E. Ladizinsky

Quantum annealing with manufactured spins

Many interesting but practically intractable problems can be reduced to that of finding the ground state of a system of interacting spins; however, finding such a ground state remains computationally difficult. It is believed that the ground state of some naturally occurring spin systems can be effectively attained through a process called quantum annealing. If it could be harnessed, quantum annealing might improve on known methods for solving certain types of problem. However, physical investigation of quantum annealing has been largely confined to microscopic spins in condensed-matter systems. Here we use quantum annealing to find the ground state of an artificial Ising spin system comprising an array of eight superconducting flux quantum bits with programmable spin–spin couplings. We observe a clear signature of quantum annealing, distinguishable from classical thermal annealing through the temperature dependence of the time at which the system dynamics freezes. Our implementation can be configured in situ to realize a wide variety of different spin networks, each of which can be monitored as it moves towards a low-energy configuration. This programmable artificial spin network bridges the gap between the theoretical study of ideal isolated spin networks and the experimental investigation of bulk magnetic samples. Moreover, with an increased number of spins, such a system may provide a practical physical means to implement a quantum algorithm, possibly allowing more-effective approaches to solving certain classes of hard combinatorial optimization problems.

Experimental investigation of an eight-qubit unit cell in a superconducting optimization processor

A superconducting chip containing a regular array of flux qubits, tunable interqubit inductive couplers, an XY-addressable readout system, on-chip programmable magnetic memory, and a sparse network of analog control lines has been studied. The architecture of the chip and the infrastructure used to control it were designed to facilitate the implementation of an adiabatic quantum optimization algorithm. The performance of an eight-qubit unit cell on this chip has been characterized by measuring its success in solving a large set of random Ising spin-glass problem instances as a function of temperature. The experimental data are consistent with the predictions of a quantum mechanical model of an eight-qubit system coupled to a thermal environment. These results highlight many of the key practical challenges that we have overcome and those that lie ahead in the quest to realize a functional large-scale adiabatic quantum information processor.

Entanglement in a quantum annealing processor

Abstract : Entanglement lies at the core of quantum algorithms designed to solve problems that are intractable by classical approaches. One such algorithm, quantum annealing (QA), provides a promising path to a practical quantum processor. We have built a series of architecturally scalable QA processors consisting of networks of manufactured interacting spins (qubits). Here, we use qubit tunneling spectroscopy to measure the energy eigen spectrum of two- and eight-qubit systems within one such processor, demonstrating quantum coherence in these systems. We present experimental evidence that, during a critical portion of QA, the qubits become entangled and entanglement persists even as these systems reach equilibrium with a thermal environment. Our results provide an encouraging sign that QA is a viable technology for large scale quantum computing.

Thermally assisted quantum annealing of a 16-qubit problem

Efforts to develop useful quantum computers have been blocked primarily by environmental noise. Quantum annealing is a scheme of quantum computation that is predicted to be more robust against noise, because despite the thermal environment mixing the systems state in the energy basis, the system partially retains coherence in the computational basis, and hence is able to establish well-defined eigenstates. Here we examine the environments effect on quantum annealing using 16 qubits of a superconducting quantum processor. For a problem instance with an isolated small-gap anticrossing between the lowest two energy levels, we experimentally demonstrate that, even with annealing times eight orders of magnitude longer than the predicted single-qubit decoherence time, the probabilities of performing a successful computation are similar to those expected for a fully coherent system. Moreover, for the problem studied, we show that quantum annealing can take advantage of a thermal environment to achieve a speedup factor of up to 1,000 over a closed system.

Experimental Demonstration of a Robust and Scalable Flux Qubit

Received 23 September 2009; revised manuscript received 11 February 2010; published 7 April 2010 A rf–superconducting quantum interference device SQUID flux qubit that is robust against fabrication variations in Josephson-junction critical currents and device inductance has been implemented. Measurements of the persistent current and of the tunneling energy between the two lowest-lying states, both in the coherent and incoherent regimes, are presented. These experimental results are shown to be in agreement with predictions of a quantum-mechanical Hamiltonian whose parameters were independently calibrated, thus justifying the identification of this device as a flux qubit. In addition, measurements of the flux and critical current noise spectral densities are presented that indicate that these devices with Nb wiring are comparable to the best Al wiring rf SQUIDs reported in the literature thus far, with a 1 /f flux noise spectral density at 1 Hz of 1.3 �0.5 0 /Hz. An explicit formula for converting the observed flux noise spectral density into a freeinduction-decay time for a flux qubit biased to its optimal point and operated in the energy eigenbasis is presented.

A scalable control system for a superconducting adiabatic quantum optimization processor

We have designed, fabricated and operated a scalable system for applying independently programmable time-independent, and limited time-dependent flux biases to control superconducting devices in an integrated circuit. Here we report on the operation of a system designed to supply 64 flux biases to devices in a circuit designed to be a unit cell for a superconducting adiabatic quantum optimization system. The system requires six digital address lines, two power lines, and a handful of global analog lines.

A scalable readout system for a superconducting adiabatic quantum optimization system

We have designed, fabricated and tested an XY-addressable readout system that is specifically tailored for the reading of superconducting flux qubits in an integrated circuit that could enable adiabatic quantum optimization. In such a system, the flux qubits only need to be read at the end of an adiabatic evolution when quantum mechanical tunneling has been suppressed, thus simplifying many aspects of the readout process. The readout architecture for an N-qubit adiabatic quantum optimization system comprises N hysteretic dc SQUIDs and N rf SQUID latches controlled by bias lines. The latching elements are coupled to the qubits and the dc SQUIDs are then coupled to the latching elements. This readout scheme provides two key advantages: first, the latching elements provide exceptional flux sensitivity that significantly exceeds what may be achieved by directly coupling the flux qubits to the dc SQUIDs using a practical mutual inductance. Second, the states of the latching elements are robust against the influence of ac currents generated by the switching of the hysteretic dc SQUIDs, thus allowing one to interrogate the latching elements repeatedly so as to mitigate the effects of stochastic switching of the dc SQUIDs. We demonstrate that it is possible to achieve single-qubit read error rates of < 10 − 6 with this readout scheme. We have characterized the system level performance of a 128-qubit readout system and have measured a readout error probability of 8 × 10 − 5 in the presence of optimal latching element bias conditions.

An improved NbN integrated circuit process featuring thick NbN ground plane and lower parasitic circuit inductances

We report on the development of a 10 K, NbN superconductive integrated circuit (IC) technology that utilizes an improved SiO/sub 2/ interlevel dielectric (ILD) deposition process and a thick NbN ground plane layer to reduce parasitic circuit inductances. The ILD process uses a novel low frequency (40 kHz) substrate bias during sputter deposition of SiO/sub 2/, which produces very smooth oxide films having a roughness less than 0.1 nm (rms) as measured by atomic force microscopy (AFM). Bias-sputtered SiO/sub 2/ is used to planarize and to smooth the surface of the NbN ground plane layer in preparation for fabrication of NbN/MgO/NbN tunnel junctions. High current density tunnel junctions ranging from 1000 A/cm/sup 2/ to 5000 A/cm/sup 2/, fabricated over NbN ground planes up to 1 /spl mu/m thick, exhibit low subgap leakage (V/sub m//spl sim/15 mV at 10 K) and high subgap voltage (V/sub g/=4.4 mV at 10 K). Typical wiring inductance over ground plane has been reduced by 25% compared to our present NbN foundry process.

Geometrical dependence of the low-frequency noise in superconducting flux qubits

A general method for directly measuring the low-frequency flux noise (below 10 Hz) in compound Josephson-junction superconducting flux qubits has been used to study a series of 85 devices of varying design. The variation in flux noise across sets of qubits with identical designs was observed to be small. However, the levels of flux noise systematically varied between qubit designs with strong dependence upon qubit wiring length and wiring width. Furthermore, qubits fabricated above a superconducting ground plane yielded lower noise than qubits without such a layer. These results support the hypothesis that local impurities in the vicinity of the qubit wiring are a key source of low-frequency flux noise in superconducting devices.

The distributed Josephson inductance phase shifter

The authors report on a novel microwave phase shifter featuring rapid electronic adjustment, continuous phase control true time delay operation, high device fault tolerance, and very broadband operation. By coupling a large number of superconducting quantum interference devices (SQUIDs) to a superconducting microstrip transmission line, a variable magnetic medium in which the wave velocity is controlled electronically is created. The authors have measured 60 degrees phase shift at 10 GHz, and wideband operation from 5 to 15 GHz for an 8-cm-long Nb transmission line coupled to 1600 SQUIDs, each containing a single Nb/AlO/sub x//Nb tunnel junction. The observed phase shift corresponds to a change in wave velocity of about 1 part in 60.<<ETX>>