161 research outputs found
The McKinsey-Tarski theorem for locally compact ordered spaces
We prove that the modal logic of a crowded locally compact generalized ordered space is S4. This provides a version of the McKinsey–Tarski theorem for generalized ordered spaces. We then utilize this theorem to axiomatize the modal logic of an arbitrary locally compact generalized ordered space
Wide-Field Precision Kinematics of the M87 Globular Cluster System
We present the most extensive combined photometric and spectroscopic study to
date of the enormous globular cluster (GC) system around M87, the central giant
elliptical galaxy in the nearby Virgo cluster. Using observations from DEIMOS
and LRIS at Keck, and Hectospec on the MMT, we derive new, precise radial
velocities for 451 GCs around M87, with projected radii from ~ 5 to 185 kpc. We
combine these measurements with literature data for a total sample of 737
objects, which we use for a re-examination of the kinematics of the GC system
of M87. The velocities are analyzed in the context of archival wide-field
photometry and a novel Hubble Space Telescope catalog of half-light radii,
which includes sizes for 344 spectroscopically confirmed clusters. We use this
unique catalog to identify 18 new candidate ultra-compact dwarfs, and to help
clarify the relationship between these objects and true GCs.
We find much lower values for the outer velocity dispersion and rotation of
the GC system than in earlier papers, and also differ from previous work in
seeing no evidence for a transition in the inner halo to a potential dominated
by the Virgo cluster, nor for a truncation of the stellar halo. We find little
kinematical evidence for an intergalactic GC population. Aided by the precision
of the new velocity measurements, we see significant evidence for kinematical
substructure over a wide range of radii, indicating that M87 is in active
assembly. A simple, scale-free analysis finds less dark matter within ~85 kpc
than in other recent work, reducing the tension between X-ray and optical
results. In general, out to a projected radius of ~ 150 kpc, our data are
consistent with the notion that M87 is not dynamically coupled to the Virgo
cluster; the core of Virgo may be in the earliest stages of assembly.Comment: 47 pages, ApJS in press. Redacted long data tables available on
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Readout of a quantum processor with high dynamic range Josephson parametric amplifiers
We demonstrate a high dynamic range Josephson parametric amplifier (JPA) in
which the active nonlinear element is implemented using an array of rf-SQUIDs.
The device is matched to the 50 environment with a Klopfenstein-taper
impedance transformer and achieves a bandwidth of 250-300 MHz, with input
saturation powers up to -95 dBm at 20 dB gain. A 54-qubit Sycamore processor
was used to benchmark these devices, providing a calibration for readout power,
an estimate of amplifier added noise, and a platform for comparison against
standard impedance matched parametric amplifiers with a single dc-SQUID. We
find that the high power rf-SQUID array design has no adverse effect on system
noise, readout fidelity, or qubit dephasing, and we estimate an upper bound on
amplifier added noise at 1.6 times the quantum limit. Lastly, amplifiers with
this design show no degradation in readout fidelity due to gain compression,
which can occur in multi-tone multiplexed readout with traditional JPAs.Comment: 9 pages, 8 figure
Measurement-Induced State Transitions in a Superconducting Qubit: Within the Rotating Wave Approximation
Superconducting qubits typically use a dispersive readout scheme, where a
resonator is coupled to a qubit such that its frequency is qubit-state
dependent. Measurement is performed by driving the resonator, where the
transmitted resonator field yields information about the resonator frequency
and thus the qubit state. Ideally, we could use arbitrarily strong resonator
drives to achieve a target signal-to-noise ratio in the shortest possible time.
However, experiments have shown that when the average resonator photon number
exceeds a certain threshold, the qubit is excited out of its computational
subspace, which we refer to as a measurement-induced state transition. These
transitions degrade readout fidelity, and constitute leakage which precludes
further operation of the qubit in, for example, error correction. Here we study
these transitions using a transmon qubit by experimentally measuring their
dependence on qubit frequency, average photon number, and qubit state, in the
regime where the resonator frequency is lower than the qubit frequency. We
observe signatures of resonant transitions between levels in the coupled
qubit-resonator system that exhibit noisy behavior when measured repeatedly in
time. We provide a semi-classical model of these transitions based on the
rotating wave approximation and use it to predict the onset of state
transitions in our experiments. Our results suggest the transmon is excited to
levels near the top of its cosine potential following a state transition, where
the charge dispersion of higher transmon levels explains the observed noisy
behavior of state transitions. Moreover, occupation in these higher energy
levels poses a major challenge for fast qubit reset
Overcoming leakage in scalable quantum error correction
Leakage of quantum information out of computational states into higher energy
states represents a major challenge in the pursuit of quantum error correction
(QEC). In a QEC circuit, leakage builds over time and spreads through
multi-qubit interactions. This leads to correlated errors that degrade the
exponential suppression of logical error with scale, challenging the
feasibility of QEC as a path towards fault-tolerant quantum computation. Here,
we demonstrate the execution of a distance-3 surface code and distance-21
bit-flip code on a Sycamore quantum processor where leakage is removed from all
qubits in each cycle. This shortens the lifetime of leakage and curtails its
ability to spread and induce correlated errors. We report a ten-fold reduction
in steady-state leakage population on the data qubits encoding the logical
state and an average leakage population of less than
throughout the entire device. The leakage removal process itself efficiently
returns leakage population back to the computational basis, and adding it to a
code circuit prevents leakage from inducing correlated error across cycles,
restoring a fundamental assumption of QEC. With this demonstration that leakage
can be contained, we resolve a key challenge for practical QEC at scale.Comment: Main text: 7 pages, 5 figure
Measurement-induced entanglement and teleportation on a noisy quantum processor
Measurement has a special role in quantum theory: by collapsing the
wavefunction it can enable phenomena such as teleportation and thereby alter
the "arrow of time" that constrains unitary evolution. When integrated in
many-body dynamics, measurements can lead to emergent patterns of quantum
information in space-time that go beyond established paradigms for
characterizing phases, either in or out of equilibrium. On present-day NISQ
processors, the experimental realization of this physics is challenging due to
noise, hardware limitations, and the stochastic nature of quantum measurement.
Here we address each of these experimental challenges and investigate
measurement-induced quantum information phases on up to 70 superconducting
qubits. By leveraging the interchangeability of space and time, we use a
duality mapping, to avoid mid-circuit measurement and access different
manifestations of the underlying phases -- from entanglement scaling to
measurement-induced teleportation -- in a unified way. We obtain finite-size
signatures of a phase transition with a decoding protocol that correlates the
experimental measurement record with classical simulation data. The phases
display sharply different sensitivity to noise, which we exploit to turn an
inherent hardware limitation into a useful diagnostic. Our work demonstrates an
approach to realize measurement-induced physics at scales that are at the
limits of current NISQ processors
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