We generalize past work on quantum sensor networks to show that, for d input parameters, entanglement can yield a factor O(d) improvement in mean squared error when estimating an analytic function of these parameters. We show that the protocol is optimal for qubit sensors, and conjecture an optimal protocol for photons passing through interferometers. Our protocol is also applicable to continuous variable measurements, such as one quadrature of a field operator. We outline a few potential applications, including calibration of laser operations in trapped ion quantum computing.

%8 01/25/2019 %G eng %U https://arxiv.org/abs/1901.09042 %0 Journal Article %J Phys. Rev. X 9, 031006 %D 2019 %T Locality and digital quantum simulation of power-law interactions %A Minh Cong Tran %A Andrew Y. Guo %A Yuan Su %A James R. Garrison %A Zachary Eldredge %A Michael Foss-Feig %A Andrew M. Childs %A Alexey V. Gorshkov %XThe propagation of information in non-relativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance r as a power law, 1/rα. The bound implies an effective light cone tighter than all previous bounds. Our approach is based on a technique for approximating the time evolution of a system, which was first introduced as part of a quantum simulation algorithm by Haah et al. [arXiv:1801.03922]. To bound the error of the approximation, we use a known Lieb-Robinson bound that is weaker than the bound we establish. This result brings the analysis full circle, suggesting a deep connection between Lieb-Robinson bounds and digital quantum simulation. In addition to the new Lieb-Robinson bound, our analysis also gives an error bound for the Haah et al. quantum simulation algorithm when used to simulate power-law decaying interactions. In particular, we show that the gate count of the algorithm scales with the system size better than existing algorithms when α>3D (where D is the number of dimensions).

%B Phys. Rev. X 9, 031006 %V 9 %8 07/10/2019 %G eng %U https://arxiv.org/abs/1808.05225 %N 031006 %R https://doi.org/10.1103/PhysRevX.9.031006 %0 Journal Article %J Phys. Rev. Lett %D 2019 %T Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator %A Su-Kuan Chu %A Guanyu Zhu %A James R. Garrison %A Zachary Eldredge %A Ana Valdés Curiel %A Przemyslaw Bienias %A I. B. Spielman %A Alexey V. Gorshkov %XThe multi-scale entanglement renormalization ansatz (MERA) postulates the existence of quantum circuits that renormalize entanglement in real space at different length scales. Chern insulators, however, cannot have scale-invariant discrete MERA circuits with finite bond dimension. In this Letter, we show that the continuous MERA (cMERA), a modified version of MERA adapted for field theories, possesses a fixed point wavefunction with nonzero Chern number. Additionally, it is well known that reversed MERA circuits can be used to prepare quantum states efficiently in time that scales logarithmically with the size of the system. However, state preparation via MERA typically requires the advent of a full-fledged universal quantum computer. In this Letter, we demonstrate that our cMERA circuit can potentially be realized in existing analog quantum computers, i.e., an ultracold atomic Fermi gas in an optical lattice with light-induced spin-orbit coupling.

%B Phys. Rev. Lett %V 122 %8 03/27/2019 %G eng %U https://arxiv.org/abs/1807.11486 %N 120502 %R https://doi.org/10.1103/PhysRevLett.122.120502 %0 Journal Article %D 2018 %T Distributed Quantum Metrology and the Entangling Power of Linear Networks %A Wenchao Ge %A Kurt Jacobs %A Zachary Eldredge %A Alexey V. Gorshkov %A Michael Foss-Feig %XWe derive a bound on the ability of a linear optical network to estimate a linear combination of independent phase shifts by using an arbitrary non-classical but unentangled input state, thereby elucidating the quantum resources required to obtain the Heisenberg limit with a multi-port interferometer. Our bound reveals that while linear networks can generate highly entangled states, they cannot effectively combine quantum resources that are well distributed across multiple modes for the purposes of metrology: in this sense linear networks endowed with well-distributed quantum resources behave classically. Conversely, our bound shows that linear networks can achieve the Heisenberg limit for distributed metrology when the input photons are hoarded in a small number of input modes, and we present an explicit scheme for doing so. Our results also have implications for measures of non-classicality.

%8 2018/07/25 %G eng %U https://arxiv.org/abs/1707.06655 %R https://doi.org/10.1103/PhysRevLett.121.043604 %0 Journal Article %J Phys. Rev. Lett. 121, 043604 %D 2018 %T Distributed Quantum Metrology and the Entangling Power of Linear Networks %A Wenchao Ge %A Kurt Jacobs %A Zachary Eldredge %A Alexey V. Gorshkov %A Michael Foss-Feig %XWe derive a bound on the ability of a linear optical network to estimate a linear combination of independent phase shifts by using an arbitrary non-classical but unentangled input state, thereby elucidating the quantum resources required to obtain the Heisenberg limit with a multi-port interferometer. Our bound reveals that while linear networks can generate highly entangled states, they cannot effectively combine quantum resources that are well distributed across multiple modes for the purposes of metrology: in this sense linear networks endowed with well-distributed quantum resources behave classically. Conversely, our bound shows that linear networks can achieve the Heisenberg limit for distributed metrology when the input photons are hoarded in a small number of input modes, and we present an explicit scheme for doing so. Our results also have implications for measures of non-classicality.

%B Phys. Rev. Lett. 121, 043604 %8 2018/07/25 %G eng %U https://arxiv.org/abs/1707.06655 %R https://doi.org/10.1103/PhysRevLett.121.043604 %0 Journal Article %D 2018 %T Optimal and Secure Measurement Protocols for Quantum Sensor Networks %A Zachary Eldredge %A Michael Foss-Feig %A Steven L. Rolston %A Alexey V. Gorshkov %XStudies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared to product states. In this paper, we quantify the metrological advantage of entanglement in a setting where the quantity to be measured is a linear function of parameters coupled to each qubit individually. We first generalize the Heisenberg limit to the measurement of non-local observables in a quantum network, deriving a bound based on the multi-parameter quantum Fisher information. We then propose a protocol that can make use of GHZ states or spin-squeezed states, and show that in the case of GHZ states the procedure is optimal, i.e., it saturates our bound.

%8 2018/03/23 %G eng %U http://arxiv.org/abs/1607.04646 %R https://doi.org/10.1103/PhysRevA.97.042337 %0 Journal Article %D 2018 %T Unitary Entanglement Construction in Hierarchical Networks %A Aniruddha Bapat %A Zachary Eldredge %A James R. Garrison %A Abhinav Desphande %A Frederic T. Chong %A Alexey V. Gorshkov %XThe construction of large-scale quantum computers will require modular architectures that allow physical resources to be localized in easy-to-manage packages. In this work, we examine the impact of different graph structures on the preparation of entangled states. We begin by explaining a formal framework, the hierarchical product, in which modular graphs can be easily constructed. This framework naturally leads us to suggest a class of graphs, which we dub hierarchies. We argue that such graphs have favorable properties for quantum information processing, such as a small diameter and small total edge weight, and use the concept of Pareto efficiency to identify promising quantum graph architectures. We present numerical and analytical results on the speed at which large entangled states can be created on nearest-neighbor grids and hierarchy graphs. We also present a scheme for performing circuit placement--the translation from circuit diagrams to machine qubits--on quantum systems whose connectivity is described by hierarchies.

%G eng %U https://arxiv.org/abs/1808.07876 %0 Journal Article %J Physical Review Letters %D 2017 %T Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions %A Zachary Eldredge %A Zhe-Xuan Gong %A Ali Hamed Moosavian %A Michael Foss-Feig %A Alexey V. Gorshkov %XIn short-range interacting systems, the speed at which entanglement can be established between two separated points is limited by a constant Lieb-Robinson velocity. Long-range interacting systems are capable of faster entanglement generation, but the degree of the speed-up possible is an open question. In this paper, we present a protocol capable of transferring a quantum state across a distance

Tightly confined modes of light, as in optical nanofibers or photonic crystal waveguides, can lead to large optical coupling in atomic systems, which mediates long-range interactions between atoms. These one-dimensional systems can naturally possess couplings that are asymmetric between modes propagating in different directions. Strong long-range interaction among atoms via these modes can drive them to a self-organized periodic distribution. In this paper, we examine the self-organizing behavior of atoms in one dimension coupled to a chiral reservoir. We determine the solution to the equations of motion in different parameter regimes, relative to both the detuning of the pump laser that initializes the atomic dipole-dipole interactions and the degree of reservoir chirality. In addition, we calculate possible experimental signatures such as reflectivity from self-organized atoms and motional sidebands.

%B Physical Review A %V 94 %P 053855 %8 2016/11/29 %G eng %U http://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.053855 %N 5 %R 10.1103/PhysRevA.94.053855