Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session L28: Quantum Metrology, Characterization and Measurements 
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Sponsoring Units: DQI Chair: Shengshi Pang, University of Rochester Room: LACC 405 
Wednesday, March 7, 2018 11:15AM  11:27AM 
L28.00001: Quantum metrology with timedependent Hamiltonians Andrew Jordan , Shengshi Pang , Jing Yang I will give an overview of recent results [1,2,3] in generalizing the theory of quantum metrology to the situation when the Hamiltonian is time dependent. In the general case, optimal precision requires coherent control of the system, together with adaptive feedback. When these ingredients are combined, we will show that existing bounds for the precision using timeindependent Hamiltonians can be broken. Application to precisions frequency measurements will be discussed. 
Wednesday, March 7, 2018 11:27AM  11:39AM 
L28.00002: Quantum state smoothing: when the types of observed/unobserved measurement matter Ivonne Guevara , Areeya Chantasri , Howard Wiseman

Wednesday, March 7, 2018 11:39AM  11:51AM 
L28.00003: Twirling Projective Measurements in Quantum Estimation Fuyuhiko Tanaka Theoretical investigations of quantum estimation have clarified the achievable bound of the estimation error. However, the optimal estimation requires adaptive or collective schemes, where the preparation cost of experiments is too much or the quantum measurements are beyond the current technology. On the other hand, improving the accuracy of the parameter estimation is often critical in some of quantum computation experiments. Motivated with this, in the simplest case we will discuss how to improve current measurements at a reasonable cost by using the mathematical tool of asymptotic risk expansion. When estimating the expectations of two noncommutative observables, the standard method is to make a large number of repetitions of both the projective measurements corresponding to the two observables. We show that certain choices of four kinds of projective measurements, which we call twirling projective measurements, yield a smaller error when the total repetition number is fixed. This example demonstrates that an elaborate combination of projective measurements can improve accuracy without the need for advanced technology such as quantum entanglement. 
Wednesday, March 7, 2018 11:51AM  12:03PM 
L28.00004: Breeding Grid States From Schrödinger Cat States without PostSelection Daniel Weigand , Barbara Terhal Grid (or comb) states are an interesting class of bosonic states introduced by Gottesman, Kitaev and Preskill to encode a qubit into an oscillator. A method to generate or `breed' a grid state from Schrödinger cat states using beam splitters and homodyne measurements is known but this method requires postselection. We show how postprocessing of the measurement data can be used to entirely remove the need for postselection, making the scheme much more viable. 
Wednesday, March 7, 2018 12:03PM  12:15PM 
L28.00005: Randomized Benchmarking of Almost Any Gate Set Timothy Proctor , Arnaud CarignanDugas , Melissa Revelle , Daniel Lobser , Peter Maunz , Robin BlumeKohout , Kevin Young <!StartFragment>We propose and demonstrate a range of simple randomized benchmarking (RB) protocols that can be used to benchmark almost any gate set. The main RB protocol we propose consists of random circuits of gates from any gate set that generates the nqubit Clifford group. We show that this ``generator RB'' protocol is wellbehaved for all reasonably lowerror gates, and that the error rate reported by generator RB is a sensible notion of the average error per gate in this gate set. The standard approach to RB consists of implementing random circuits of nqubit Clifford gates, which, in practice, are necessarily compiled into sequences of the physically available ``primitive gates''. Our protocols have many advantages over this standard approach, including: generator RB directly reports an error per physical primitive gate, rather than an error per Clifford, and generator RB is more scalable, facilitating the benchmarking of a greater number of qubits. We demonstrate our protocols on a trapped ion qubit. <!EndFragment> 
Wednesday, March 7, 2018 12:15PM  12:27PM 
L28.00006: Quantum tomography with continuous measurement and a resource limitation Areeya Chantasri , Shengshi Pang , Teerawat Chalermpusitarak , Andrew Jordan We propose and analyze quantum state estimation (tomography) for a single qubit and two interacting qubits, where only a singlequbit observable is continuously measured. By utilizing a continuous weak probe, we can turn on sets of qubit oscillations while measuring the singlequbit observable continuously; and the information of qubit coordinates will gradually be transferred to the measured quantity via the oscillations. In the single qubit case, a combination of the weakcontinuous σ_{z} probe and a Rabi oscillation at an angle in the xz plane is sufficient to extract all three qubit coordinates. For the two interacting qubits, where only σ_{z }of the first qubit is measured, the information of twoqubit matrix elements can be transferred to the measured observable, via the qubitqubit interaction and Rabi controls applied locally on each qubit. We simulate tomographic results numerically and analyze the estimation using the Fisher information in the limit of infinitesimally weak measurement. 
Wednesday, March 7, 2018 12:27PM  12:39PM 
L28.00007: Realizing the Optimal Tomography through a Sequence of Collective Weak Measurements Ezad Shojaee , Christopher Jackson , Carlos Riofrio , Amir Kalev , Ivan Deutsch In their seminal paper, Massar and Popescu showed that in tomography, given Ncopies of a pure qubit, the optimal fidelity one can achieve (on average) is (N+1)/(N+2) [1]. Without adaptive measurement, reaching this bound requires a collective measurement on the entire ensemble, and this can be achieved through a POVM whose measurement outcomes are spin coherent states of the collective spin, J=N/2. In this work, we prove that one can realize this POVM through a sequence of weak measurements of the collective spin along random directions on the sphere. We give numerical evidence that supports this result, and show that we saturate the optimal fidelity for quantum state tomography averaged over all unknown states. We describe the connection between this protocol and tomography via continuous weak measurement in the presence of timedependent control [2]. 
Wednesday, March 7, 2018 12:39PM  12:51PM 
L28.00008: Selfconsistent quantum tomography for characterizing superaccurate quantum operations Takanori Sugiyama , Shinpei Imori , Fuyuhiko Tanaka Increasing number of qubits and improving accuracy of quantum operations are indispensable tasks for realizing a practical quantum computer. A reliable method for characterizing quantum operations is a useful tool toward further improvements of the accuracy. Randomized benchmarking protocols are current standard methods, but they can estimate only a few parameters of errors on gates and cannot characterize accuracies of state preparations and measurements. Gate set tomography is an alternative candidate and can fully characterize all of state preparations, gates, and measurements. However the SPAMerrorfreeness are not compatible with the physicality of estimates, and it can handle a limited number of gates. Here we propose a new tomographic method. We mathematically prove that our method provides estimates satisfying both of the SPAMerrorfreeness and physicality. Additionally the method can handle flexible numbers of quantum operations. 
Wednesday, March 7, 2018 12:51PM  1:03PM 
L28.00009: Bayesian Process Tomography Using Orientation Statistics Kevin Schultz Using the fact that completely positive, tracepreserving (CPTP) maps can be represented by matrices of orthonormal columns through the Stinespring representation, we consider a number of Bayesian estimation problems in quantum process tomography that use random matrices with orthonormal columns as prior distributions. The space of matrices with orthonormal columns of a given dimension is known as a Stiefel manifold, and the generalization of angular or directional statistics to random elements on Stiefel manifolds is known as orientation statistics. From the field of orientation statistics we present three main classes of probability distributions: wrapped distributions formed by exponentiating random matrix elements of the Stiefel manifold tangent space, projected distributions formed by taking the QR decomposition of a random matrix, and maximum entropy distributions derived from the statistical theory of exponential families. In particular, this last class allows for the treatment of an average CPTP map as a sufficient statistic. This presentation contains recent results for a number of Bayesian approaches to process tomography, including full Bayesian tomography, maximum a posteriori (MAP) estimation, expected a posteriori (EAP) estimation, and sequential methods. 
Wednesday, March 7, 2018 1:03PM  1:15PM 
L28.00010: Detecting Correlated StatePreparation and Measurement Device Errors with NonHolonomic Quantum Tomography Christopher Jackson , Steven van Enk In standard quantum state tomography one prepares copies of an unknown state, subjects them to a complete set of controlled measurements, records the outcome probabilities, and performs some inversion of the Born rule to determine the state. Similarly, one can characterize an unknown detector with a complete set of known states. I consider the situation where one has both statepreparation and measurement devices with various settings, but none of which are characterized. By the Born rule, recording statistics alone cannot determine the states being prepared or the measurements made. Amazingly however, one can still determine if the settings between these devices produce states and measurements with correlated errors. [PRA 92(4), 042312] The technique has many formal similarities to classical thermodynamics as well as to gauge theory. [PRA 95(5), 052328] 
Wednesday, March 7, 2018 1:15PM  1:27PM 
L28.00011: Signal processing in continuous syndrome of the three qubit quantum error correction code Jing Yang , Areeya Chantasri , Justin Dressel , Alexander Korotkov , Andrew Jordan We develop several protocols for quantum error correction of three qubit code with continuous syndrome measurements, including boxcar filter, double exponential smoothing and Bayesian filter. These protocols are realistic and efficient enough for rapid experimental realization of quantum error correction code. We also discuss the continuous feedback protocol based on Bayesian filtering, which requires real time correction. It is found numerically that for fast measurements delaying the correction until the qubit recall time is almost of the same fidelity as feeding back with pulses in real time. Thus with Bayesian filtering waiting until the end of the run will save considerable resources without losing too much fidelity. 
Wednesday, March 7, 2018 1:27PM  1:39PM 
L28.00012: Optimal Nonclassicalitybased Benchmarks for Linear Qubit Arrays Mordecai Waegell , Eric Freda , Justin Dressel A special class of sets of M ≤ N + 1 mutually commuting Nqubit Pauli operators can be used to simultaneously witness Npartite entanglement, violate a Bell inequality associated with the Nqubit GreenbergerHorneZeilinger theorem, and place a tight lower bound on the fidelity of particular stabilizer state preparations. This fidelity bound is tight in the sense that if the true fidelity is 1, then the lower bound obtained from M measurement settings also goes to 1, but it grows worse as the true fidelity degrades. Example sets are given for N = 3,...,9 qubits, along with the corresponding circuit designs, which are optimized to require only nearestneighbor controlledZ operations on a linear array of physical qubits, with a uniform gate depth of four  local rotations to initialize each qubit, two rounds of staggered nearest neighbor controlledZ gates, and local rotations to set the readout basis. These circuits were simulated to estimate their practicality with a range of stateofthe art T_{1} decoherence times, T_{2} dephasing times, and gate fidelities. 
Wednesday, March 7, 2018 1:39PM  1:51PM 
L28.00013: On Pins and Needles: The Geometry of Quantum Measurements Jonathan Gross , Carlton Caves Stepping up to big quantum systems with the intuitions learned from qubits is dangerous business, but studying the geometric properties of these higherdimensional quantum state spaces can keep us from stumbling. I will discuss properties of tangent cones relevant to the complexity of compressed sensing and convex optimization in quantum state tomography, revealing the state space to be quite sharply pointed. I will also describe the measurementbased metrics in which these properties must be quantified, highlighting their incompatibility with the most widely used metrics on the state space. 
Wednesday, March 7, 2018 1:51PM  2:03PM 
L28.00014: Resilience of Measurement Protocols for OutofTimeOrdered Correlators Jose Raul Gonzalez Alonso , Nicole Yunger Halpern , Justin Dressel Outoftimeorderedcorrelators (OTOCs) have emerged as a useful tool to study quantum chaos and the scrambling and delocalization of information in manybody systems. While challenging, their experimental measurement has been achieved in NMR and trapped ion systems. In this work, we study the effect of experimental nonidealities on two measurement protocols, namely, one based on quantum clocks and the other on sequential weak measurements. For concreteness, we consider circuit implementations for the spin chain and kickedtop that may be achieved with current hardware. 
Wednesday, March 7, 2018 2:03PM  2:15PM 
L28.00015: Efficient Classical Simulation of Quantum Circuits beyond the Stabilizer Formalism Patrick Rall , James Troupe The GottesmannKnill theorem states that stabilizer states and operations can be simulated efficiently on a classical computer. Using quasiprobability distributions over stabilizer states and operations, a 2017 algorithm by Bennink et al. achieves efficient simulation of mixed states and quantum channels whenever the distribution is nonnegative. We extend their algorithm to arbitrary quasiprobability representations that need not be restricted by the stabilizer formalism. This opens the possibility for efficient classical simulation of larger regions of quantum mechanics. Since negative quasiprobability is a manifestation of quantum contextuality, this analysis highlights a connection between efficient classical simulation and noncontextuality. 
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