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Register a new userQuantum-enhanced algorithms for classical target detection in complex environments
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Authors
Peter B. Weichman
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Quantum computational approaches to some classic target identification and localization algorithms, especially for radar images, are investigated, and are found to raise a number of quantum statistics and quantum measurement issues with much broader applicability. Such algorithms are computationally intensive, involving coherent processing of large sensor data sets in order to extract a small number of low profile targets from a cluttered background. Target enhancement is accomplished through accurate statistical characterization of the environment, followed by optimal identification of statistical outliers. The key result of the work is that the environmental covariance matrix estimation and manipulation at the heart of the statistical analysis actually enables a highly efficient quantum implementation. The algorithm is inspired by recent approaches to quantum machine learning, but requires significant extensions, including previously overlooked `quantum analog--digital conversion steps (which are found to substantially increase the required number of qubits), `quantum statistical generalization of the classic phase estimation and Grover search algorithms, and careful consideration of projected measurement operations. Application regimes where quantum efficiencies could enable significant overall algorithm speedup are identified. Key possible bottlenecks, such as data loading and conversion, are identified as well.
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We give efficient quantum algorithms to estimate the partition function of (i) the six vertex model on a two-dimensional (2D) square lattice, (ii) the Ising model with magnetic fields on a planar graph, (iii) the Potts model on a quasi 2D square lattice, and (iv) the Z_2 lattice gauge theory on a three-dimensional square lattice. Moreover, we prove that these problems are BQP-complete, that is, that estimating these partition functions is as hard as simulating arbitrary quantum computation. The results are proven for a complex parameter regime of the models. The proofs are based on a mapping relating partition functions to quantum circuits introduced in [Van den Nest et al., Phys. Rev. A 80, 052334 (2009)] and extended here.
In this work we investigate quantum-enhanced target detection in the presence of large background noise using multidimensional quantum correlations between photon pairs generated through spontaneous parametric down-conversion. Until now similar experiments have only utilized one of the photon pairs many degrees of freedom such as temporal correlations and photon number correlations. Here, we utilized both temporal and spectral correlations of the photon pairs and achieved over an order of magnitude reduction to the background noise and in turn significant reduction to data acquisition time when compared to utilizing only temporal modes. We believe this work represents an important step in realizing a practical, real-time quantum-enhanced target detection system. The demonstrated technique will also be of importance in many other quantum sensing applications and quantum communications.
We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and study their mutual relationships. Additionally, we prove that quantum query complexity of distinguishing two probability distributions is given by their inverse Hellinger distance, which gives a quadratic improvement over classical query complexity for any pair of distributions. The results are obtained by using the adversary method for state-generating input oracles and for distinguishing probability distributions on input strings.
We consider the task of estimating the expectation value of an $n$-qubit tensor product observable $O_1otimes O_2otimes cdots otimes O_n$ in the output state of a shallow quantum circuit. This task is a cornerstone of variational quantum algorithms for optimization, machine learning, and the simulation of quantum many-body systems. Here we study its computational complexity for constant-depth quantum circuits and three types of single-qubit observables $O_j$ which are (a) close to the identity, (b) positive semidefinite, (c) arbitrary. It is shown that the mean value problem admits a classical approximation algorithm with runtime scaling as $mathrm{poly}(n)$ and $2^{tilde{O}(sqrt{n})}$ in cases (a,b) respectively. In case (c) we give a linear-time algorithm for geometrically local circuits on a two-dimensional grid. The mean value is approximated with a small relative error in case (a), while in cases (b,c) we satisfy a less demanding additive error bound. The algorithms are based on (respectively) Barvinoks polynomial interpolation method, a polynomial approximation for the OR function arising from quantum query complexity, and a Monte Carlo method combined with Matrix Product State techniques. We also prove a technical lemma characterizing a zero-free region for certain polynomials associated with a quantum circuit, which may be of independent interest.
As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to execute quantum algorithms was only a theoretical possibility, recent advances in hardware mean that quantum computing devices now exist that can carry out quantum computation on a limited scale. Thus it is now a real possibility, and of central importance at this time, to assess the potential impact of quantum computers on real problems of interest. One of the earliest and most compelling applications for quantum computers is Feynmans idea of simulating quantum systems with many degrees of freedom. Such systems are found across chemistry, physics, and materials science. The particular way in which quantum computing extends classical computing means that one cannot expect arbitrary simulations to be sped up by a quantum computer, thus one must carefully identify areas where quantum advantage may be achieved. In this review, we briefly describe central problems in chemistry and materials science, in areas of electronic structure, quantum statistical mechanics, and quantum dynamics, that are of potential interest for solution on a quantum computer. We then take a detailed snapshot of current progress in quantum algorithms for ground-state, dynamics, and thermal state simulation, and analyze their strengths and weaknesses for future developments.
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