arXiv subjects

Christopher Ferrie

Publications and source records attributed to Christopher Ferrie.

At least 37 records · Page 2Linked to original sources

arXiv2019

Experimental realization of self-guided quantum process tomography

Characterization of quantum processes is a preliminary step necessary in the development of quantum technology. The conventional method uses standard quantum process tomography, which requires $d^2$ input states and $d^4$ quantum measurements for a $d$-dimensional Hilbert space. These experimental requirements are compounded by the complexity of processing the collected data, which can take several orders of magnitude longer than the experiment itself. In this paper we propose an alternative self-guided algorithm for quantum process tomography, tuned for the task of finding an unknown unitary process. Our algorithm is a fully automated and adaptive process characterization technique. The advantages of our algorithm are: inherent robustness to both statistical and technical noise; requires less space and time since there is no post-processing of the data; requires only a single input state and measurement; and, provides on-the-fly diagnostic information while the experiment is running. Numerical results show our algorithm achieves the same $1/n$ scaling as standard quantum process tomography when $n$ uses of the unknown process are used. We also present experimental results wherein the algorithm, and its advantages, are realized for the task of finding an element of $SU(2)$.

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arXiv2019

Efficient online quantum state estimation using a matrix-exponentiated gradient method

In this paper, we explore an efficient online algorithm for quantum state estimation based on a matrix-exponentiated gradient method previously used in the context of machine learning. The state update is governed by a learning rate that determines how much weight is given to the new measurement results obtained in each step. We show convergence of the running state estimate in probability to the true state for both noiseless and noisy measurements. We find that in the latter case the learning rate has to be chosen adaptively and decreasing to guarantee convergence beyond the noise threshold. As a practical alternative we then propose to use running averages of the measurement statistics and a constant learning rate to overcome the noise problem. The proposed algorithm is numerically compared with batch maximum-likelihood and least-squares estimators. The results show a superior performance of the new algorithm in terms of accuracy and runtime complexity.

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arXiv2019

Minimax quantum state estimation under Bregman divergence

We investigate minimax estimators for quantum state tomography under general Bregman divergences. First, generalizing the work of Komaki et al. $\href{http://dx.doi.org/10.3390/e19110618}{\textrm{[Entropy 19, 618 (2017)]}}$ for relative entropy, we find that given any estimator for a quantum state, there always exists a sequence of Bayes estimators that asymptotically perform at least as well as the given estimator, on any state. Second, we show that there always exists a sequence of priors for which the corresponding sequence of Bayes estimators is asymptotically minimax (i.e. it minimizes the worst-case risk). Third, by re-formulating Holevo's theorem for the covariant state estimation problem in terms of estimators, we find that any covariant measurement is, in fact, minimax (i.e. it minimizes the worst-case risk). Moreover, we find that a measurement is minimax if it is only covariant under a unitary 2-design. Lastly, in an attempt to understand the problem of finding minimax measurements for general state estimation, we study the qubit case in detail and find that every spherical 2-design is a minimax measurement.

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arXiv2018

Maximum likelihood quantum state tomography is inadmissible

Maximum likelihood estimation (MLE) is the most common approach to quantum state tomography. In this letter, we investigate whether it is also optimal in any sense. We show that MLE is an inadmissible estimator for most of the commonly used metrics of accuracy, i.e., some other estimator is more accurate for every true state. MLE is inadmissible for fidelity, mean squared error (squared Hilbert-Schmidt distance), and relative entropy. We prove that almost any estimator that can report both pure states and mixed states is inadmissible. This includes MLE, compressed sensing (nuclear-norm regularized) estimators, and constrained least squares. We provide simple examples to illustrate why reporting pure states is suboptimal even when the true state is itself pure, and why "hedging" away from pure states generically improves performance.

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arXiv2017

Bayesian Quantum Noise Spectroscopy

As commonly understood, the noise spectroscopy problem---characterizing the statistical properties of a noise process affecting a quantum system by measuring its response---is ill-posed. Ad-hoc solutions assume implicit structure which is often never determined. Thus it is unclear when the method will succeed or whether one should trust the solution obtained. Here we propose to treat the problem from the point of view of statistical estimation theory. We develop a Bayesian solution to the problem which allows one to easily incorporate assumptions which render the problem solvable. We compare several numerical techniques for noise spectroscopy and find the Bayesian approach to be superior in many respects.

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arXiv2017

Explaining quantum correlations through evolution of causal models

We propose a framework for the systematic and quantitative generalization of Bell's theorem using causal networks. We first consider the multi-objective optimization problem of matching observed data while minimizing the causal effect of nonlocal variables and prove an inequality for the optimal region that both strengthens and generalizes Bell's theorem. To solve the optimization problem (rather than simply bound it), we develop a novel genetic algorithm treating as individuals causal networks. By applying our algorithm to a photonic Bell experiment, we demonstrate the trade-off between the quantitative relaxation of one or more local causality assumptions and the ability of data to match quantum correlations.

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arXiv2017

QInfer: Statistical inference software for quantum applications

Characterizing quantum systems through experimental data is critical to applications as diverse as metrology and quantum computing. Analyzing this experimental data in a robust and reproducible manner is made challenging, however, by the lack of readily-available software for performing principled statistical analysis. We improve the robustness and reproducibility of characterization by introducing an open-source library, QInfer, to address this need. Our library makes it easy to analyze data from tomography, randomized benchmarking, and Hamiltonian learning experiments either in post-processing, or online as data is acquired. QInfer also provides functionality for predicting the performance of proposed experimental protocols from simulated runs. By delivering easy-to-use characterization tools based on principled statistical analysis, QInfer helps address many outstanding challenges facing quantum technology.

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arXiv2017

Logical Randomized Benchmarking

Extrapolating physical error rates to logical error rates requires many assumptions and thus can radically under- or overestimate the performance of an error correction implementation. We introduce logical randomized benchmarking, a characterization procedure that directly assesses the performance of a quantum error correction implementation at the logical level, and is motivated by a reduction to the well-studied case of physical randomized benchmarking. We show that our method reliably reports logical performance and can estimate the average probability of correctable and uncorrectable errors for a given code and physical channel.

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arXiv2016

Bayes estimator for multinomial parameters and Bhattacharyya distances

We derive the Bayes estimator for the parameters of a multinomial distribution under two loss functions ($1-B$ and $1-B^2$) that are based on the Bhattacharyya coefficient $B(\vec{p},\vec{q}) = \sum{\sqrt{p_kq_k}}$. We formulate a non-commutative generalization relevant to quantum probability theory as an open problem. As an example application, we use our solution to find minimax estimators for a binomial parameter under Bhattacharyya loss ($1-B^2$).

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arXiv2016

Practical adaptive quantum tomography

We introduce a fast and accurate heuristic for adaptive tomography that addresses many of the limitations of prior methods. Previous approaches were either too computationally intensive or tailored to handle special cases such as single qubits or pure states. By contrast, our approach combines the efficiency of online optimization with generally applicable and well-motivated data-processing techniques. We numerically demonstrate these advantages in several scenarios including mixed states, higher-dimensional systems, and restricted measurements.

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arXiv2016

Fisher-symmetric informationally complete measurements for pure states

We introduce a new kind of quantum measurement that is defined to be symmetric in the sense of uniform Fisher information across a set of parameters that injectively represent pure quantum states in the neighborhood of a fiducial pure state. The measurement is locally informationally complete---i.e., it uniquely determines these parameters, as opposed to distinguishing two arbitrary quantum states---and it is maximal in the sense of a multi-parameter quantum Cramer-Rao bound. For a $d$-dimensional quantum system, requiring only local informational completeness allows us to reduce the number of outcomes of the measurement from a minimum close to but below $4d-3$, for the usual notion of global pure-state informational completeness, to $2d-1$.

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arXiv2016

Experimental Demonstration of Self-Guided Quantum Tomography

Robust, accurate and efficient quantum tomography is key for future quantum technologies. Traditional methods are impractical for even medium sized systems and are not robust against noise and errors. Here we report on an experimental demonstration of self-guided quantum tomography; an autonomous, fast, robust and precise technique for measuring quantum states with significantly less computational resources than standard techniques. The quantum state is iteratively learned by treating tomography as a projection measurement optimization problem. We experimentally demonstrate robustness against both statistical noise and experimental errors on both single qubit and entangled two-qubit states. Our demonstration provides a method of full quantum state characterization in current and near-future experiments where standard techniques are unfeasible.

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arXiv2015

Near-optimal quantum tomography: estimators and bounds

We give bounds on the average fidelity achievable by any quantum state estimator, which is arguably the most prominently used figure of merit in quantum state tomography. Moreover, these bounds can be computed online---that is, while the experiment is running. We show numerically that these bounds are quite tight for relevant distributions of density matrices. We also show that the Bayesian mean estimator is ideal in the sense of performing close to the bound without requiring optimization. Our results hold for all finite dimensional quantum systems.

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arXiv2015

Why protective measurement does not establish the reality of the quantum state

"Protective measurement" refers to two related schemes for finding the expectation value of an observable without disturbing the state of a quantum system, given a single copy of the system that is subject to a "protecting" operation. There have been several claims that these schemes support interpreting the quantum state as an objective property of a single quantum system. Here we provide three counter-arguments, each of which we present in two versions tailored to the two different schemes. Our first argument shows that the same resources used in protective measurement can be used to reconstruct the quantum state in a different way via process tomography. Our second argument is based on exact analyses of special cases of protective measurement, and our final argument is to construct explicit "$ψ$-epistemic" toy models for protective measurement, which strongly suggest that protective measurement does not imply the reality of the quantum state. The common theme of the three arguments is that almost all of the information comes from the "protection" operation rather than the quantum state of the system, and hence the schemes have no implications for the reality of the quantum state.

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arXiv2015

Weak-value amplification: state of play

Weak values arise in quantum theory when the result of a weak measurement is conditioned on a subsequent strong measurement. The majority of the trials are discarded, leaving only very few successful events. Intriguingly those can display a substantial signal amplification. This raises the question of whether weak values carry potential to improve the performance of quantum sensors, and indeed a number of impressive experimental results suggested this may be the case. By contrast, recent theoretical studies have found the opposite: using weak-values to obtain an amplification generally worsens metrological performance. This survey summarises the implications of those studies, which call for a reappraisal of weak values' utility and for further work to reconcile theory and experiment.

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arXiv2015

Cost of postselection in decision theory

Postselection is the process of discarding outcomes from statistical trials that are not the event one desires. Postselection can be useful in many applications where the cost of getting the wrong event is implicitly high. However, unless this cost is specified exactly, one might conclude that discarding all data is optimal. Here we analyze the optimal decision rules and quantum measurements in a decision theoretic setting where a prespecified cost is assigned to discarding data. Our scheme interpolates between unambiguous state discrimination (when the cost of postselection is zero) and a minimum error measurement (when the cost of postselection is maximal). We also relate our formulation to previous approaches which focus on minimizing the probability of indecision.

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arXiv2015

Robust and efficient in situ quantum control

Precision control of quantum systems is the driving force for both quantum technology and the probing of physics at the quantum and nano-scale. We propose an implementation independent method for in situ quantum control that leverages recent advances in the direct estimation of quantum gate fidelity. Our algorithm takes account of the stochasticity of the problem and is suitable for closed-loop control and requires only a constant number of fidelity estimating experiments per iteration independent of the dimension of the control space. It is efficient and robust to both statistical and technical noise.

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arXiv2015

On the novelty, efficacy, and significance of weak measurements for quantum tomography

The use of weak measurements for performing quantum tomography is enjoying increased attention due to several recent proposals. The advertised merits of using weak measurements in this context are varied, but are generally represented by novelty, increased efficacy, and foundational significance. We critically evaluate two proposals that make such claims and find that weak measurements are not an essential ingredient for most of their advertised features.

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