Andrew Lutomirski

Precision Calibration of Radio Interferometers Using Redundant Baselines

Growing interest in 21-cm tomography has led to the design and construction of broad-band radio interferometers with low noise, moderate angular resolution, high spectral resolution and wide fields of view. With characteristics somewhat different from traditional radio instruments, these interferometers may require new calibration techniques in order to reach their design sensitivities. Self-calibration or redundant calibration techniques that allow an instrument to be calibrated off complicated sky emission structures are ideal. In particular, the large number of redundant baselines possessed by these new instruments makes redundant calibration an especially attractive option. In this paper, we explore the errors and biases in existing redundant calibration schemes through simulations, and show how statistical biases can be eliminated. We also develop a general calibration formalism that includes both redundant baseline methods and basic point source calibration methods as special cases, and show how slight deviations from perfect redundancy and coplanarity can be taken into account.

MITEoR: a scalable interferometer for precision 21 cm cosmology

We report on the MIT Epoch of Reionization (MITEoR) experiment, a pathfinder low-frequency radio interferometer whose goal is to test technologies that improve the calibration precision and reduce the cost of the high-sensitivity 3D mapping required for 21 cm cosmology. MITEoR accomplishes this by using massive baseline redundancy, which enables both automated precision calibration and correlator cost reduction. We demonstrate and quantify the power and robustness of redundancy for scalability and precision. We find that the calibration parameters precisely describe the effect of the instrument upon our measurements, allowing us to form a model that is consistent with

Quantum State Restoration and Single-Copy Tomography for Ground States of Hamiltonians

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per degree of freedom < 1.2 for as much as 80% of the observations. We use these results to develop an optimal estimator of calibration parameters using Wiener filtering, and explore the question of how often and how finely in frequency visibilities must be reliably measured to solve for calibration coefficients. The success of MITEoR with its 64 dual-polarization elements bodes well for the more ambitious Hydrogen Epoch of Reionization Array (HERA) project and other next-generation instruments, which would incorporate many identical or similar technologies.

Solving the Corner-Turning Problem for Large Interferometers

Given a single copy of an unknown quantum state, the no-cloning theorem limits the amount of information that can be extracted from it. Given a gapped Hamiltonian, in most situations it is impractical to compute properties of its ground state, even though in principle all the information about the ground state is encoded in the Hamiltonian. We show in this Letter that if you know the Hamiltonian of a system and have a single copy of its ground state, you can use a quantum computer to efficiently compute its local properties. Specifically, in this scenario, we give efficient algorithms that copy small subsystems of the state and estimate the full statistics of any local measurement.

Brute-force mapmaking with compact interferometers: a MITEoR northern sky map from 128 to 175 MHz

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Efficient Large Almost Wait-Free Single-Writer Multireader Atomic Registers

The so-called corner-turning problem is a major bottleneck for radio telescopes with large numbers of antennas. The problem is essentially that of rapidly transposing a matrix that is too large to store on one single device; in radio interferometry, it occurs because data from each antenna need to be routed to an array of processors each of which will handle a limited portion of the data (say, a frequency range) but requires input from each antenna. We present a low-cost solution allowing the correlator to transpose its data in real time, without contending for bandwidth, via a butterfly network requiring neither additional RAM memory nor expensive general-purpose switching hardware. We discuss possible implementations of this using FPGA, CMOS, analog logic and optical technology, and conclude that the corner-turner cost can be small even for upcoming massive radio arrays.

Breaking and making quantum money: toward a new quantum cryptographic protocol

We present a new method for interferometric imaging that is ideal for the large fields of view and compact arrays common in 21 cm cosmology. We first demonstrate the method with simulations for two very different low frequency interferometers, the Murchison Widefield Array (MWA) and the MIT Epoch of Reionization (MITEoR) Experiment. We then apply the method to the MITEoR data set collected in July 2013 to obtain the first northern sky map from 128 MHz to 175 MHz at about 2 degree resolution, and find an overall spectral index of -2.73+/-0.11. The success of this imaging method bodes well for upcoming compact redundant low-frequency arrays such as HERA. Both the MITEoR interferometric data and the 150 MHz sky map are publicly available at this http URL.

An online attack against Wiesner's quantum money

We present a nonblocking algorithm for implementing single-writer multireader atomic registers of arbitrary size given registers only large enough to hold a single word. The algorithm has several properties that make it practical: It is simple and has low memory overhead, readers do not write, write operations are wait-free, and read operations are almost wait-free. Specifically, to implement a register with w words, the algorithm uses N (w + O (1)) words, where N is a parameter of the algorithm. Write operations take amortized O (w ) and worst-case O (Nw ) steps, and a read operation completes in O (w (log(k + 2) + Nk ·2*** N )) steps, where k is the number of write operations it overlaps.