Session J33: Focus Session: Superconducting Qubits II

Two Superconducting Charge Qubits Coupled by a Josephson Inductance

When the quantum oscillations [Pashkin {\it et al.}, Nature {\bf 421}, 823 (2003)] and the conditional gate operation [Yamamoto {\it et al.}, Nature {\bf 425}, 941 (2003)] were demonstrated using superconducting charge qubits, the charge qubits were coupled capacitively, where the coupling was always on and the coupling strength was not tunable. This fixed coupling, however, is not ideal because for example, it makes unconditional gate operations difficult. In this work, we aimed to {\it tunably} couple two charge qubits. We fabricated circuits based on the theoretical proposal by You, Tsai, and Nori [PRB {\bf 68}, 024510 (2003)], where the inductance of a Josephson junction, which has a much larger junction area than the qubit junctions, couples the qubits and the coupling strength is controlled by the external magnetic flux. We confirmed by spectroscopy that the large Josephson junction was indeed coupled to the qubits and that the coupling was turned on and off by the external magnetic flux. In the talk, we will also discuss the quantum oscillations in the circuits.   

Kinetics of quasiparticle trapping in a Cooper-pair box.

We study the kinetics of the quasiparticle capture and emission process in a small superconducting island (Cooper-pair box) connected by a tunnel junction to a massive superconducting lead. At low temperatures, the charge on the box fluctuates between two states, even and odd in the number of electrons. Assuming that the odd-electron state has the lowest energy, we evaluate the distribution of lifetimes of the even- and odd-electron states of the Cooper-pair box. The lifetime in the even-electron state is an exponentially distributed random variable corresponding to a homogenous Poisson process of ``poisoning'' the island with a quasiparticle. The distribution of lifetimes of the odd- electron state may deviate from the exponential one. The deviations come from two sources - the peculiarity of the quasiparticle density of states in a superconductor, and the possibility of quasiparticle energy relaxation via phonon emission. In addition to the lifetime distribution, we also find spectral density of charge fluctuations generated by capture and emission processes. The complex statistics of the quasiparticle dwell times in the Cooper-pair box may result in strong deviations of the noise spectrum from the Lorenzian form.   

Narrow band microwave radiation from a biased single-Cooper-pair transistor

We have spectroscopically measured narrow-band microwave radiation emitted from a single-Cooper-pair transistor (SCPT) electrometer biased in its sub-gap region. This radiation was detected by photon-assisted quasiparticle tunneling in a nearby SCPT, in a configuration that closely mimics a qubit-electrometer integrated circuit. In addition to the usual Josephson radiation generated by the electrometer, we also find emission lines whose frequency depend on both the gate charge and bias voltage of the electrometer, and attribute these lines to radiative Cooper-pair transport processes in the biased transistor. Our results suggest that the dissipative operation of an SCPT electrometer, when used as a qubit readout device, may severely disrupt the system it attempts to measure. This radiative coupling between Josephson charge devices, which dominates when coupling in the charge channel is negligible, may impose design constraints on a large scale multi-qubit quantum computer.   

Measurement of the Excited State Lifetime of a Cooper-Pair Box

We have used a radio frequency superconducting single electron transistor (rf-SET) biased around the double Josephson quasiparticle peak to measure the lifetime T$_{1}$ of the excited state of an Al/AlO$_{\mbox{x}}$/Al Cooper-pair box (CPB) qubit. The CPB had a charging energy E$_{C}$/k$_{B}$ = 0.78 K and a maximum Josephson coupling energy E$_{J}$/k$_{B}$ = 0.70 K and all measurements were made at about 40 mK. T$_{1}$ was found by sending a pulse of microwaves to the gate of the CPB and then using the rf-SET to observe the decay rate of the charge signal on the CPB. Near the degeneracy point of the CPB, we observed T$_{1}$ of approximately 100 ns, which was near the limit of the rf-SET bandwidth. As we move away from the degeneracy point, T$_{1}$ varies, reaching a maximum of approximately 400 ns. We examine whether these changes in T$_{1}$ are commensurate with the quantum noise spectral density from the rf-SET.   

Efficient one- and two-qubit pulse gates for an oscillator stabilized Josephson flux qubit

We present schemes for one- and two-qubit dc pulse gates for the IBM qubit. As reported previously by our group, the qubit consists of three Josephson junctions, three loops, and a superconducting transmission line. The qubit-qubit coupling is assumed to be inductive. We show that there are settings of the flux control parameters for which the effective qubit-qubit coupling can be made negligible, allowing one to perform high fidelity single qubit gates. Assuming the presence of no decoherence processes, we are able to reach gates of 99$\%$ fidelity for pulse times in the range of 20-30$\rm{n}s$. Our $T_2$ estimates indicate coherence times long enough to perform approximately 50 of those gates. The control of leakage plays an important role in the design of our dc pulses, preventing shorter pulse times. Also, we look for schemes which may alleviate the errors due the $1/f$ noise. In addition, we show how to perform two-qubit gates in the system, demonstrating a controlled phase operation.   

A Quantum Computer based on Tunable Flux Qubits

Based on the experimental and theoretical results on the different types of superconducting qubits, we feel there are several features which are desirable for the development a scalable quantum computer: (1) Tunable qubits, (2) Tunable coupling, and (3) Storage. We present two and three junction versions of the IBM tunable flux qubit coupled to a harmonic oscillator which exhibit all these features. We can adiabatically move the information from the flux qubit into the harmonic oscillator for storage and back. When the information is in the harmonic oscillator, coherence times are limited by the quality factor of the harmonic oscillator which is known to be high. When the information is in the flux qubit, one and two-qubit gates are implemented using microwave pulses with gate times of about 10-20ns. Coherence times at the operating point are limited by 1/f flux noise with estimated dephasing times of about 100ns. Using shaped pulses simulations show that the overall unitary gate can be made relatively insensitive to frequency drifts, resulting in errors of about 10$^{-3}$ even for total gate lengths similar to the dephasing time. Further improvements will most likely involve reducing flux noise.   

The voltage-controlled superconducting flux qubit

We study a voltage-controlled version of the superconducting flux qubit [Chiorescu \textit{et al.}, Science {\bf 299}, 1869 (2003)] and show that full control of qubit rotations on the entire Bloch sphere can be achieved. Circuit graph theory is used to study a setup where voltage sources are attached to the two superconducting islands formed between the three Josephson junctions in the flux qubit. Applying a voltage allows qubit rotations about the $y$ axis, in addition to pure $x$ and $z$ rotations obtained in the absence of applied voltages. The orientation and magnitude of the rotation axis on the Bloch sphere can be tuned by the gate voltages, the external magnetic flux, and the ratio $\alpha$ between the Josephson energies via a flux-tunable junction. We compare the single-qubit control in the known regime $\alpha<1$ with the unexplored range $\alpha>1$ and estimate the decoherence due to voltage fluctuations.   

Microwave-Induced Cooling of a Superconducting Persistent-Current Qubit

We present the experimental demonstration of microwave-induced cooling of a persistent-current qubit. Our qubit is a multi-level artificial atom. Thermal population of the first-excited qubit state is driven to a higher-excited state, from which it preferentially relaxes to the qubit ground state. Cooling is realized, because the driving-induced population transfer to the ground state is faster than the thermal repopulation of the excited state. We achieve effective qubit temperatures < 3 mK, a factor 10x-100x lower than the dilution refrigerator ambient temperature. This talk will present and discuss these experimental results. [1] S.O. Valenzuela, W.D. Oliver, D.M. Berns, et al., Science (2006).   

Coherent Quasiclassical Dynamics of a Superconducting Persistent-Current Qubit

A new regime of coherent quantum dynamics of a qubit is realized at low driving frequencies in the strong driving limit. Coherent transitions between qubit states occur via the Landau-Zener process when the system is swept through an energy-level avoided crossing. The quantum interference mediated by repeated transitions gives rise to an oscillatory dependence of the qubit population on the driving field amplitude and flux detuning. These interference fringes, which at high frequencies consist of individual multiphoton resonances, persist even for driving frequencies smaller than the decoherence rate, where individual resonances are no longer distinguishable. A theoretical model that incorporates dephasing agrees well with the observations. \newline [1] D.M. Berns, W.D. Oliver, S.O. Valenzuela et al., PRL 97, 150502 (2006).   

Adiabatic Evolution of a System of Four Coupled Flux Qubits

We report upon experimental results from a system consisting of four flux qubits linked via in-situ sign and magnitude tunable coupling elements. The device was operated as an adiabatic quantum computer to solve NP-complete problems whose solutions are encoded in the groundstate configuration of the qubits. Each qubit was coupled to its own dedicated dc-SQUID in order to measure the state of each qubit, thus allowing for unambiguous identification of the groundstate of the coupled qubit system at the end of a computation. Results will be compared to a quantum model of the system's evolution.   

Studies of decoherence in a large area Nb flux qubit

We report measurements using pulsed microwaves to investigate the decoherence mechanisms in a large area Nb based flux qubit. Our qubit uses an rf-SQUID in a gradiometer configuration and has independent, in situ, controls for the relative positions of levels in different fluxoid wells and the barrier height between the wells. We present measurements of decoherence times from coherent oscillations and microwave spectroscopy. These measurements are well suited to evaluate potential improvements in the materials and the fabrication process of both flux and phase qubits based on different flux states.   

Measurement of relaxation time in a large-inductance superconducting flux qubit

Superconducting flux qubits with large geometric inductance are promising candidates for scalable quantum computing because it is easier to couple many of them together to form a quantum circuit sufficiently large for useful computational task. Recently, it has been shown that the dominant decoherence mechanism in superconducting flux qubit carefully isolated from environment is energy relaxation. It is therefore important to understand various relaxation mechanisms. We report here a systematic study of relaxation time as a function of flux bias, temperature, and operating point of the readout circuit in an rf SQUID flux qubit. Determination of the qubit's parameters via microwave and resonant tunneling spectroscopies allow quantitative comparisons to theoretical models. Implications of the result will be discussed.   

Long-range coupling mechanism and architecture for superconducting flux qubits

Devising a scalable mechanism enabling long-range interaction of qubits in a solid-state quantum computer is an important open problem. With only nearest neighbour interactions, gate error rates of order $10^{-7}$ or lower would be required to perform an arbitrarily large computation. If the right kinds of long- range interactions are available, gate error rates of order $10^ {-4}$, and possibly higher, would be acceptable. We discuss exactly what kinds of long-range interactions are required, present a simple mechanism for superconducting flux qubits, a scalable architecture based on this mechanism, and discuss the challenges on the road to physical realisation.