Ray Simmonds probes the resistance of Josephson
junctions on a new wafer of quantum bits.
To develop techniques for making highly coherent quantum systems using integrated circuits. This includes developing new high fidelity measurements techniques for quantum systems. Ultimately, we want to make large-scale quantum information processing systems a reality.
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Ray Simmonds probes the resistance of Josephson
junctions on a new wafer of quantum bits. |
The integrated circuit components of classical computers are rapidly approaching the so-called "quantum limit". Instead of avoiding quantum effects, we have the opportunity to exploit them as a means for more effective computation. A quantum computer has the ability to use the intrinsic properties of quantum systems to naturally perform parallel processing during a calculation. This allows a quantum computer to solve problems considered intractable for classical computers. Three such problems are of considerable interest: discrete logarithms, factorization, and search algorithms for large databases. The practical significance of building a successful large scale quantum computer is tremendous:
In a conventional computer, information is often stored as electrical charge on tiny capacitors. The presence or absence of charge on a single capacitor represents a (classical) bit which can store two (classical) information states “0” and “1”. All logical computations are done using groups and combinations of this binary information. A quantum bit or “qubit” is described in terms of two quantum states denoted by “|0>” and “|1>”. Remarkably, a quantum bit can be placed in a state that is a mixture of both “|0>” and “|1>”! Even more remarkable is the fact that multiple qubits can be placed in a massive mixture of all combinations of their possible states, a phenomenon known as entanglement. Entanglement is the magic of quantum mechanics and allows a quantum computer to stir up quantum information in order to produce a meaningful calculation with incredible speed.
Whether or not quantum computing becomes practical, our work will produce new knowledge for the precise measurement of quantum systems. Through our research with quantum mechanical superconducting circuits, we are learning how to custom design, fabricate, and operate quantum systems. Through direct control and measurements we are developing new ways to utilize the quantum mechanics. We have already shown (as described below) the ability to detect previously unknown nanoscale quantum systems which could never be seen before. Ultimately, we are exploring untouched regimes of nature and may find ways to direct unforeseen advancements in nanotechnology.
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(a) The phase qubit schematic circuit.
(b) The potential energy at a particular flux bias applied
to the qubit loop. |
The strategy of this effort is to develop a highly coherent set of quantum bits which can be isolated, controlled, coupled and measured. These are the building blocks for quantum computing. Along these lines, we have developed a high impedance current bias and measurement scheme for controlling a Josephson “phase” qubit, while providing sufficient isolation from the external environment. Josephson junctions are electrical circuit elements which resemble capacitors. They are made from two pieces of metal separated by a thin insulating barrier. When the metal electrodes become superconductors at low temperatures (in this case, the superconducting temperature is about 1 K while the measurement temperature is below 0.030 K or 30 mK) current can flow through this capacitor due to the quantum mechanical mixture of the superconducting wavefunctions on either side of the junction. Each wavefunction is described with the help of a quantum mechanical “phase” whose gradient is related to the zero-resistance flow of superconducting (Cooper) pairs of electrons. The current that flows through the Josephson junction is proportional to the sine of the quantum mechanical phase difference d across the junction. A qubit is made by including a Josephson junction in a superconducting loop, as shown in Figure 817-xx-2(a). Microwave current lines are capacitively coupled to the junction while a d.c. bias coil is placed some distance from the “qubit loop”. For an applied magnetic flux through the loop, the potential energy stored in the Josephson junction as a function of the superconducting phase difference d is shown in the figure. The flux bias is chosen so that the qubit states, |0> and |1>, are formed in the left (~cubic) well. One can imagine these states as very rapid phase or current oscillations in this well. The |1> state is measured by an induced tunneling event to states in the (~quadratic) right well. This changes the flux in the qubit loop by roughly a flux quantum, a relatively large flux difference that can easily be detected using a pulsed d.c. SQUID magnetometer.
The qubit transition frequency ω10, which is directly related to the energy level separation of the |0> and |1> state, is measured spectroscopically as a function of the applied flux bias to the qubit loop. First we prepare the qubit in the |0> (ground) state. If we apply a microwave drive current at frequency ω and ω = ω10, then the qubit will make a transition to the |1> state, otherwise it will remain in the ground state. If we sweep the value of ω and measure the occupation probability of state |1>, we can determine the precise value for ω10 at that particular flux bias. We measure the occupation of the |1> state using a “fast” qubit state measurement technique. This is done by applying a quick dc flux pulse to the qubit loop so that the potential barrier ΔU is lowered just enough so that, if occupied, the |1> state has a high probability for tunneling to the right well and will be detected using the SQUID. This procedure is done for many different values of the flux bias in order to determine the energy level separation or transition frequency ω10 as a function of the qubit loop flux bias. If we know the transition frequency ω10, then we are able to fully control the state of the qubit. Varying the flux bias, simply allows us to operate the qubit at different frequencies (typically from 7 to 10 GHz).
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| An example of qubit spectroscopy for qubits (a)
and (b) showing the transition frequency ω10 for
various flux biases to the qubit loop. Notice the small “splittings” indicative
of microscopic quantum systems residing within the tunnel junction
coupling to our superconducting quantum bit. Top inset shows
Rabi oscillations away from resonators. |
An example of “qubit spectroscopy” is shown in the figure. We find the expected decrease in the transition frequency with flux bias as the current through the junction approaches its critical or maximum current. Notice (in the lower inset) that there are “gaps” or “splittings” in the spectra. We have identified these spurious resonators as nanoscopic two level systems within the junction’s insulating barrier. Away from any spurious resonators, we have applied microwaves on resonance (ω = ω10 ) to perform coherent state oscillations, known as “Rabi oscillations”, between the |0> and |1> state (upper inset). Near spurious resonators, we have found coupled interactions between the qubit and the resonator as described briefly in Accomplishments. Although these resonators are undesirable in an ideal qubit, so far they have been useful for testing coupled interactions and estimating the limits of coherence in solid state nanosystems. An effort is being lead by David Pappas to improve the quality of Josephson junctions by growing epitaxial tunnel barriers to remove these nanoscopic defects.
Our long term strategy is to produce highly coherent superconducting qubits for building small systems to successfully perform error tolerant quantum logic operations. With these building blocks, we should be able to quickly take advantage of existing integrated circuit technology to make progress towards a full scale superconducting quantum computer.
The development of the phase qubit was just a start. This program is interested in understanding decoherence sources and producing high quality superconducting qubits. We plan to study all three types of qubits: charge, flux, and phase as well as harmonic oscillators or microwave resonators which also operate in the quantum regime. We will also extend these investigations to qubits coupled to harmonic oscillators and coupled qubits.
Although this project began only four years ago, we have made significant progress over this short period of time. Our work on coupled qubits has shown that two-qubit gates should be feasible. We have developed high quality harmonic oscillators or microwave resonators in order to investigate energy loss from dielectric materials. Our research has led the way to understanding how to improve future qubits by eliminating dielectric materials in the fabrication of qubits. We have managed to improve the materials and design properties of our qubits to more than double their coherence times. Most significantly we have developed a frequency tunable Josephson junction resonator which allows us to asses the quality of Josephson junction in an entirely new way. Many of our accomplishments over the past year are included in the list below.
Using our new improved qubit we have developed spectroscopic measurements of the qubit transition frequency over a wide range of possible operating flux biases. In doing so, we discovered nanoscopic spurious resonators within the tunnel junctions of the qubit. Elimination of these resonators in future Josephson junctions could improve the performance of all superconducting devices.
We have implemented a new qubit state measurement technique that is an order of magnitude faster than our former method. In less than 5 ns, a flux bias pulse is applied to the qubit so that the |1> state, if occupied, rapidly tunnels to the right well. This new advance has allowed us to monitor rapid qubit state variations such as the coupled interactions between phase qubits and other quantum systems.
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| (a) A fabricated coupled qubit circuit. (b) Simultaneous
measurement of two coupled qubits during state oscillations. |
Through the first ever simultaneous measurement of two superconducting qubits, we have recently witnessed two coupled phase qubits entangle themselves by performing coherent state oscillations. This is a tremendous step forward! Soon, we hope to have the ability to perform simple logic operations between two qubits, the building blocks for a full scale quantum computer.
Dielectric loss from two-level defects was shown to be a dominant decoherence source in superconducting quantum bits. Depending on the qubit design, dielectric loss from insulating materials or the tunnel junction can lead to short coherence times. We have shown that a variety of microwave and qubit measurements are well modeled by loss from resonant absorption of two-level defects. Our results demonstrate that this loss can be significantly reduced by using better dielectrics and fabricating junctions of small area and by removing dielectric material completely. Redesigned phase qubits reducing the amount of dielectric and using an improved dielectric have improved energy relaxation rates by a factor of 20.
We have developed a unique microwave resonator using a single Josephson junction as a tunable inductance in the circuit. This flux tunable circuit allows spectroscopic measurements for frequencies that vary over a range >1 GHz. Information can be gathered to test the quality of Jospehson junctions in terms of individual nanoscopic defects as well as excess energy loss. This device is very similar to a phase qubit but is extremely simple to fabricate and operate, and it allows us to obtain a maximum amount of information. Moreover, this device operates as a low loss fluxometer ideal for future qubit readout.
David Pappas – Quantum
Devices Group, NIST, Boulder, Epitaxial Josephson junctions
with new materials.
John Martinis – University of California, Santa Barbara, Measurement
electronics and qubit development.
Dale Van Harlingen – University of Illinois, Urbana-Champaign, 1/f
noise measurements of Josephson junctions.
Lev Ioffe – Rutgers University, Theoretical study of two-level systems
S. Oh, K. Cicak, J. S. Kline, M. A. Sillanpää, K. D. Osborn, J. D. Whittaker, R. W. Simmonds, D. P. Pappas, “Elimination of two level fluctuators in superconducting quantum bits by an epitaxial tunnel barrier”, Phys. Rev. B 74, 100502 (2006)
J.M. Martinis, K. B. Cooper, R McDermott, M. Steffen, M. Ansmann, K. D. Osborn, K Cicak, S. Oh, D. P. Pappas, R. W. Simmonds, C. C. Yu, “Decoherence in Josephson qubits from dielectric loss”, Phys. Rev. Lett. 95, 210503 (2005).
R. McDermott, R. W. Simmonds, M. Steffen, K. B. Cooper, K. Cicak, K. D. Osborn, S. Oh, D. P. Pappas, J. M. Martinis, “Simultaneous state measurement of coupled Josephson phase qubits”, Science 307,1299 (2005)
K. B. Cooper, M. Steffen, R. McDermott, R. W. Simmonds, S. Oh, D. A. Hite, D. P. Pappas, J. M. Martinis, “Observation of quantum oscillations between a Josephson phase qubit and a microscopic resonator using fast readout”, Phys. Rev. Lett. 95, 066089 (2004).
R. W. Simmonds, K. M. Lang, D. A. Hite, D. P. Pappas, John M. Martinis, “Decoherence
in Josephson Phase Qubits from Junction Resonators”, Phys. Rev.
Lett. 93, 077003 (2004).