A superconducting microwave multivibrator produced by coherent feedback

We investigate a coherent nonlinear feedback circuit constructed from pre-existing superconducting microwave devices. The network exhibits emergent bistable and astable states, and we demonstrate its operation as a latch and the frequency locking of its oscillations. While the network is tedious to model by hand, our observations agree quite well with the semiclassical dynamical model produced by a new software package [N. Tezak et al., arXiv:1111.3081v1] that systematically interpreted an idealized schematic of the system as a quantum optic feedback network.Comment: 9 double-spaced pages, 5 figures and supplement. To appear in Phys. Rev. Let

Triangulations and volume form on moduli spaces of flat surfaces

In this paper, we are interested in flat metric structures with conical singularities on surfaces which are obtained by deforming translation surface structures. The moduli space of such flat metric structures can be viewed as some deformation of the moduli space of translation surfaces. Using geodesic triangulations, we define a volume form on this moduli space, and show that, in the well-known cases, this volume form agrees with usual ones, up to a multiplicative constant.Comment: 42 page

Upgrading the Local Ergodic Theorem for planar semi-dispersing billiards

The Local Ergodic Theorem (also known as the `Fundamental Theorem') gives sufficient conditions under which a phase point has an open neighborhood that belongs (mod 0) to one ergodic component. This theorem is a key ingredient of many proofs of ergodicity for billiards and, more generally, for smooth hyperbolic maps with singularities. However the proof of that theorem relies upon a delicate assumption (Chernov-Sinai Ansatz), which is difficult to check for some physically relevant models, including gases of hard balls. Here we give a proof of the Local Ergodic Theorem for two dimensional billiards without using the Ansatz.Comment: 17 pages, 2 figure

High fidelity state preparation, quantum control, and readout of an isotopically enriched silicon spin qubit

Quantum systems must be prepared, controlled, and measured with high fidelity in order to perform complex quantum algorithms. Control fidelities have greatly improved in silicon spin qubits, but state preparation and readout fidelities have generally been poor. By operating with low electron temperatures and employing high-bandwidth cryogenic amplifiers, we demonstrate single qubit readout visibilities >99%, exceeding the threshold for quantum error correction. In the same device, we achieve average single qubit control fidelities >99.95%. Our results show that silicon spin qubits can be operated with high overall operation fidelity

Escape orbits and Ergodicity in Infinite Step Billiards

In a previous paper we defined a class of non-compact polygonal billiards, the infinite step billiards: to a given decreasing sequence of non-negative numbers $\{p_{n}$, there corresponds a table \Bi := \bigcup_{n\in\N} [n,n+1] \times [0,p_{n}]. In this article, first we generalize the main result of the previous paper to a wider class of examples. That is, a.s. there is a unique escape orbit which belongs to the alpha and omega-limit of every other trajectory. Then, following a recent work of Troubetzkoy, we prove that generically these systems are ergodic for almost all initial velocities, and the entropy with respect to a wide class of ergodic measures is zero.Comment: 27 pages, 8 figure

Stabilizing entanglement autonomously between two superconducting qubits

Quantum error-correction codes would protect an arbitrary state of a multi-qubit register against decoherence-induced errors, but their implementation is an outstanding challenge for the development of large-scale quantum computers. A first step is to stabilize a non-equilibrium state of a simple quantum system such as a qubit or a cavity mode in the presence of decoherence. Several groups have recently accomplished this goal using measurement-based feedback schemes. A next step is to prepare and stabilize a state of a composite system. Here we demonstrate the stabilization of an entangled Bell state of a quantum register of two superconducting qubits for an arbitrary time. Our result is achieved by an autonomous feedback scheme which combines continuous drives along with a specifically engineered coupling between the two-qubit register and a dissipative reservoir. Similar autonomous feedback techniques have recently been used for qubit reset and the stabilization of a single qubit state, as well as for creating and stabilizing states of multipartite quantum systems. Unlike conventional, measurement-based schemes, an autonomous approach counter-intuitively uses engineered dissipation to fight decoherence, obviating the need for a complicated external feedback loop to correct errors, simplifying implementation. Instead the feedback loop is built into the Hamiltonian such that the steady state of the system in the presence of drives and dissipation is a Bell state, an essential building-block state for quantum information processing. Such autonomous schemes, broadly applicable to a variety of physical systems as demonstrated by a concurrent publication with trapped ion qubits, will be an essential tool for the implementation of quantum-error correction.Comment: 39 pages, 7 figure

Lives on track? Long-term earnings returns to selective school placement in England and Denmark

We explore the influence of between-school ability placement at lower secondary education on earnings across the life course in England and Denmark. We go beyond the mid-career snapshot provided by previous studies by exploiting the availability of four decades worth of earnings data for individuals born in the mid-1950s. Members of this cohort who were judged to be among the most academically able attended grammar schools in England (19 percent) and advanced secondary schools (Realskole) in Denmark (51 percent) prior to the start of comprehensivisation. This key difference makes England and Denmark interesting cases for comparison, not least since pro-selection policies have re-emerged in England based on the claim that grammar schools lead to better educational and labour market outcomes. Our analysis of the influence of selective school placement on earnings finds little support for this contention. We find that those from socioeconomically disadvantaged backgrounds were strikingly under-represented in schools ear-marked for higher ability pupils in both countries, even after taking into account social class differences in measured ability. Our analysis for England finds only modest earnings returns to attending a grammar school, totalling just £39,000 across the life course, while in Denmark the lifetime earnings returns to attending Realskole are somewhat larger (£194,000). Because those from advantaged backgrounds were substantially over-represented at grammar schools and Realskoles, these returns accrue disproportionately to pupils from more advantaged backgrounds. Lower secondary school placement in Denmark accounts for forty percent of the intergenerational reproduction of socioeconomic advantage and disadvantage, more than half of which is due to selection into school types based on socioeconomic background rather than measured ability. Our findings question the wisdom of expanding grammar schools when they appear to do little to improve individuals’ earnings or increase social mobility