The interaction of matter and light is one of the fundamental processes occurring in nature, and its most elementary form is realized when a single atom interacts with a single photon. Reaching this regime has been a major focus of research in atomic physics and quantum optics1 for several decades and has generated the field of cavity quantum electrodynamics2,3. Here we perform an experiment in which a superconducting two-level system, playing the role of an artificial atom, is coupled to an on-chip cavity consisting of a superconducting transmission line resonator. We show that the strong coupling regime can be attained in a solid-state system, and we experimentally observe the coherent interaction of a superconducting two-level system with a single microwave photon. The concept of circuit quantum electrodynamics opens many new possibilities for studying the strong interaction of light and matter. This system can also be exploited for quantum information processing and quantum communication and may lead to new approaches for single photon generation and detection.

https://arxiv.org/pdf/cond-mat/0407325.pdf

Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics

A quantum computer can solve hard problems, such as prime factoring, database searching and quantum simulation, at the cost of needing to protect fragile quantum states from error. Quantum error correction provides this protection by distributing a logical state among many physical quantum bits (qubits) by means of quantum entanglement. Superconductivity is a useful phenomenon in this regard, because it allows the construction of large quantum circuits and is compatible with microfabrication. For superconducting qubits, the surface code approach to quantum computing is a natural choice for error correction, because it uses only nearest-neighbour coupling and rapidly cycled entangling gates. The gate fidelity requirements are modest: the per-step fidelity threshold is only about 99 per cent. Here we demonstrate a universal set of logic gates in a superconducting multi-qubit processor, achieving an average single-qubit gate fidelity of 99.92 per cent and a two-qubit gate fidelity of up to 99.4 per cent. This places Josephson quantum computing at the fault-tolerance threshold for surface code error correction. Our quantum processor is a first step towards the surface code, using five qubits arranged in a linear array with nearest-neighbour coupling. As a further demonstration, we construct a five-qubit Greenberger-Horne-Zeilinger state using the complete circuit and full set of gates. The results demonstrate that Josephson quantum computing is a high-fidelity technology, with a clear path to scaling up to large-scale, fault-tolerant quantum circuits.

/pdf/superconducting-quantum-circuits-at-the-surface-code-45sj5u1z1o.pdf

Superconducting quantum circuits at the surface code threshold for fault tolerance

Superconducting circuits are macroscopic in size but have generic quantum properties such as quantized energy levels, superposition of states, and entanglement, all of which are more commonly associated with atoms. Superconducting quantum bits (qubits) form the key component of these circuits. Their quantum state is manipulated by using electromagnetic pulses to control the magnetic flux, the electric charge or the phase difference across a Josephson junction (a device with nonlinear inductance and no energy dissipation). As such, superconducting qubits are not only of considerable fundamental interest but also might ultimately form the primitive building blocks of quantum computers.

Superconducting quantum bits

Microfabricated superconducting circuit elements can harness the power of quantum behaviour for information processing. Unlike classical information bits, quantum information bits (qubits) can form superpositions or mixture states of ON and OFF, offering a faster, natural form of parallel processing. Previously, direct qubit–qubit coupling has been achieved for up to four qubits, but now two independent groups demonstrate the next crucial step: communication and exchange of quantum information between two superconducting qubits via a quantum bus, in the form of a resonant cavity formed by a superconducting transmission line a few millimetres long. Using this microwave cavity it is possible to store, transfer and exchange quantum information between two quantum bits. It can also perform multiplexed qubit readout. This basic architecture lends itself to expansion, offering the possibility for the coherent interaction of many superconducting qubits. The cover illustrates a zig-zag-shaped resonant cavity or quantum bus linking two superconducting phase qubits. One of two papers that demonstrate the communication of individual quantum states between superconducting qubits via a quantum bus. This quantum bus is a resonant cavity formed by a superconducting transmission line of several millimetres. Quantum information, initially defined in one qubit on one end, can be stored in this quantum bus and at a later time retrieved by a second qubit at the other end. Superconducting circuits are promising candidates for constructing quantum bits (qubits) in a quantum computer; single-qubit operations are now routine1,2, and several examples3,4,5,6,7,8,9 of two-qubit interactions and gates have been demonstrated. These experiments show that two nearby qubits can be readily coupled with local interactions. Performing gate operations between an arbitrary pair of distant qubits is highly desirable for any quantum computer architecture, but has not yet been demonstrated. An efficient way to achieve this goal is to couple the qubits to a ‘quantum bus’, which distributes quantum information among the qubits. Here we show the implementation of such a quantum bus, using microwave photons confined in a transmission line cavity, to couple two superconducting qubits on opposite sides of a chip. The interaction is mediated by the exchange of virtual rather than real photons, avoiding cavity-induced loss. Using fast control of the qubits to switch the coupling effectively on and off, we demonstrate coherent transfer of quantum states between the qubits. The cavity is also used to perform multiplexed control and measurement of the qubit states. This approach can be expanded to more than two qubits, and is an attractive architecture for quantum information processing on a chip.

/pdf/coupling-superconducting-qubits-via-a-cavity-bus-551agh8huk.pdf

Coupling superconducting qubits via a cavity bus.

By exploiting two key aspects of quantum mechanics — the superposition and entanglement of physical states — quantum computers may eventually outperform their classical equivalents. A team based at Yale has achieved an important step towards that goal — the demonstration of the first solid-state quantum processor, which was used to execute two quantum algorithms. Quantum processors based on a few quantum bits have been demonstrated before using nuclear magnetic resonance, cold ion traps and optical systems, all of which bear little resemblance to conventional computers. This new processor is based on superconducting quantum circuits fabricated using conventional nanofabrication technology. There is still a long way to go before quantum computers can challenge the classical type. The processor is very basic, containing just two quantum bits, and operates at a fraction of a degree above absolute zero. But the chip contains all the essential features of a miniature working quantum computer and may prove scalable to more quantum bits and more complex algorithms. Quantum computers, which harness the superposition and entanglement of physical states, hold great promise for the future. Here, the demonstration of a two-qubit superconducting processor and the implementation of quantum algorithms, represents an important step in quantum computing. Quantum computers, which harness the superposition and entanglement of physical states, could outperform their classical counterparts in solving problems with technological impact—such as factoring large numbers and searching databases1,2. A quantum processor executes algorithms by applying a programmable sequence of gates to an initialized register of qubits, which coherently evolves into a final state containing the result of the computation. Building a quantum processor is challenging because of the need to meet simultaneously requirements that are in conflict: state preparation, long coherence times, universal gate operations and qubit readout. Processors based on a few qubits have been demonstrated using nuclear magnetic resonance3,4,5, cold ion trap6,7 and optical8 systems, but a solid-state realization has remained an outstanding challenge. Here we demonstrate a two-qubit superconducting processor and the implementation of the Grover search and Deutsch–Jozsa quantum algorithms1,2. We use a two-qubit interaction, tunable in strength by two orders of magnitude on nanosecond timescales, which is mediated by a cavity bus in a circuit quantum electrodynamics architecture9,10. This interaction allows the generation of highly entangled states with concurrence up to 94 per cent. Although this processor constitutes an important step in quantum computing with integrated circuits, continuing efforts to increase qubit coherence times, gate performance and register size will be required to fulfil the promise of a scalable technology.

Demonstration of two-qubit algorithms with a superconducting quantum processor

We present spectroscopic evidence for the creation of entangled macroscopic quantum states in two current-biased Josephson-junction qubits coupled by a capacitor. The individual junction bias currents are used to control the interaction between the qubits by tuning the energy level spacings of the junctions in and out of resonance with each other. Microwave spectroscopy in the 4 to 6 gigahertzrange at 20 millikelvin reveals energy levels that agree well with theoretical results for entangled states. The single qubits are spatially separate, and the entangled states extend over the 0.7-millimeter distance between the two qubits.

https://science.sciencemag.org/content/sci/300/5625/1548.full.pdf

Entangled macroscopic quantum States in two superconducting qubits.

Based on a quantum analysis of two capacitively coupled current-biased Josephson junctions, we propose two fundamental two-qubit quantum logic gates. Each of these gates, when supplemented by single-qubit operations, is sufficient for universal quantum computation. Numerical solutions of the time-dependent Schrodinger equation demonstrate that these operations can be performed with good fidelity.

https://www.physast.uga.edu/~mgeller/PRL91p167005.pdf

Quantum logic gates for coupled superconducting phase qubits.

Magnetic susceptibility has been measured in ${\mathrm{Pb}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Mn}}_{\mathrm{x}}$Te, ${\mathrm{Pb}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Mn}}_{\mathrm{x}}$Se, and ${\mathrm{Pb}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Gd}}_{\mathrm{x}}$Te with values of x from 0 to 0.08. The susceptibility followed the Curie-Weiss behavior with a small paramagnetic Curie temperature that indicated a weak antiferromagnetic exchange coupling between magnetic ions. We analyze our results together with previously published data for ${\mathrm{Pb}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Mn}}_{\mathrm{x}}$S and ${\mathrm{Pb}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Eu}}_{\mathrm{x}}$Te and present a review of susceptibility parameters in IV-VI compound diluted magnetic semiconductors. We find that the exchange constants obtained from high-temperature susceptibility data in IV-VI diluted magnetic semiconductors are generally an order of magnitude lower than those in II-VI compound diluted magnetic semiconductors. This fact can be explained by assuming that superexchange is the dominant exchange mechanism in all investigated systems. Within this mechanism we estimate the exchange parameters taking into account the crystalline and electronic structure of II-VI and IV-VI semiconductors. Our estimations agree with the experimental results and predict the large difference in exchange parameters between II-VI and IV-VI diluted magnetic semiconductors.

Magnetic susceptibility and exchange in IV-VI compound diluted magnetic semiconductors

Mesure a 4,2 K de l'aimantation de systemes semiconducteurs magnetiques dilues a compose IV-VI par la methode de l'extraction d'echantillon dans des champs magnetiques stables allant jusqu'a 30 T. Les resultats peuvent etre exprimes par une expression contenant une fonction de Brillouin representant les ions magnetiques isoles et un terme representant les interactions de paires. Mise en evidence de l'importance des paires de plus proches voisins dans l'interaction d'echange antiferromagnetique

Influence of pair-exchange interaction on the magnetization of IV-VI-compound diluted magnetic semiconductors

We report a large discrepancy between the measured and theoretically predicted Fermi wave-vector dependence of the transport lifetime to single-particle lifetime ratio for a modulation-doped GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As heterostructure when the carrier density is varied by thermally cycling the sample, grown using molecular-beam epitaxy (MBE), after illumination by a light pulse. The results suggest that the deep centers responsible for the persistent photoconductivity effect, which may originate from nonstoichiometric MBE growth, are the dominant factor in limiting the single-particle lifetime in GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As.

J. R. Anderson

Papers

Entangled macroscopic quantum States in two superconducting qubits.

Quantum logic gates for coupled superconducting phase qubits.

Magnetic susceptibility and exchange in IV-VI compound diluted magnetic semiconductors

Influence of pair-exchange interaction on the magnetization of IV-VI-compound diluted magnetic semiconductors

Study of the single-particle and transport lifetimes in GaAs/Al x Ga 1-x As