We derive a bound on the ability of a linear-optical network to estimate a linear combination of independent phase shifts by using an arbitrary nonclassical but unentangled input state, thereby elucidating the quantum resources required to obtain the Heisenberg limit with a multiport 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 concentrated in a small number of input modes, and we present an explicit scheme for doing so.

Studies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared with unentangled states. In this paper, we quantify the metrological advantage of entanglement in a setting where the measured quantity is a linear function of parameters individually coupled to each qubit. We first generalize the Heisenberg limit to the measurement of nonlocal observables in a quantum network, deriving a bound based on the multiparameter quantum Fisher information. We then propose measurement protocols that can make use of Greenberger–Horne–Zeilinger (GHZ) states or spin-squeezed states and show that in the case of GHZ states the protocol is optimal, i.e., it saturates our bound. We also identify nanoscale magnetic resonance imaging as a promising setting for this technology.

The 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/r α . 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., FOCS'18. 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).

In 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 L in d dimensions using long-range interactions with strength bounded by 1/r α . If α < d, the state transfer time is asymptotically independent of L; if α = d, the time scales logarithmically with the distance L; if d < α < d + 1, transfer occurs in time proportional to L α−d ; and if α ≥ d + 1, it occurs in time proportional to L. We then use this protocol to upper bound the time required to create a state specified by a MERA (multiscale entanglement renormalization ansatz) tensor network and show that if the linear size of the MERA state is L, then it can be created in time that scales with L identically to state transfer up to logarithmic corrections. This protocol realizes an exponential speed-up in cases of α = d, which could be useful in creating large entangled states for dipole-dipole (1/r 3 ) interactions in three dimensions.Entanglement generation in a quantum system is limited, even in a non-relativistic setting, by the available interactions. In a lattice system with short-range interactions, Lieb and Robinson showed that there exists a linear light cone defined by a speed proportional to both the interaction range and strength [1]. Suppose two operators A and B are supported on single sites separated by a distance r. Then the Lieb-Robinson bound states that, after time t, [A(t), B] ≤ c A B e vt−r where c is a constant, v is another constant known as the Lieb-Robinson velocity, and · represents the operator norm. If a system initially in a product state begins evolving under a short-range Hamiltonian, correlations decrease exponentially outside of the causal cone defined by r = vt [2-4]. However, in physical systems including polar molecules [5][6][7], Rydberg atoms [8,9], or trapped ions [10,11], the interactions fall off with distance r as a power law 1/r α . For these interactions, generalizations of the Lieb-Robinson bound are known, but they may not be tight [12][13][14]. In addition, for sufficiently longranged interactions the causal region may even encompass infinite space at finite time, signaling a breakdown of emergent locality [15][16][17][18].These bounds on entanglement have direct implications for quantum information processing. The LiebRobinson bound, even if time dependence is allowed [19,20], limits the speed at which operations can be performed or states created using local Hamiltonians, including states with important applications in quantum metrology and communication [21][22][23][24][25]. In this paper, we consider the task of using long-range interactions to speed up certain quantum information processes, such as quantum state transfer, GHZ (Greenberger-Horne-Zeilinger) state preparati...

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.Entanglement is a valuable resource for quantum technology. In metrology, entangled probes are capable of more accurate measurements than unentangled probes [1][2][3][4][5][6]. In addition to using entangled probes to enhance the measurement of a single parameter, using entanglement to estimate many parameters at once, or a function of those parameters, has recently been an area of interest due to potential applications in tasks such as nanoscale nuclear magnetic resonance imaging [7][8][9][10][11][12][13][14][15].In this Letter, we are interested in generalizing the work of Ref. [15], which demonstrated a lower bound on the variance of an estimator of a linear combination of d parameters coupled to d qubits. We will generalize this approach to measuring an arbitrary real-valued, analytic function of d parameters and show that entanglement can reduce the variance of such an estimate by a factor of O(d). Finally, we present a protocol which achieves optimal variance asymptotically in the limit of long measurement time. In addition, when the parameters are coupled to d interferometers or to a combination of interferometers and qubits, we propose an analogous Heisenbergscaling protocol to improve measurement noise. However, in this case, we lack a proof of optimality. We also can use the protocol presented in Ref.[16] to couple the parameters to continuous variables detected by homodyne measurements.We will also examine the application of such a protocol to field interpolation. Suppose sensors are placed at d spatially separated locations, but we wish to know the field at a point with no sensor. We may pick a reasonable ansatz for the field with no more than d parameters, use our d measurements to fix the degrees of freedom of that ansatz, and compute the field at our desired point. Because the field of interest is a function of the field at d other locations, our protocol offers reduced noise over FIG. 1. An illustration of a quantum sensor network of spatially separated nodes. At each node, there is an unknown parameter θi coupled to a qubit, which accumulates phase proportional to θi.performing the same procedure without using entanglement.Setup.-In this Letter, bold is used to indicate vectors, hats (as inĤ) indicate operators, and variables with a tilde (such asf ) are estimators of the corresponding quantity with no tilde (such as f ). The notation E Y [X] means the expected value of X over all possible Y . If we merely write E[X], then w...

We propose a protocol for sympathetically cooling neutral atoms without destroying the quantum information stored in their internal states. This is achieved by designing state-insensitive Rydberg interactions between the data-carrying atoms and cold auxiliary atoms. The resulting interactions give rise to an effective phonon coupling, which leads to the transfer of heat from the data atoms to the auxiliary atoms, where the latter can be cooled by conventional methods. This can be used to extend the lifetime of quantum storage based on neutral atoms and can have applications for long quantum computations. The protocol can also be modified to realize state-insensitive interactions between the data and the auxiliary atoms but tunable and non-trivial interactions among the data atoms, allowing one to simultaneously cool and simulate a quantum spin-model. arXiv:1907.11156v2 [quant-ph]

Quantum computing is a new field of computing that relies on the laws of quantum mechanics to perform types of information processing that are not possible on traditional ("classical") computers. As a result, quantum computers are capable of using problem-solving approaches which are not available to classical computers. Thus far, most research in quantum computing has taken place in physics and theoretical computer science, leaving a disconnect between these researchers and practical problems/applications. There is a need to identify good near-term problems to demonstrate quantum computing's problem-solving potential. One possible area of contribution is in renewable energy. Adoption and scale-up of renewable resources in the next several decades will introduce many new challenges to the electrical grid due to the need to control many more distributed resources and to account for the variability of weather-dependent generation flows. We identify a few places where quantum computing is most likely to contribute to renewable energy problems: in simulation, in scheduling and dispatch, and in reliability analyses. The problems have the common theme that there are potential future issues concerning scalability of current approaches that quantum computing may address. We then recommend potentially fruitful areas of crossover research to advance applications of quantum computing and renewable energy. Keywords Quantum computing • Renewable energyThis article is part of the topical collection "Quantum Computing: Circuits Systems Automation and Applications" guest-edited by Himanshu Thapliyal and Travis S. Humble.

The 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.