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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 would like to help make large-scale quantum information processing systems a reality.

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 have been 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:

• It could provide a powerful tool for encryption. A quantum computer is seen as the only instrument that could break the most secure encryption codes in use today. This is an immensely important subject for national security.

• It could be used to solve highly complex (manybody) problems in a reasonable amount of time. This will become increasingly important for the chemical and biological sciences

• It could provide rapid search engines to help navigate us through the information age

• It could allow us to simulate large quantum systems efficiently.

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 directly control and measure quantum systems in new ways. We have already shown (as described below) the ability to detect previously unknown nanoscale quantum systems which could never be seen before. By gaining the ability to control quantum systems directly, we are exploring untouched regimes of nature and may find ways to direct unforeseen advancements in nanotechnology

TECHNICAL STRATEGY

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 δ across the junction. A qubit is made by including a Josephson junction in a superconducting loop, as shown in Figure 2(a). Microwav current lines are capacitively coupled to the junction while a dc 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 δ is shown in Figure 2(b). 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 dc 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).

An example of “qubit spectroscopy” is shown in Figure 3. 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 performed 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. At present we are collaborating with David Pappas in the Electromagnetics Division to improve the materials properties of our Josephson junctions to eliminatethese defects.

Our long term strategy is to produce highly coherent single and coupled qubits, and 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

DELIVERABLES

We will continue to refine qubit designs and materials with the objective of increasing energy relaxation and Rabi decay times. We will also extend out investigations of coupled qubits

ACCOMPLISHMENTS

Although this project began only three years ago, we have made significant progress over this short period of time. The first qubit design used a current biased Josephson junction made from niobium with an amorphous aluminum-oxide tunnel barrier. It was successful in showing Rabi oscillations by varying the power of the microwave drive. The energy relaxation time was 300 ns and the Rabi decay time was estimated to be 10 ns. The next qubit design was made from aluminum with an amorphous aluminum-oxide barrier and incorporated copper-gold quasiparticle traps along with a normal metal-insulator-superconductor shunt across the current biased qubit junction. This showed a reduction in excess tunneling events caused by quasiparticle heating. Many of our accomplishments over the past year are included in the list below.

Developed a New Flux Biased Josephson Phase Qubit. We developed a new qubit design that is well isolated from the external environment while still providing an extremely sensitive readout. In addition, this qubit does not generate quasiparticles during measurement. This system has shown Rabi oscillations with up to 75 % visibility with 100 ns decay times. We have also seen energy relaxation times as long as 500 ns.

• Discovered spurious resonators within Josephson tunnel junctions. 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.

Developed a method for characterizing tunnel junctions and phase qubits. Using a low frequency nonlinear current bias, we have developed an effective way to measure extremely small quasiparticle currents in the current-voltage characteristics of tunnel junctions fabricated using various novel methods. These measurements are then correlated with qubit spectroscopy, Rabi oscillations, and energy relaxation times in order to characterize the performance of these new tunnel junctions and the qubits which incorporate them.

• Developed a new, faster method to read out the phase qubit. We have implemented a new qubit state measurement technique that is an order of magnitude faster than our former method. Previously, we utilized a microwave pulse tuned to promote transitions between the |1> state and the |3> state, inducing a tunneling event when the |1> state was occupied. In this new method, with a temporal resolution of less than 5 ns, a flux bias pulse is applied to the qubit so that the |1> state, if occupied, is suddenly presented with a very small energy barrier, which it rapidly tunnels through. This new advance has allowed us to monitor rapid qubit state variations, opening the door to tracking strongly coupled interactions between phase qubits and other quantum systems.

Observed quantum oscillations between a Josephson phase qubit and a nanoscopic resonator. We have detected coherent quantum oscillations between Josephson phase qubits and two-level resonator within the tunnel barrier of a superconducting phase qubit. These results reveal a new aspect of the quantum behavior of Josephson junctions, and they demonstrate the means to measure twoqubit interactions in the time domain. The junction- resonator interaction also points to a possible mechanism for decoherence and reduced fidelity in superconducting qubits

• Coupled qubit interactions. 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

COLLABORATIONS

David Pappas – Electromagnetics Division, 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.

Contacts: Ray Simmonds, simmonds@boulder.nist.gov
www.boulder.nist.gov/div814/
In the image
Ray Simmonds probes the resistance of Josephson junctions on a new wafer of quantum bits.