Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session B52: Quantum Characterization, Validation, and Verification |
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Sponsoring Units: GQI Chair: Marcus da Silva, Raytheon BBN Room: 399 |
Monday, March 13, 2017 11:15AM - 11:27AM |
B52.00001: Experimental demonstration of cheap and accurate phase estimation Kenneth Rudinger, Shelby Kimmel, Daniel Lobser, Peter Maunz We demonstrate experimental implementation of robust phase estimation (RPE) to learn the phases of X and Y rotations on a trapped Yb$^+$ ion qubit.. Unlike many other phase estimation protocols, RPE does not require ancillae nor near-perfect state preparation and measurement operations. Additionally, its computational requirements are minimal. Via RPE, using only 352 experimental samples per phase, we estimate phases of implemented gates with errors as small as $\sim10^{-4}$ radians, as validated using gate set tomography. We also demonstrate that these estimates exhibit Heisenberg scaling in accuracy.\\\\ Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. [Preview Abstract] |
Monday, March 13, 2017 11:27AM - 11:39AM |
B52.00002: The randomized benchmarking number is not what you think it is Timothy Proctor, Kenneth Rudinger, Robin Blume-Kohout, Mohan Sarovar, Kevin Young Randomized benchmarking (RB) is a widely used technique for characterizing a gate set, whereby random sequences of gates are used to probe the average behavior of the gate set. The gates are chosen to ideally compose to the identity, and the rate of decay in the survival probability of an initial state with increasing length sequences is extracted from a set of experiments -- this is the `RB number'. For reasonably well-behaved noise and particular gate sets, it has been claimed that the RB number is a reliable estimate of the average gate fidelity (AGF) of each noisy gate to the ideal target unitary, averaged over all gates in the set. Contrary to this widely held view, we show that this is not the case. We show that there are physically relevant situations, in which RB was thought to be provably reliable, where the RB number is many orders of magnitude away from the AGF. These results have important implications for interpreting the RB protocol, and immediate consequences for many advanced RB techniques. Sandia National Laboratories is a multi-mission laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. [Preview Abstract] |
Monday, March 13, 2017 11:39AM - 11:51AM |
B52.00003: Randomized Benchmarking as a Simulation of the Ising Model Bryan Fong We show how the decay of randomized benchmarking under non-Markovian dephasing can be cast as a solution to the partition function of an Ising model, with the power spectral density providing the range of coupling and the dephasing time providing the effective inverse temperature. We compute the expected randomized benchmarking sequence fidelity assuming free evolution under Hamiltonian Gaussian noise interleaved between perfect instantaneous Clifford pulses. For a single qubit system we show that the expected sequence fidelity is given by the partition function of a long-range coupled spin-one Ising model, with each site in the Ising model corresponding to a free evolution interval. The covariance of error phase angles accumulated in different free evolution intervals gives the coupling constants of the Ising model, while the ratio of the noise-driven characteristic decay time to the free evolution time determines the effective temperature for the partition function. With a leaked state coupled to the qubit subspace, the benchmarking sequence fidelity is given by the partition function of a vector Potts model. In both cases, the sequence fidelity as a function of sequence length varies from exponential decay for uncorrelated noise to power law decay for quasi-static noise. [Preview Abstract] |
Monday, March 13, 2017 11:51AM - 12:03PM |
B52.00004: Multiqubit Randomized Benchmarking Using Few Samples Jonas Helsen, Joel J. Wallman, Steven T. Flammia, Stephanie Wehner Randomized benchmarking (RB) is an efficient and robust method to characterize gate errors in quantum circuits. Averaging over random sequences of gates leads to estimates of gate errors in terms of the average fidelity that are isolated from the state preparation and measurement errors that plague other methods like channel tomography and direct fidelity estimation. A decisive factor in the feasibility of randomized benchmarking is the number of samples required to obtain rigorous confidence intervals. Previous bounds were either prohibitively loose or required the number of sampled sequences to scale exponentially with the number of qubits. Here, we introduce a bound on the number of sampled sequences that dramatically outperforms previous bounds. In particular, we show that the number of sampled sequences required for a fixed confidence interval is essentially independent of the number of qubits. We also show that the number of samples required with a single qubit is substantially smaller than previous rigorous results, especially in the limit of large sequence lengths. Our results bring rigorous randomised benchmarking on systems with many qubits closer to experimental feasibility. [Preview Abstract] |
Monday, March 13, 2017 12:03PM - 12:15PM |
B52.00005: When states can create gates, quantum process tomography becomes quantum state tomography Shelby Kimmel, Christopher Granade, Nathan Wiebe Lloyd, Mohseni, and Rebenstrost devised a way to simulate Hamiltonian evolution when the Hamiltonian is given by the density matrix of a state, and the experimenter is given access to copies of the state [Nat. Phys., 10(9):631–633, 2014]. When the state is unknown, this produces an unknown evolution. Existing quantum process tomography techniques can characterize this evolution, which in turn can characterize properties of the unknown state. Thus we can use quantum process tomography to perform state tomography. We examine advantages and disadvantages of applying Hamiltonian learning [PRL, 112.19 (2014): 190501] to the task of state tomography using this approach. [Preview Abstract] |
Monday, March 13, 2017 12:15PM - 12:27PM |
B52.00006: How distinguishable are two quantum processes? a.k.a. “What is the error rate of a quantum gate?” Robin Blume-Kohout I will try to convince you that the two titles of this talk are, in fact, synonymous — that “error rate” and “distinguishability of quantum processes” are the same thing. Whether or not I succeed, I will go on to discuss (1) the various ways that this has been quantified, (2) the state of the art in doing so, and (3) why I’m not (and you shouldn’t be) satisfied. Having spent most of my time just establishing what the “right” problem is, I will then propose to solve it by sandwiching “distinguishability” between “distillable distinguishability” and “distinguishability of formation”. To demonstrate the utility of this approach, I’ll prove that the diamond norm is not always the right measure of distinguishability (or even close to it!). I will then do a 180-degree turn and argue that for most of the case that we care about, the diamond norm is a good measure of distinguishability, and finally conclude with another 180-degree turn in which I argue that maybe it’s not. [Preview Abstract] |
Monday, March 13, 2017 12:27PM - 12:39PM |
B52.00007: Behavior of the Maximum Likelihood in Quantum State Tomography Travis Scholten, Robin Blume-Kohout Quantum state tomography on large systems — e.g. multiple qubits, or optical modes — is hard because it demands resources (number of measurements, offline data processing time, etc.) that grow with the number of parameters in the density matrix, and thus with the dimension of the system’s Hilbert space. We can eliminate some of those parameters by using statistical model selection. We investigated the behavior of a canonical model selection technique based on ratios of maximum likelihoods (loglikelihood ratio statistics), and discovered state tomography violates crucial assumptions necessary for using this technique -- and others similar to it -- due to the nature of the state space boundaries. We derived an expression for the expected value of the loglikelihood ratio statistic (roughly, the logarithm of the maximum likelihood), which could be used as a complexity penalty, e.g. to select an effective Hilbert space dimension (d) for tomography. [Preview Abstract] |
Monday, March 13, 2017 12:39PM - 12:51PM |
B52.00008: Quantum process tomography of optical unitaries Kevin Valson Jacob, Sushovit Adhikari, Jonathan Dowling Characterizing quantum evolutions are of prime importance in quantum information. In the emerging area of photonic quantum technologies, this amounts to determining the unitary matrix which transforms the mode operators of a linear optical circuit. We propose a loss-tolerant method to fully characterize such unitaries by using only single photons. By inputting a single photon in a given input mode and finding the probability for it to be detected in all output modes, we find the moduli of all the matrix elements of the unitary. To find the phases of the matrix elements, we need the matrix elements to `interfere' with each other. This is found by measuring the phase difference between two different paths taken by a photon. To implement this, we can either send in a photon superposed between any two input modes, or measure the output photon in a different mode basis. The former can be implemented by placing a 50:50 beamsplitter before the unknown unitary while the latter can be implemented by placing a beamsplitter after the unitary. We develop a scheme which optimizes the number of experimental configurations necessary for the full tomography of a `d' dimensional unitary. Although the Hilbert space is exponentially large in the dimension, only $O(d^2)$ measurements suffice. [Preview Abstract] |
Monday, March 13, 2017 12:51PM - 1:03PM |
B52.00009: Efficiently characterizing the total error in quantum circuits Arnaud Carignan-Dugas, Joel J. Wallman, Joseph Emerson A promising technological advancement meant to enlarge our computational means is the quantum computer. Such a device would harvest the quantum complexity of the physical world in order to unfold concrete mathematical problems more efficiently. However, the errors emerging from the implementation of quantum operations are likewise quantum, and hence share a similar level of intricacy. Fortunately, randomized benchmarking protocols provide an efficient way to characterize the operational noise within quantum devices. The resulting figures of merit, like the fidelity and the unitarity, are typically attached to a set of circuit components. While important, this doesn't fulfill the main goal: determining if the error rate of the total circuit is small enough in order to trust its outcome. In this work, we fill the gap by providing an optimal bound on the total fidelity of a circuit in terms of component-wise figures of merit. Our bound smoothly interpolates between the classical regime, in which the error rate grows linearly in the circuit's length, and the quantum regime, which can naturally allow quadratic growth. Conversely, our analysis substantially improves the bounds on single circuit element fidelities obtained through techniques such as interleaved randomized benchmarking. [Preview Abstract] |
Monday, March 13, 2017 1:03PM - 1:15PM |
B52.00010: Single plane SIC-POVM tomography of double slit qubits Karen Fonseca-Romero, Edwin Chaparro, Daniela Angulo |
Monday, March 13, 2017 1:15PM - 1:27PM |
B52.00011: Abstract Withdrawn There are various physical scenarios in which one can only implement operations with a certain symmetry. Under such restriction, a system in a symmetry-breaking state can be used as a catalyst, e.g. to prepare another system in a desired symmetry-breaking state. This sort of (approximate) catalytic state transformations are relevant in the context of (i) state preparation using a bounded-size quantum clock or reference frame, where the clock or reference frame acts as a catalyst, (ii) quantum thermodynamics, where again a clock can be used as a catalyst to prepare states which contain coherence with respect to the system Hamiltonian, and (iii) cloning of unknown quantum states, where the given copies of state can be interpreted as a catalyst for preparing the new copies. Using a recent result of Fawzi and Renner on approximate recoverability, we show that the achievable accuracy in this kind of catalytic transformations can be determined by a single function, namely the relative entropy of asymmetry, which is equal to the difference between the entropy of state and its symmetrized version: if the desired state transition does not require a large increase of this quantity, then it can be implemented with high fidelity using only symmetric operations. Our lower bound on the achievable fidelity is tight in the case of cloners, and can be achieved using the Petz recovery map, which interestingly turns out to be the optimal cloning map found by Werner. |
Monday, March 13, 2017 1:27PM - 1:39PM |
B52.00012: Quantum-like approach for a wave-particle system in fluid mechanics Remy Dubertrand, Maxime Hubert, Peter Schlagheck, Nicolas Vandewalle, Thierry Bastin, John Martin A droplet bouncing on a vibrating bath can mimic, close to the Faraday instability threshold, a wave particle system called a walker. Walkers have attracted considerable attention during the past decade due to their remarkable analogy with quantum duality. This was initiated by the pioneering experiment by Y. Couder et al. in 2006, which reported the observation of a diffraction pattern in the angular resolved profile of walkers, which go to a single slit. While the occurrence of this wave-like phenomenon can be qualitatively linked to the coupling of the droplet with the associated bath surface wave, a quantitative model for the description of the motion of a droplet propelled by the surface wave in the presence of boundaries and obstacles still represents a highly difficult question. This problem is all the more stimulating as several recent experiments have reported clear effects of the geometry on the dynamics of walking droplets. I will present a simple model [1] inspired from quantum mechanics to model a walker in an arbitrary geometry. We propose to describe its trajectory via a Green function approach. The Green function is associated to the Helmholtz equation with Neumann boundary conditions on the obstacle(s). [1] R. Dubertrand et al., New J. Phys. (2016), in press [Preview Abstract] |
Monday, March 13, 2017 1:39PM - 1:51PM |
B52.00013: Temporal Quantum Correlation in Inelastic Light Scattering from Water Andre Saraiva, Mark Kasperczyk, Filomeno de Aguiar Junior, Cassiano Rabelo, Marcelo Santos, Lukas Novotny, Ado Jorio Water is one of the most prevalent chemicals on our planet, an integral part of both our environment and our existence as a species. Yet it is also rich in anomalous behaviors. Here we reveal that liquid water is a novel - yet ubiquitous - source for quantum correlated photon pairs. The photon pairs are produced through Raman scattering, and the correlations arise from the shared quantum of a vibrational mode between the Stokes and anti-Stokes scattering events. We confirm the nonclassical nature of the produced photon pairs by showing that the cross-correlation and autocorrelations of the signals violate a Cauchy-Schwarz inequality by over five orders of magnitude. The unprecedented degree of violating the inequality in pure water, as well as the well-defined polarization properties of the photon pairs, points to its usefulness in quantum information. [Preview Abstract] |
Monday, March 13, 2017 1:51PM - 2:03PM |
B52.00014: Conditional Mutual Information and Quantum Steering Eneet Kaur, Xiaoting Wang, Mark Wilde Quantum steering has recently been formalized in the framework of a resource theory of steering, and several quantifiers have already been introduced. We propose the intrinsic steerability as an information-theoretic quantifier of steering that uses conditional mutual information to measure the deviation of a given assemblage from an assemblage having a local hidden-state model. We prove that this quantifier is a steering monotone (i.e., it is faithful, convex, and non-increasing under one-way local operations and classical communication). This suggests that the intrinsic steerability should find applications in protocols where steering is relevant. We then consider a restricted version of intrinsic steerability, which is a steering monotone under a restricted set of free operations. The restricted intrinsic steerability is additive with respect to tensor-product assemblages, and it is also monogamous. [Preview Abstract] |
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