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I. Introduction to Quantum Computing
Computer components have been steadily decreasing in size and increasing in speed, tending to follow Moore 's empirical "law," which states that computing power doubles approximately every 18 months. However, extrapolation suggests that within about 10 years the size of a transistor logic gate element will be only a few atoms. Consequently, computer power will soon reach a limit, unless another approach for computing can be developed. Quantum computing is one possible approach.
An ordinary computer uses two-level logic, zero and one. A quantum computer, on the other hand, has states corresponding to zero and one and all linear combinations in a single element called a qubit. A quantum computer would consist of many qubit gates with entangled states. These gates could be addressed in parallel by unitary transformations, which must be carried out reversibly, implying no loss of energy in a gate operation. Quantum computers are “wired” so that they can do many calculations at the same time. This is known as “quantum parallelism” and represents the power of a quantum computer.
There is nothing a quantum computer can do that cannot also be done by an ordinary computer. However, for some problems, a quantum computer may be many orders of magnitude faster. There are presently two important problems involving commerce and security for which a quantum computer is believed to be superior: finding the factors of a large number and searching an unstructured database. A quantum computer would also be superior for simulating the behavior of quantum systems, and thus have enormous implications for physics.
Since it is far easier to find the product of two numbers than to find the factors of such a product, a nearly impossible task for conventional computers, industry and banks use this asymmetry to transmit information securely. In other words, the factors of a particular product are the key to many encrypted security systems, and if one could find the factors of a large number quickly, this security would be lost.
Suppose that the number to be factored has N digits. The time to factor this number, using the most efficient known algorithm running on a conventional computer, scales roughly as exp(N1/3), the exponential of the cube root of N. For a quantum computer, however, there is the celebrated Shor algorithm for which the factoring time scales only as N3.
Searching an unstructured database may become crucial as the information on the World Wide Web expands. With regard to this problem, consider a phone book containing N names. Then, given a name, finding the phone number requires a time that scales as log(N) since the data for this search are (alphabetically) ordered. But suppose you are given the phone number and asked to find the name. The time for this search (with respect to which the data is unordered) scales as N/2 since on average you (personally or using an ordinary computer) must look through half the book to find the specified number and to see what name is beside it. However, for a quantum computer there is the famous Grover algorithm for which the running time scales only as the square root of N. Since many computer algorithms involve search as one of their components, this speed up potentially has broad application.
The simulation of an N-degree of freedom quantum system on a conventional computer typically requires a time that scales as some power of the dimension of the Hilbert space required for a reasonable (perhaps truncated) description of the system, and this dimension grows exponentially with N. By contrast, a quantum computer would require a time that scales only as some power of N.
An ordinary computer is based on bits, two-level systems that can take on the values 0 or 1. Computations are carried out by logic gates that act on these bits to produce other bits. Unless there is duplicate (parallel) hardware, only one problem instance (i.e. input data set) can be handled at a time.
A quantum computer is based on qubits (quantum bits), two-level quantum systems commonly labeled by the basis vectors |0> and |1>. Since each qubit is quantum mechanical, it can be in a superposition of |0> and |1> as well as in either |0> or |1>. The number of possibilities grows exponentially with the number of qubits. For example, for a 2-qubit system there are all possible superpositions of the states |00>, |01>, |10>, and |11>, including entangled states of the form (|01> ± |10>). If there are N qubits, the vector space required to describe their states has dimension 2 N . Calculations are carried out on vectors by quantum gates that apply unitary transformations to these vectors to produce other vectors. Since quantum computers can process superpositions, they can (at least for some problems) be viewed as devices that can process all possible inputs simultaneously.
II. Superconducting Quantum Bits
Several systems have been proposed for quantum computing including photons in nonlinear optical systems, trapped ions, electron and nuclear spins, quantum dots, and Josephson junctions. There are advantages and disadvantages to all these approaches. Some, such as those employing light or trapped ions, have demonstrated that they can provide individual qubits of excellent quality. But, it is not yet known if they can be scaled up to produce systems with many qubits and many possible quantum gate operations. Others, such as those employing solid-state devices or Josephson junctions, are readily scalable using integrated circuit technology. However, the quality of the individual qubits produced by this approach is presently not as good. We believe that, when properly fabricated and properly employed, Josephson junctions have promise for the construction of devices that simulate high dimensional vector spaces (many good quality qubits) and a large set of unitary transformations (quantum gates) that act on these vector spaces.
In 1961, Brian Josephson, a graduate student at Cambridge University , published a Physics Letter with a remarkable conclusion: coupled electron pairs could tunnel across a narrow insulating barrier between a pair of superconductors without the development of a potential difference across this junction (See Fig. 1). In addition, if a voltage were applied across the junction, the phase difference of the electron wavefunctions on the two sides of this barrier would be oscillatory with its derivative proportional to the voltage. If this barrier were part of a superconducting loop, an applied voltage would produce an alternating current. These conclusions were confirmed by experiment shortly after Josephson's publication.
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Figure 1. Schematic of a Josephson junction. A thin insulator of aluminum dioxide is sandwiched between two superconducting layers of niobium or aluminum.
The first Josephson-based qubit studied used radio frequency (rf) superconducting quantum interference devices (SQUIDs) as qubits. An rf SQUID is a single Josephson junction loop, which can be modeled as a loop inductance L combined with the junction, a capacitance C, and a resistance R (See Fig. 2). If we ignore the resistance and apply an appropriate small biasing magnetic field through the loop, then we believe that it is possible to treat the rf SQUID as a qubit with flux (magnetic field times area of the loop) as the relevant macroscopic quantum variable. That is, in a simple picture, clockwise current through the loop can be taken as 1 and counter-clockwise current as 0. This can be modeled as a double potential well. Coupling among qubits arises because the magnetic field from one qubits influences the properties of a neighboring qubit. This approach is analogous to using electron spins as qubits.
Figure 2. Schematic of an rf SQUID. A thin wire of aluminum is formed into a loop and cooled to superconducting temperatures, with an insulator at the join forming a Josephson junction.
III. Single Junction Qubits
At Maryland, we are focusing on a different superconducting qubit, a single Josephson junction. This idea was suggested by members of our research group a number of years ago. 1 The single-junction qubit has both advantages and disadvantages when compared with the rf SQUID, which includes a current loop. The enemy of the qubits of a quantum system is interaction with the environment, which leads to decoherence and destroys the coherent superposition states. Producing qubits with long coherence times is an important goal on the way to a quantum computer. The junctions themselves, which are typically of micrometer dimensions, are much less sensitive to decoherence sources such as magnetic flux and charge noise. In addition, the junction properties, such as the critical current and phase difference across the barrier, can be controlled rather easily by the bias current and an applied magnetic field. The main disadvantage is that, because single junctions require current-bias lines, the junctions are very sensitive to current noise and these lines must be filtered well to block extraneous signals. Since the field of superconductivity has a long history in developing junction arrays, we do not expect scalability up to a large number of single-junction or rf-SQUID qubits to be a limiting factor in this program.
Fig. 3a shows schematically the junction configuration with its bias current and parallel capacitance and resistance. Such a single-junction qubit uses metastable energy levels in the so-called “washboard potential” to form the 0 and 1 states and their linear combinations. This potential, tilted in the presence of a bias current, depends on the phase difference of the wave functions across the junction g (see Fig. 2b). At typical experimental conditions, the separation of the energy levels is small compared to the energy corresponding to room temperature. For this reason our experiments must be carried out at millikelvin temperatures in a dilution refrigerator.
Figure 3. a) Schematic of the current-biased junction X, with junction capacitance C and resistance R in parallel.1 b) Schematic of the tilted washboard potential E vs. phase difference g. Metastable levels 0, 1, and 2 are shown in one of the wells. c) I vs. V for the current-biased junction showing the critical current I0 and switching events. The arrows show the hysteresis in the I-V characteristics. 2Δ/e is the superconducting energy gap voltage, which is of the order of 10-3 volts, depending on the superconducting material used for the junction. d) Histogram of the number of switching events vs. bias current in the presence of a microwave signal at fixed frequency.
The behavior of the current-biased junction and the “escape” to the voltage state are analogous to a ball, perhaps we should call it a “phase-ball”, rolling in a landscape like a tilted washboard. With zero or small bias currents the ball has only a little kinetic energy and oscillates in a valley of the washboard. That is, the state of the junction remains in the metastable level of the potential well, corresponding to the zero-dc-voltage condition as shown in Fig. 3b. As the bias current increases the potential barrier decreases and it becomes possible for the ball to leave one potential well and roll continuously down hill. This corresponds to the “escape” for the junction, thereby producing a measurable voltage. The appearance of this voltage is the signature of escape, and can be related to the value of the bias current at which this escape occurs. This voltage could constitute the readout of the status of the junction for a quantum computer.
In Fig. 3c we show the current-voltage (I-V) characteristics of a junction. Starting at zero, the current can be increased up to or near the limiting value, i.e. the critical current I0. At some current less than I0 the junction will switch to the voltage state and the value of the current at which this switching or “escape” takes place can be recorded. For our initial experiments on single junctions we ramped the bias current and noted the value of the current at which escape occurred. We repeated this experiment many times and obtained a histogram of switching events, bias current vs. number of escapes. Using this technique at slow ramping rates and at different temperatures, we have been able to estimate the relaxation time of these qubits. This appears to be a useful and simple method for establishing an upper bound on the coherence times of our qubits and systems of qubits and allows us to test quickly different schemes for isolating our qubits from the environment.2
Next we applied a microwave signal in addition to the ramped bias current and studied the influence of the microwave signal on the escape rate. This is a form of microwave spectroscopy, called energy level spectroscopy, and is similar to optical absorption spectroscopy, which is used to study transitions between energy levels in atoms. The microwave signal at frequencies of the order of a few GHz produces an enhancement of the escape rate corresponding to the separation of energy levels in the washboard potential. This separation decreases with increasing bias current. Fig. 3d shows schematically a histogram of the bias current vs. the increased number of events due to the presence of microwaves of fixed frequency. That is, n=0 represents the enhancement due to microwave induced transitions from the n = 0 level to the next level, n = 1; n = 1 represents the transition from the n = 1 level to the next higher level, n = 2. Note that higher bias currents are required to produce escape from the lower level. In this manner we have mapped out the dependence of the energy levels on the bias current. Xu et al. have carried out calculations to simulate the resonant activation that we have observed in our current-biased junctions.3
IV. Entangled Josephson Qubits
Recently we have coupled two of these junction qubits with a capacitor and carried out energy level spectroscopy on this system. Since we are able to bias each junction separately and to control the coupling between the junctions with these bias currents, we are able to study the energy levels as a function of the amount of this coupling. We observed an avoided crossing of the energy levels as shown in Fig. 4.4 Such an avoided crossing would not be expected if the junctions were uncoupled. This avoided level crossing agrees quantitatively with a quantum mechanical model of the experimental circuit including the junctions. This model, first explored by our group in a theoretical study, shows that the excited energy levels are maximally entangled when the bias currents are approximately the same.5 We believe that this is evidence for quantum entanglement of the two junctions, which is surprising since a macroscopic distance of nearly a millimeter separates the junctions. The research has been published4 and was described by Dr. Andrew Berkley in his thesis.6
Figure 4. Microwave spectroscopy, i.e. microwave absorption frequency vs. bias current through junction 2, for two junctions, coupled and uncoupled. The dot-dash line shows the results for an uncoupled junction 1 at fixed bias current Ib1. The black squares represent data points for uncoupled junction 2 and the dashed line is a theoretical fit. The white circles show data corresponding to microwave excitation to the second and third energy levels of the coupled junctions as a function of the bias current through junction 2 with the constant bias current through junction 1. The colors represent the amount of microwave enhancement of the escape rates with red being the highest and blue the lowest. The white lines are theoretical fits.
In order to use phase states of Josephson junctions as qubits, the coherence times of these interacting “entangled” junctions must be much longer than the times required to perform two-qubit gate operations such as Controlled Phase, SWAP, or CNOT (also referred to as an exclusive OR). (The Controlled Phase gate in its simplest form leaves one bit, the control bit, unchanged and changes the sign of the other bit, the target bit, depending on the value of the control bit. The SWAP gate swaps the values of the two qubits. The CNOT gate leaves the control qubit unchanged and switches the state of the target qubit only if the control qubit is in the |1> state.)
At the present time the coherence times are much too short, of the order of nanoseconds, and we must provide better isolation for our junctions. We are experimenting with different schemes for filtering the current bias and microwave lines by means of resistance, capacitance, and inductance combinations, metal-powder filters, and active filters composed of superconducting elements. For these configurations we have been studying the escape rates of single and coupled junctions and from these measurements we have extracted correlation times. Fig. 5 shows an example of these escape rates as a function of current bias both with and without the addition of microwaves. Recently, as described below, we have been able to increase our coherence times with an inductance-junction isolation scheme and have observed Rabi oscillations (the reversible evolution of a qubit between |0> and |1> states correlated with the emission and absorption of a microwave photon) in single and coupled qubits.
Figure 5. Escape rates at a base temperature of 25 mK as a function of bias current without (blue data points) and with (green data points) application of microwave power. The microwave frequency is 5.5 GHz. Small peaks, which correspond to enhanced escape by microwave excitation from level |0> to level |1> and from level |1> to level |2>, are shown by the green data points.
We have extended our microwave spectroscopy experiments on two capacitively coupled qubits, as shown in Fig. 4, to higher microwave frequencies. Experimental and theoretical studies suggest that the system is better represented as two qubits coupled by an LC quantum resonator in a macroscopic superconducting circuit. This system is analogous to two atoms and a cavity in atomic cavity quantum electrodynamics, but our qubits are distinguishable and independently tunable. We are able to couple all three degrees of freedom together to obtain spectroscopic splittings that are in agreement with quantum mechanics calculations. Some results are shown in Fig. 6.
Figure 6. Microwave spectroscopic measurements of the microwave enhancement in the escape rate of two Josephson junction qubits that are coupled by an LC resonator. The resonator is formed from a superconducting inductor in series with a capacitor. The system is cooled to about 0.02 K in a dilution refrigerator and the two 10μm x 10 μm Nb/Al2O3/Nb tunnel junctions are separated by 0.7 mm. The bias current Ib1 for junction J1 is ramped (x-axis) and the response of the system is measured at different frequencies (y-axis) while junction J2 is biased at a constant current of Ib2. Red corresponds to highest enhancement and light blue to zero response. The black dashed lines are from a three-body quantum mechanical simulation with just one free parameter, the fixed current in the second junction Ib2 =22.330 μA. The solid curves indicate the predicted uncoupled 0 to 1 level spacing for J1 (red curved) and J2 (blue horizontal), and the LC resonator at f = 7.1 GHz (green horizontal). The inset, below the main figure, shows schematically the uncoupled energy levels in the three sub-systems at the degeneracy point and the vertical black arrow shows the point of triple degeneracy in the frequency vs. Ib1 plot.
By adjusting the current flowing through the two junctions, the energy levels in the junctions can be brought into coincidence with the LC resonator (see inset). At the triple degeneracy point, Ib1 = 21. 15μA (see inset and vertical arrow), the theory reveals that the three lowest excited states of the coupled system are |100>- |010> - √2|001>, |100>+|010>, and |100>- |010> + √2|001>. The good agreement between the data and the theory supports the existence of entangled states of all three qubits in this macroscopic quantum system. 7
Using LJ isolation, we have also observed Rabi oscillations in a single junction as shown in Fig. 7. The Rabi oscillations, driven by a microwave signal, represent transitions between the lowest energy level and the first excited level of the junction. The microwave frequency corresponds to the separation of the two levels when the bias current is near its critical value. A plot of the Rabi oscillation frequency vs. the square root of the microwave power is expected to be linear with an intercept on the frequency axis that represents the amount the microwave frequency is off –resonance. A plot showing a linear fit to our data is given in Fig. 8.
Figure 7. Microwave enhancement of the tunneling escape rate (Rabi oscillations). A 7.6 GHz microwave pulse is applied at time t = 0 to an inductively isolated junction at a temperature of 25 mK. This causes a 175 MHz coherent oscillation of the occupation probabilities in the ground and first excited states. P1 represents the occupation probability of the first excited state.
Figure 8. Rabi oscillation frequency vs. (RF Power)1/2. At higher power there may be heating, which leads to additional sources for decoherence; thus there is more uncertainty in the data.
Theoretical studies of coupling, switching, and gate operations by members of our group are used to guide the experimental program. We have published the first detailed calculations for the operation of the SWAP and controlled-phase gates based on our Josephson-junction implementation of qubits.8 Aided by such theoretical simulations and model calculations we plan to investigate the coupling of more than two qubits and incorporate additional qubits for error correction. A succeeding step will be to demonstrate simple gate operations. These are not simple goals.
At the present time the members of our quantum computing group include Fred Wellstood (PI); Chris Lobb, Alex Dragt, and Robert Anderson (CoPIs); Phil Johnson and Fred Strauch (both now at NIST); Roberto Ramos (now an assistant professor at Drexel); post-doc Rupert Lewis; graduate students, Sudeep Dutta, Kaushik Mitra, Hanhee Paik, Tauno Palomaki, Anthony Przybysz, and Benjamin Cooper; and undergraduate students, Mohamed Abutaleb and John Wyrwas. Andrew Berkley received his Ph.D. and is now at DWave Systems Inc. in Vancouver , Canada . Bill Parsons graduated and is now in a Masters Program in Applied Physics at Johns Hopkins University . Huizhong Xu graduated and is now a post-doc at Cornell University . Fig. 9 shows members of our group “posing” near the screen room of our larger dilution refrigerator.
Figure 9. Members of the QC group in front of the screen room. From left to right: Front row – Fred Wellstood, Hanhee Paik, Robert Anderson, Roberto Ramos, and Huizhong Xu; Back row - Phil Johnson, Alex Dragt, Chris Lobb, Fred Strauch, and Sudeep Dutta.
Figure 10. Members of the QC group clockwise: Rupert Lewis, Hanhee Paik, Robert Anderson, Sudeep Dutta, and Tauno Palomaki.
Recently, we have begun to install a third dilution refrigerator system under the direction of Dr. Rupert Lewis. Figure 10 shows several members of the group looking up at the one meter diameter hole in the floor needed to accommodate the cryostat for this "fridge".
References
1 R. C. Ramos, M. A. Gubrud, A. J. Berkley, J. R. Anderson, C. J. Lobb, and F. C. Wellstood, “ Design for Effective Thermalization of Junctions for Quantum Coherence”, IEEE Trans. Appl. Supercond. 11 , 998 (2001).
2 S. K. Dutta, H. Xu, A. J. Berkley, R. C. Ramos, M. A. Gubrud, J. R. Anderson, C. J. Lobb, and F. C. Wellstood, “ Determination of Relaxation Time of a Josephson Junction Qubit”, Phys. Rev. B 70 , 140502 (Rapid Communications) (2004).
3 H. Xu, A. J. Berkley, M. Gubrud, R. Ramos, J. R. Anderson, C. J. Lobb, F. C. Wellstood, “Analysis of Energy Level Quantization and Tunneling from the Zero-Voltage State of a Current-Biased Josephson Junction,” IEEE Trans. Appl. Supr. 13 , 956 (2003).
4 A. J. Berkley, H. Xu, M. Gubrud, R. Ramos, F. W. Strauch, P. R. Johnson, J. R. Anderson, A. J. Dragt, C. J. Lobb, and F. C. Wellstood, “Entangled Macroscopic Quantum States in Two Superconducting Qubits”, Science 300 , 1548 (2003).
5 P. R. Johnson, F. W. Strauch, A. J. Dragt, R. C. Ramos, C. J. Lobb, J. R. Anderson, and
F. C. Wellstood, “Spectroscopy of Capacitively Coupled Josephson-Junction Qubits”,
Phys. Rev. B 67 , 020509 (Rapid Communications) (2003).
6 Andrew J. Berkley , Ph. D. Thesis (2003).
7 Huizhong Xu, Frederick W. Strauch, Sudeep Dutta, Phillip R. Johnson, R. C. Ramos, A. J. Berkley, H. Paik, J. R. Anderson, A. J. Dragt, C. J. Lobb, and F. C. Wellstood, “Spectroscopy of Three-Particle Entanglement in a Macroscopic Superconducting Circuit”, Phys. Rev. Lett. 94 , 027003 (2005).
8 F. W. Strauch, P. R. Johnson, A. J. Dragt, C. J. Lobb, J. R. Anderson, and F. C. Wellstood, “Quantum Logic Gates for Coupled Superconducting Phase Qubits”, Phys. Rev. Lett. 91 , 167005 (2003).
Other QC Publications
1. A. J. Berkley, H. Xu, M. Gubrud, R. Ramos, F. W. Strauch, P. R. Johnson, A. J. Dragt, C. J. Lobb, F. C. Wellstood and J. R. Anderson, “Response to Defining Entanglement by Antoni Wojcik”, Science 301 , 1183-1184 (2003).
2. A. J. Berkley, H. Xu, M. Gubrud, R. Ramos, J. R. Anderson, C. J. Lobb, F. C. Wellstood, “Decoherence in a Josephson junction qubit,” Phys. Rev. B 68 (Rapid Communications), 060502-1 to 060502-4 (2003).
3. A. J. Berkley, H. Xu, M. Gubrud, R. Ramos, J. R. Anderson, C. J. Lobb, F. C. Wellstood, “Characterization of an LC isolated Josephson junction qubit,” IEEE Trans. Appl. Supr. 13 , 952 (2003).
4. J. R. Anderson, A. J. Berkley, A. J. Dragt, M. A. Gubrud, P. R. Johnson, C. J. Lobb, R. C. Ramos, F. W. Strauch, F. C. Wellstood, H. Xu, “Josephson-junction qubits: entanglement and coherence,” Superlattices and Microstructures, Elsevier Science, vol. 32, Numbers 4-6, p. 231 (2003).
5. R. C. Ramos, F. W. Strauch, P. R. Johnson, A. J. Berkley, H. Xu, M. A. Gubrud, J. R. Anderson, C. J. Lobb, A. J. Dragt, F. C. Wellstood, “Capacitively coupled Josephson junctions: a two-qubit system,” IEEE Trans. Appl. Supr. 13 , 994 (2003).
6. T. Hakioglu, J. R. Anderson, and F. C. Wellstood, "Single and double bit quantum gates by manipulating four-fold degeneracy", Phys. Rev. B 66 , 115324 (2002).
7. M. Gubrud, M. Ejrnaes, A. J. Berkley, R. Ramos, I. Jin, J. R. Anderson, C. J. Lobb, F. C. Wellstood, “Sub-gap leakage in Nb/AlO x /Nb and Al/AlO x /Al Josephson junctions”, IEEE Trans. Appl. Supr. 11 , 1001 (2001).
8. J. R. Anderson, A. J. Dragt, C. J. Lobb, F. C. Wellstood, M. Gubrud, M. Ejrnaes, M. M. Górska, and T. Rusin, "Beyond Moore's Law: quantum computing with rf SQUIDs", in Clusters and Nanostructure Interfaces , edited by P. Jena, S. N. Khanna, and B. K. Rao, World Scientific Pub. Co. p. 241 (2000).
9. H. Xu, A. J. Berkley, R. C. Ramos, M. A. Gubrud, P. R. Johnson, F. W. Strauch, A. J. Dragt, J. R. Anderson, C. J. Lobb, and F. C. Wellstood, “ Spectroscopic resonance broadening in a Josephson junction qubit due to current noise”, Phys. Rev. B 71 , 064512 (2005).
10. J. R. Anderson, A. J. Berkley, A. J. Dragt, S. Dutta, M. Górska, M. A. Gubrud, P. R. Johnson, C. J. Lobb, R. C. Ramos, F. W. Strauch, F. C. Wellstood, H. Xu, “Single Josephson Junctions as Qubits”, in Clusters and Nano-Assemblies, Physical and Biological Systems, edited by P. Jena, S.N. Khanna, and B.K. Rao, p. 151 (2005).
11. Phillip R. Johnson, William T. Parsons, Frederick W. Strauch, J. R. Anderson, Alex Dragt, C. J. Lobb, and F. C. Wellstood, “Macroscopic tunnel splittings in superconducting phase qubits”, Phys. Rev. Lett., 94, 187005 (2005)
12. Hanhee Paik, F. W. Strauch, R. C. Ramos, A. J. Berkley, H. Xu. S. K. Dutta, P. R. Johnson, A. J. Dragt, J. R. Anderson, C. J. Lobb, and F. C. Wellstood, “Cooper pair box as a variable capacitor”, IEEE Trans. Appl. Supr. – to be published.
Theses
1. A. J. Berkley, “A Josephson junction qubit,” Ph.D. thesis, University of Maryland (2003).
2. Huizhong Xu, “Quantum Computing with Josephson junction circuits,” Ph.D. thesis, University of Maryland (2004).
3. Frederick W. Strauch, “Theory of Superconducting Phase Qubits”, Ph.D. thesis, University of Maryland (2004).
Links:
MSNBC article on quantum computing
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