of an embodiment of the invention.  
         [0026]    [0026]FIG. 4 illustrates an embodiment of the invention.  
         [0027]    [0027]FIGS. 5 a  through  5   d  illustrate the fabrication of an embodiment of the invention.  
         [0028]    [0028]FIGS. 6 a  through  6   d  illustrate the fabrication of an embodiment of the invention.  
         [0029]    [0029]FIG. 7 a  illustrates a superconducting loop inside a dc-SQUID.  
         [0030]    [0030]FIG. 7 b  illustrates an embodiment of the invention, wherein the dc-SQUID can be decoupled from the inner superconducting loop.  
         [0031]    [0031]FIG. 8 illustrates an embodiment of the invention, involving superconductors with pairing symmetry corresponding to non-zero angular momentum.  
         [0032]    [0032]FIG. 9 illustrates an embodiment of the invention involving multiple qubits. 
     
    
     DETAILED DESCRIPTION  
       [0033]    [0033]FIG. 1 illustrates a phase diagram for high temperature superconductors in the doping concentration—temperature, or (x,T), plane. At zero temperature for x greater than x c  the system is in its superconducting phase. At finite temperature the superconducting region shrinks, as illustrated by region  101 . Region  102  represents a region where the material is an insulator at low temperatures and a “strange metal” at higher temperatures. The material is an anti-ferromagnet in region  103 . A superconductor-insulator transition takes place at zero temperature at the critical doping level x c . The ferroelectric field changes the effective doping of the material. As shown by the arrows  109 , the ferroelectric effect can increase or decrease the effective doping. Therefore when the nominal doping is near x c , the ferroelectric field can induce a phase transition between the superconducting state and the insulating state.  
         [0034]    In operation, the polarized ferroelectric exerts an electric field on the superconductor, modifying its local chemical potential. Change in the local chemical potential in turn increases or decreases x depending on the polarity of the electric field of the ferroelectric: up (↑), which represents a positive charge at the top of the material and a negative charge at the bottom, or down (↓), which is charged oppositely to that of the up polarization. Thus, if the chemical composition of the superconductor is tuned so that its nominal doping is very close to x c  in the absence of an external electric field, the ferroelectric field can modify x such that x↑&gt;x c  and x↓&lt;x c . Here, x↑ and x↓ denote the effective doping of the superconductor for the up (↑) and down (↓) polarization states of the ferroelectric, respectively.  
         [0035]    Coherent switches can be fabricated using the just described ferroelectric effect. In an embodiment of the invention a superconductor overlies a substrate, a ferroelectric material overlies the superconductor, and a electrode overlies the ferroelectric. The superconducting material can be, for example, a high temperature superconductor, or a superconductor with a pairing symmetry corresponding to a non-zero angular momentum. In some embodiments a buffer overlies the substrate. The buffer can have a lattice structure that matches closely that of the superconducting material. In another embodiment, a buffer can be deposited on the superconductor. The buffer can donate hole carriers to the underlying superconducting material, thus increasing the effective doping level of the superconductor without changing the actual chemical structure of the superconductor. This has been shown to induce superconductivity in ultra-thin films that otherwise would not be superconducting, as described, for example, by T. Terashima, K. Shimura, and Y. Bando, “Superconductivity of One-Unit-Cell Thick YBa 2 Cu 3 O 7  Thin Film,” Phys. Rev. Lett. 67, 1362 (Sep. 2, 1991).  
         [0036]    [0036]FIGS. 2 a  through  2   e  illustrate some further embodiment of the invention. FIG. 2 a  illustrates a cross-sectional view of the materials that can be used to provide coherent switch  200 . A superconductor  210  of thickness T 210  can overlie a substrate  201 , a buffer  202  of thickness T 202  can overlie superconductor  210 , and a mask  205  can overlie buffer  202 . Using well-known lithographic techniques a masked region  290  can be removed from superconductor  210 . FIG. 2 b  illustrates masked region  290  removed with width W 230 . Next a ferroelectric  230  can be deposited with a thickness T 230 , using, for example, off axis radio-frequency magnetron sputtering. Finally, an electrode  220  can be deposited on ferroelectric  230  with width W 220  and thickness T 220 .  
         [0037]    In some further embodiment, the thickness T 210  of superconductor  210  can be about 1 nm to about 20 nm, preferably about 2.4 nm, the thickness T 202  of buffer layer can be about 2 nm to about 100 nm, preferably about 7.2 nm, the thickness of the ferroelectric layer T 230  can be about 50 nm to about 10,000 nm, preferably about 300 nm. In another embodiment, no buffer layer is used and ferroelectric  230  can be deposited epitaxially on superconductor  210 .  
         [0038]    [0038]FIG. 2 d  illustrates a top view of some further embodiment. Electrode  220  can extend across the width of ferroelectric  230 . Ferroelectric  230  can extend across the width of superconductor  210 . In operation, application of a voltage to electrode  220  can polarize ferroelectric  230 . The polarized ferroelectric  230  can pull dopant charge carriers out of underlying superconductor  210 , modifying the effective doping of superconductor  210 . When the voltage is removed, ferroelectric  230  loses its polarization, and the charge carriers can return to superconductor  210 .  
         [0039]    [0039]FIG. 2 e  illustrates a top view of some further embodiment. Electrode  220  may include a group of electrodes  220 - 1  through  220 - n , positioned across the width of ferroelectric  230 . In operation, electrodes  220 - 1  through  220 - n  provide local electric fields that effect localized regions of underlying superconductor  210 . This embodiment is capable of turning localized regions of superconductor  210  individually insulating, as well as coherently switching the entire superconductor  210  insulating.  
         [0040]    [0040]FIG. 3 a  illustrates a possible mode of operation of the invention. In FIG. 3 a  no voltage is applied to electrode  220 , thus ferroelectric  230  is relaxed. The relaxed state of ferroelectric  230  is illustrated by a random arrangement of its internal charges. Underlying superconducting region  240  underneath ferroelectric  230  is unaffected by the relaxed state of ferroelectric  230 . FIG. 3 b  illustrates that applying a sufficient voltage to electrode  220  can polarize ferroelectric  230  by aligning the charges within. Polarized ferroelectric  230  generates an electric field, which affects underlying superconducting region  240 . The electric field can remove charge carriers from underlying superconducting region  240 , changing its effective doping. If this change of effective doping sweeps through the critical doping x c , underlying superconducting region  240  changes from superconducting to insulating.  
         [0041]    In other embodiments of the invention additional layers can be included as well. These layers may include buffer layers, whose lattice structure closely matches that of the superconducting material, and additional superconducting layers.  
         [0042]    [0042]FIG. 4 illustrates a cross-sectional schematic of an embodiment of the invention. Buffer layer  202 - 1  can overlie substrate  201 . Superconductor  210 - 1  can overlie buffer layer  202 - 1 . A second buffer layer  202 - 2  can overlie superconductor  210 - 1 . A second superconductor  210 - 2  can overlie buffer  202 - 2 . With the above-described masking procedure a ferroelectric  230  can be formed within superconductor  210 - 2 . Finally electrode  220  can be formed overlying ferroelectric  230 . The thicknesses T 202-1  and T 202-2  of buffer layers  202 - 1  and  202 - 2  can be about 2 nm to about 50 nm, preferably about 7.2 nm, the thickness T 240  of superconductor  210 - 1  can be about 1 nm to about 20 nm, preferably about 2.4 nm, and the thickness T 230  of ferroelectric  230  can be about 50 nm to about 2000 nm, preferably about 300 nm.  
         [0043]    In various embodiments of the invention superconductor  210  can be YBa 2 Cu 3 O 7-x  (YBCO), or GdBa 2 Cu 3 O 7-x  (GBCO), where in both cases x can be between 0 and 0.4. Superconductor  210  can be any superconducting material having a pairing symmetry corresponding to a zero or a non-zero angular momentum. Buffer layers  202 - 1  and  202 - 2  can be, for example, PrBa 2 Cu 3 O 7  (PrBCO), which is a semi-conductor with a lattice structure closely matching the lattice structure of YBCO and GBCO. Ferroelectric  230  can be, for example, Pb(Zr x Ti 1-x )O 3 (PZT). Substrate  201  can be, for example, SrTiO 3 , or sapphire, which has a higher relaxation rate than SrTiO 3 .  
         [0044]    [0044]FIGS. 5 a  through  5   d  illustrate another embodiment of the invention. FIG. 5 a  illustrates a cross-sectional view of substrate  201 , superconductor  210  of thickness T 210 , overlying substrate  201 , and mask  205 , overlying superconductor  210 . FIG. 5 b  shows that using well-known techniques of lithography, for example electron beam lithography, masked region of width W 240  can be removed from superconductor  210 . FIG. 5 c  illustrates the addition of buffer layer  202 , superconducting layer  240 , and ferroelectric  230 , with thicknesses of T 202 , T 240 , and T 230 , respectively. In FIG. 5 d  electrode  220  has been deposited with thickness T 220 , while mask  205  has been removed. In a further embodiment of the invention, a second buffer layer can be added between supreconducting layer  240  and ferroelectric  230 .  
         [0045]    [0045]FIGS. 6 a  through  6   d  illustrate additional embodiments of the invention, where superconductor  210  is doped near the superconductor-insulator transition point, but the thickness of the superconductor  210  is greater than is required for the ferroelectric field effect to work. FIG. 6 a  illustrates a cross-sectional view of substrate  201 , superconductor  210  of thickness T 210 , overlying substrate  201 , and mask  205 , overlying superconductor  210 . Lithographic techniques can be used to remove masked region  290  of mask  205  and superconductor  210  of width W 240 , so that superconducting layer  240  remains with thickness T 240 , as illustrated in FIG. 6 b . FIG. 6 c  illustrates ferroelectric  230 , of thickness T 230 , overlying superconducting layer  240 . FIG. 6 d  illustrates electrode  220 , of thickness T 220  and width W 220 , overlying ferroelectric  230 . Buffer layer  202  can be deposited between superconductor  240  and ferroelectric  230 .  
         [0046]    The quantum mechanical evolution of the qubits of a quantum computer can be secured by completely decoupling them from the surrounding system and environment. However, in order to apply quantum algorithms, certain operations are performed, including entangling the quantum states of the qubits at some points, applying quantum gates at other points, and reading and initializing the state of the qubit. Each of these operations require coupling the qubit to some aspect of the surrounding system. For example, in order to read the state of a qubit with a SQUID architecture, the supercurrents of the SQUID have to be directly manipulated. Also, entangling the quantum states of two qubits requires establishing a direct contact between the qubits, for example by establishing a coherent superconducting switch between them. One requisite of a coherent switch  200  is that the phases of the supercurrents remain unperturbed during the transitions of the switch.  
         [0047]    [0047]FIG. 7 a  illustrates another solid state realization of a qubit, as first proposed in Caspar H. van der Wal, A. C. J. ter Haar, F. K. Wilhelm, R. N. Schouten, C. J. P. M. Harmans, T. P. Orlando, Seth Loyd, and J. E. Mooij, “Quantum Superposition of Macroscopic Persistent-Current States,” Science 290, 773 (Oct. 27, 2000), which is incorporated herein by reference in its entirety. The qubit is the inner superconducting loop,  850 , which can include three or four Josephson junctions  850 - 1  through  850 - 3 . In order to interact with the qubit, dc-SQUID  860  can be fabricated to surround loop  850 . Dc-SQUID  860  also can contain Josephson junctions  861 - 1 ,  861 - 2 , and can be coupled to the rest of the circuitry through leads  870  and  871 . Since the supercurrents of the quantum states of loop  850  are directly related to the supercurrents of dc-SQUID  860  through a coupling of their magnetic fluxes, the quantum state of the qubit can be read by sensing the supercurrents of dc-SQUID  860 . However, when loop  850  performs quantum computations, it is decoupled from dc-SQUID  860 . In the experiment by van der Wal et al., the surrounding DC-SQUID  860  could not be decoupled from the inner superconducting loop  850 , a problem described in the reference as limiting the coherence of the system. Thus, quantum computation is limited in such a system.  
         [0048]    An embodiment of the invention could provide a mechanism for decoupling dc-SQUID  860  reversibly from superconducting loop  850  by including coherent switch  200  into dc-SQUID  860 . When coherent switch  200  is closed, the supercurrent of superconducting loop  850  is inductively coupled to the dc-SQUID  860 , thus causing the flow of supercurrent in dc-SQUID  860 . By sensing the supercurrent of dc-SQUID  860  the quantum state of the qubit can be read out. When the switch is open, no supercurrent can flow in dc-SQUID  860 , thus loop  850  is well isolated and can perform quantum computations undisturbed by dc-SQUID  860 .  
         [0049]    [0049]FIG. 7 b  shows an embodiment of a coherent switch. In order to minimize coupling between coherent switch  200  and loop  850 , a portion of dc-SQUID  860  can form elongated branch  880 . When a sufficient voltage V g  is applied to electrode  220 , ferroelectric material  230  polarizes and changes the underlying region of dc-SQUID  860  from superconducting to insulating. This insulating region prevents the flow of a supercurrent in dc-SQUID  860 , thus decoupling dc-SQUID  860  from loop  850 . When the voltage is removed, ferroelectric  230  relaxes, allowing the underlying region of dc-SQUID  860  to change from insulating back to superconducting. This change allows the flow of supercurrents in dc-SQUID  860  again, thus allowing the reading of the quantum states of loop  850  by dc-SQUID  860 .  
         [0050]    [0050]FIG. 8 illustrates another embodiment of the invention, where a qubit system is formed with superconductors, having a pairing symmetry corresponding to a non-zero angular momentum. This qubit system was first disclosed by Alexandre Zagoskin, U.S. patent application Ser. No. 09/452,749, “Permanent Readout Superconducting Qubit”, filed Dec. 1, 1999, incorporated herein by reference in its entirety. The orientation of the main axes of the lattice of superconductor  190  is shown by the square hatching. The orientation of the pairing symmetry is shown by d-wave order parameter  222 . Crystal field effects typically align the orientation of the pairing symmetry with the main lattice axes. Qubits  199 - 1  and  199 - 2  have their lattice axes and correspondingly their pairing symmetry orientation rotated by 45 degree relative to that of superconductor  190 , as shown by d-wave order parameters  222 - 1  and  222 - 2 . The orientation of the order parameters  222 - 1  and  222 - 2  of the qubits can have any angle relative to order parameter  222 . Superconductor  190  can be coupled to qubits  199 - 1  and  199 - 2 , respectively, by tunnel junctions, proximity junctions, or any other well known ways of forming a weak link between superconductors, as indicated by the dotted line. The quantum states of qubits  199 - 1  and  199 - 2  can be the different amount of flux, which can be trapped at the boundary between qubits  199 - 1  and  199 - 2  and superconductor  190 .  
         [0051]    Qubits  199 - 1  and  199 - 2  can be coupled to each other through a superconducting bridge  890 , interrupted by coherent switch  200 . Similarly to the previous embodiments, electrode  220  can overlie ferroelectric  230 , which can either overlie, or be embedded or be partially embedded into superconductor  210 . In analogy to previous embodiments, coherent switch  200  can be opened by applying a sufficient voltage V g  to electrode  220 . The electric field of the polarized ferroelectric  230  can change superconductor  210  from superconducting to insulating, thus preventing the flow of a supercurrent, and decoupling qubits  199 - 1  and  199 - 2 . Coherent switch  200  can be closed by not applying a sufficient voltage to electrode  220 , either by completely removing voltage V g , or by applying a voltage too small to polarize ferroelectric  230 . Then ferroelectric  230  will relax, allowing superconductor  210  to change back from insulating to superconducting. Once superconductor  210  is superconducting again, the connection between qubits  199 - 1  and  199 - 2  is restored. Superconductor  210  can have a thickness of about 1 nm to about 20 nm, preferably about 2.4 nm. Superconductor  210  can be covered by a buffer layer as well.  
         [0052]    [0052]FIG. 9 illustrates another embodiment of the invention, where coherent switches  200 - 1  through  200 -N couple qubit  199 - 1 - 1  to qubit  199 - 1 - 2  through qubit  199 -N- 1  to qubit  199 -N- 2 . The operation of individual coherent switches  200 - 1  through  200 -N is analogous to the previously described embodiments. This embodiment is capable of manipulating selected qubits within a system of qubits, a necessary step towards applying the present invention in quantum computer systems.  
         [0053]    Although the invention has been described with reference to particular embodiments, the described embodiments were meant only to serve as examples. Various adaptations and combinations of the features of the disclosed embodiments are intended to be within the scope of the invention, as defined by the following claims.