@article {3408, title = {A general approach to backaction-evading receivers with magnetomechanical and electromechanical sensors}, year = {2023}, month = {11/16/2023}, abstract = {

Today\&$\#$39;s mechanical sensors are capable of detecting extremely weak perturbations while operating near the standard quantum limit. However, further improvements can be made in both sensitivity and bandwidth when we reduce the noise originating from the process of measurement itself -- the quantum-mechanical backaction of measurement -- and go below this \&$\#$39;standard\&$\#$39; limit, possibly approaching the Heisenberg limit. One of the ways to eliminate this noise is by measuring a quantum nondemolition variable such as the momentum in a free-particle system. Here, we propose and characterize theoretical models for direct velocity measurement that utilize traditional electric and magnetic transducer designs to generate a signal while enabling this backaction evasion. We consider the general readout of this signal via electric or magnetic field sensing by creating toy models analogous to the standard optomechanical position-sensing problem, thereby facilitating the assessment of measurement-added noise. Using simple models that characterize a wide range of transducers, we find that the choice of readout scheme -- voltage or current -- for each mechanical detector configuration implies access to either the position or velocity of the mechanical sub-system. This in turn suggests a path forward for key fundamental physics experiments such as the direct detection of dark matter particles.

}, url = {https://arxiv.org/abs/2311.09587}, author = {Brittany Richman and Sohitri Ghosh and Daniel Carney and Gerard Higgins and Peter Shawhan and C. J. Lobb and Jacob M. Taylor} } @article {3419, title = {General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory}, journal = {Quantum}, volume = {7}, year = {2023}, month = {12/14/2023}, pages = {1213}, abstract = {

With a focus on universal quantum computing for quantum simulation, and through the example of lattice gauge theories, we introduce rather general quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple (bosonic and fermionic) quantum numbers with non-trivial functional coefficients. In particular, we analyze diagonalization of Hamiltonian terms using a singular-value decomposition technique, and discuss how the achieved diagonal unitaries in the digitized time-evolution operator can be implemented. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions, for which a complete quantum-resource analysis within different computational models is presented. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories. The example chosen further demonstrates the importance of adopting efficient theoretical formulations: it is shown that an explicitly gauge-invariant formulation using loop, string, and hadron degrees of freedom simplifies the algorithms and lowers the cost compared with the standard formulations based on angular-momentum as well as the Schwinger-boson degrees of freedom. The loop-string-hadron formulation further retains the non-Abelian gauge symmetry despite the inexactness of the digitized simulation, without the need for costly controlled operations. Such theoretical and algorithmic considerations are likely to be essential in quantumly simulating other complex theories of relevance to nature.

}, issn = {2521-327X}, doi = {10.22331/q-2023-12-20-1213}, url = {https://arxiv.org/abs/2212.14030}, author = {Zohreh Davoudi and Shaw, Alexander F. and Stryker, Jesse R.} } @article {3428, title = {Generalized Hybrid Search and Applications to Blockchain and Hash Function Security}, year = {2023}, month = {11/7/2023}, abstract = {

In this work we first examine the hardness of solving various search problems by hybrid quantum-classical strategies, namely, by algorithms that have both quantum and classical capabilities. We then construct a hybrid quantum-classical search algorithm and analyze its success probability. Regarding the former, for search problems that are allowed to have multiple solutions and in which the input is sampled according to arbitrary distributions we establish their hybrid quantum-classical query complexities -- i.e., given a fixed number of classical and quantum queries, determine what is the probability of solving the search task. At a technical level, our results generalize the framework for hybrid quantum-classical search algorithms proposed by Rosmanis. Namely, for an arbitrary distribution D on Boolean functions, the probability an algorithm equipped with τc classical and τq quantum queries succeeds in finding a preimage of 1 for a function sampled from D is at most νD\⋅(2τc\−\−\√+2τq+1)2, where νD captures the average (over D) fraction of preimages of 1. As applications of our hardness results, we first revisit and generalize the security of the Bitcoin protocol called the Bitcoin backbone, to a setting where the adversary has both quantum and classical capabilities, presenting a new hybrid honest majority condition necessary for the protocol to properly operate. Secondly, we examine the generic security of hash functions against hybrid adversaries. Regarding our second contribution, we design a hybrid algorithm which first spends all of its classical queries and in the second stage runs a {\textquoteleft}{\textquoteleft}modified Grover\&$\#$39;\&$\#$39; where the initial state depends on the distribution D. We show how to analyze its success probability for arbitrary target distributions and, importantly, its optimality for the uniform and the Bernoulli distribution cases.

}, url = {arXiv:2311.03723}, author = {Alexandru Cojocaru and Juan Garay and Fang Song} } @article {3179, title = {Group coset monogamy games and an application to device-independent continuous-variable QKD}, year = {2022}, month = {12/7/2022}, abstract = {

We develop an extension of a recently introduced subspace coset state monogamy-of-entanglement game [Coladangelo, Liu, Liu, and Zhandry; Crypto\&$\#$39;21] to general group coset states, which are uniform superpositions over elements of a subgroup to which has been applied a group-theoretic generalization of the quantum one-time pad. We give a general bound on the winning probability of a monogamy game constructed from subgroup coset states that applies to a wide range of finite and infinite groups. To study the infinite-group case, we use and further develop a measure-theoretic formalism that allows us to express continuous-variable measurements as operator-valued generalizations of probability measures.
We apply the monogamy game bound to various physically relevant groups, yielding realizations of the game in continuous-variable modes as well as in rotational states of a polyatomic molecule. We obtain explicit strong bounds in the case of specific group-space and subgroup combinations. As an application, we provide the first proof of one sided-device independent security of a squeezed-state continuous-variable quantum key distribution protocol against general coherent attacks.

}, keywords = {Cryptography and Security (cs.CR), FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2212.03935}, url = {https://arxiv.org/abs/2212.03935}, author = {Culf, Eric and Vidick, Thomas and Victor V. Albert} } @article {2819, title = {Garc{\'\i}a-Pintos, Hamma, and del Campo Reply}, journal = {Phys. Rev. Lett.}, volume = {127}, year = {2021}, month = {7/9/2021}, pages = {028902}, abstract = {

We acknowledge that a derivation reported in Phys. Rev. Lett. 125, 040601 (2020) is incorrect as pointed out by Cusumano and Rudnicki. We respond by giving a correct proof of the claim \“fluctuations in the free energy operator upper bound the charging power of a quantum battery\” that we made in the Letter.

}, doi = {10.1103/PhysRevLett.127.028902}, author = {Luis Pedro Garc{\'\i}a-Pintos and Alioscia Hamma and Adolfo del Campo} } @article {2936, title = {Generalization in quantum machine learning from few training data}, year = {2021}, month = {11/9/2021}, abstract = {

Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide a comprehensive study of generalization performance in QML after training on a limited number N of training data points. We show that the generalization error of a quantum machine learning model with T trainable gates scales at worst as T/N\−\−\−\−\√. When only K<}, url = {https://arxiv.org/abs/2111.05292}, author = {Matthias C. Caro and Hsin-Yuan Huang and M. Cerezo and Kunal Sharma and Andrew Sornborger and Lukasz Cincio and Patrick J. Coles} } @article {2375, title = {Gravitational Direct Detection of Dark Matter}, journal = {Phys. Rev. D}, volume = {102}, year = {2020}, month = {10/13/2020}, type = {FERMILAB-PUB-19-082-AE-T}, abstract = {

The only coupling dark matter is guaranteed to have with the standard model is through gravity. Here we propose a concept for direct dark matter detection using only this gravitational coupling, enabling a new regime of detection. Leveraging dramatic advances in the ability to create, maintain, and probe quantum states of massive objects, we suggest that an array of quantum-limited impulse sensors may be capable of detecting the correlated gravitational force created by a passing dark matter particle. We present two concrete realizations of this scheme, using either mechanical resonators or freely-falling masses. With currently available technology, a meter-scale apparatus of this type could detect any dark matter candidate around the Planck mass or heavier.

}, doi = {https://doi.org/10.1103/PhysRevD.102.072003}, url = {https://arxiv.org/abs/1903.00492}, author = {Daniel Carney and Sohitri Ghosh and Gordan Krnjaic and J. M. Taylor} } @article {1995, title = {Graphical Methods in Device-Independent Quantum Cryptography}, journal = {Quantum}, volume = {3}, year = {2019}, month = {05/20/2019}, abstract = {

We introduce a framework for graphical security proofs in device-independent quantum cryptography using the methods of categorical quantum mechanics. We are optimistic that this approach will make some of the highly complex proofs in quantum cryptography more accessible, facilitate the discovery of new proofs, and enable automated proof verification. As an example of our framework, we reprove a recent result from device-independent quantum cryptography: any linear randomness expansion protocol can be converted into an unbounded randomness expansion protocol. We give a graphical exposition of a proof of this result and implement parts of it in the Globular proof assistant.

}, doi = {https://doi.org/10.22331/q-2019-05-27-146}, url = {https://arxiv.org/abs/1705.09213}, author = {Spencer Breiner and Carl Miller and Neil J. Ross} } @article {2369, title = {Ground-state energy estimation of the water molecule on a trapped ion quantum computer}, year = {2019}, month = {03/07/2019}, abstract = {

Quantum computing leverages the quantum resources of superposition and entanglement to efficiently solve computational problems considered intractable for classical computers. Examples include calculating molecular and nuclear structure, simulating strongly-interacting electron systems, and modeling aspects of material function. While substantial theoretical advances have been made in mapping these problems to quantum algorithms, there remains a large gap between the resource requirements for solving such problems and the capabilities of currently available quantum hardware. Bridging this gap will require a co-design approach, where the expression of algorithms is developed in conjunction with the hardware itself to optimize execution. Here, we describe a scalable co-design framework for solving chemistry problems on a trapped ion quantum computer, and apply it to compute the ground-state energy of the water molecule. The robust operation of the trapped ion quantum computer yields energy estimates with errors approaching the chemical accuracy, which is the target threshold necessary for predicting the rates of chemical reaction dynamics.

}, url = {https://arxiv.org/abs/1902.10171}, author = {Yunseong Nam and Jwo-Sy Chen and Neal C. Pisenti and Kenneth Wright and Conor Delaney and Dmitri Maslov and Kenneth R. Brown and Stewart Allen and Jason M. Amini and Joel Apisdorf and Kristin M. Beck and Aleksey Blinov and Vandiver Chaplin and Mika Chmielewski and Coleman Collins and Shantanu Debnath and Andrew M. Ducore and Kai M. Hudek and Matthew Keesan and Sarah M. Kreikemeier and Jonathan Mizrahi and Phil Solomon and Mike Williams and Jaime David Wong-Campos and Christopher Monroe and Jungsang Kim} } @article {2109, title = {Geometry of the quantum set of correlations}, journal = {Physical Review A}, volume = {97}, year = {2018}, month = {2018/02/07}, pages = {022104}, abstract = {

It is well known that correlations predicted by quantum mechanics cannot be explained by any classical (local-realistic) theory. The relative strength of quantum and classical correlations is usually studied in the context of Bell inequalities, but this tells us little about the geometry of the quantum set of correlations. In other words, we do not have good intuition about what the quantum set actually looks like. In this paper we study the geometry of the quantum set using standard tools from convex geometry. We find explicit examples of rather counter-intuitive features in the simplest non-trivial Bell scenario (two parties, two inputs and two outputs) and illustrate them using 2-dimensional slice plots. We also show that even more complex features appear in Bell scenarios with more inputs or more parties. Finally, we discuss the limitations that the geometry of the quantum set imposes on the task of self-testing.

}, doi = {10.1103/PhysRevA.97.022104}, url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.022104}, author = {Koon Tong Goh and Jedrzej Kaniewski and Elie Wolfe and Tam{\'a}s V{\'e}rtesi and Xingyao Wu and Yu Cai and Yeong-Cherng Liang and Valerio Scarani} } @article {1990, title = {Genuine N -partite entanglement without N -partite correlation functions}, journal = {Physical Review A}, volume = {95}, year = {2017}, month = {2017/06/26}, pages = {062331}, abstract = {

A genuinely\ N-partite entangled state may display vanishing\ N-partite correlations measured for arbitrary local observables. In such states the genuine entanglement is noticeable solely in correlations between subsets of particles. A straightforward way to obtain such states for odd\ N\ is to design an \“antistate\” in which all correlations between an odd number of observers are exactly opposite. Evenly mixing a state with its antistate then produces a mixed state with no\ N-partite correlations, with many of them genuinely multiparty entangled. Intriguingly, all known examples of \“entanglement without correlations\” involve an\ odd\ number of particles. Here we further develop the idea of antistates, thereby shedding light on the different properties of even and odd particle systems. We conjecture that there is no antistate to any pure even-N-party entangled state making the simple construction scheme unfeasible. However, as we prove by construction, higher-rank examples of entanglement without correlations for arbitrary even\ N\ indeed exist. These classes of states exhibit genuine entanglement and even violate an\ N-partite Bell inequality, clearly demonstrating the nonclassical features of these states as well as showing their applicability for quantum information processing.

}, doi = {doi.org/10.1103/PhysRevA.95.062331}, url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.062331}, author = {Minh C. Tran and Margherita Zuppardo and Anna de Rosier and Lukas Knips and Wieslaw Laskowski and Tomasz Paterek and Harald Weinfurter} } @article {1597, title = {Grover search and the no-signaling principle}, journal = {Physical Review Letters}, volume = {117}, year = {2016}, month = {2016/09/14}, pages = {120501}, abstract = {

From an information processing point of view, two of the key properties of quantum physics are the no-signaling principle and the Grover search lower bound. That is, despite admitting stronger-than-classical correlations, quantum mechanics does not imply superluminal signaling, and despite a form of exponential parallelism, quantum mechanics does not imply polynomial-time brute force solution of NP-complete problems. Here, we investigate the degree to which these two properties are connected. We examine four classes of deviations from quantum mechanics, for which we draw inspiration from the literature on the black hole information paradox: nonunitary dynamics, non-Born-rule measurement, cloning, and postselection. We find that each model admits superluminal signaling if and only if it admits a query complexity speedup over Grover\&$\#$39;s algorithm. Furthermore, we show that the physical resources required to send a superluminal signal scale polynomially with the resources needed to speed up Grover\&$\#$39;s algorithm. Hence, one can perform a physically reasonable experiment demonstrating superluminal signaling if and only if one can perform a reasonable experiment inducing a speedup over Grover\&$\#$39;s algorithm.

}, url = {http://arxiv.org/abs/1511.00657}, author = {Ning Bao and Adam Bouland and Stephen P. Jordan} } @article {grant2012galilean, title = {On Galilean connections and the first jet bundle}, journal = {Central European Journal of Mathematics}, volume = {10}, number = {5}, year = {2012}, month = {2012/10/01}, pages = {1889{\textendash}1895}, publisher = {Springer}, abstract = {We see how the first jet bundle of curves into affine space can be realized as a homogeneous space of the Galilean group. Cartan connections with this model are precisely the geometric structure of second-order ordinary differential equations under time-preserving transformations {\textemdash} sometimes called KCC-theory. With certain regularity conditions, we show that any such Cartan connection induces {\textquotedblleft}laboratory{\textquotedblright} coordinate systems, and the geodesic equations in this coordinates form a system of second-order ordinary differential equations. We then show the converse {\textemdash} the {\textquotedblleft}fundamental theorem{\textquotedblright} {\textemdash} that given such a coordinate system, and a system of second order ordinary differential equations, there exists regular Cartan connections yielding these, and such connections are completely determined by their torsion.}, author = {Grant, James DE and Brad Lackey} } @article {1792, title = {Gluon chain formation in presence of static charges}, journal = {Physical Review D}, volume = {86}, year = {2012}, month = {2012/12/10}, pages = {114015}, abstract = {We consider the origins of the gluon chain model. The model serves as a realization of the dynamics of the chromoelectric flux between static quark-antiquark sources. The derivation is based on the large-NC limit of the Coulomb gauge Hamiltonian in the presence of a background field introduced to model magnetic charge condensation inducing electric confinement.}, doi = {10.1103/PhysRevD.86.114015}, url = {http://link.aps.org/doi/10.1103/PhysRevD.86.114015}, author = {Aaron Ostrander and Santopinto, E. and Szczepaniak, A. P. and Vassallo, A.} } @article {1454, title = {Ground-State Spaces of Frustration-Free Hamiltonians}, journal = {Journal of Mathematical Physics}, volume = {53}, year = {2012}, month = {2012/01/01}, pages = {102201}, abstract = { We study the ground-state space properties for frustration-free Hamiltonians. We introduce a concept of {\textquoteleft}reduced spaces{\textquoteright} to characterize local structures of ground-state spaces. For a many-body system, we characterize mathematical structures for the set $\Theta_k$ of all the $k$-particle reduced spaces, which with a binary operation called join forms a semilattice that can be interpreted as an abstract convex structure. The smallest nonzero elements in $\Theta_k$, called atoms, are analogs of extreme points. We study the properties of atoms in $\Theta_k$ and discuss its relationship with ground states of $k$-local frustration-free Hamiltonians. For spin-1/2 systems, we show that all the atoms in $\Theta_2$ are unique ground states of some 2-local frustration-free Hamiltonians. Moreover, we show that the elements in $\Theta_k$ may not be the join of atoms, indicating a richer structure for $\Theta_k$ beyond the convex structure. Our study of $\Theta_k$ deepens the understanding of ground-state space properties for frustration-free Hamiltonians, from a new angle of reduced spaces. }, doi = {10.1063/1.4748527}, url = {http://arxiv.org/abs/1112.0762v1}, author = {Jianxin Chen and Zhengfeng Ji and David Kribs and Zhaohui Wei and Bei Zeng} } @article {1466, title = {Geometric-Phase-Effect Tunnel-Splitting Oscillations in Single-Molecule Magnets with Fourth-Order Anisotropy Induced by Orthorhombic Distortion }, journal = {EPL (Europhysics Letters)}, volume = {86}, year = {2009}, month = {2009/04/30}, pages = {27002}, abstract = { We analyze the interference between tunneling paths that occurs for a spin system with both fourth-order and second-order transverse anisotropy. Using an instanton approach, we find that as the strength of the second-order transverse anisotropy is increased, the tunnel splitting is modulated, with zeros occurring periodically. This effect results from the interference of four tunneling paths connecting easy-axis spin orientations and occurs in the absence of any magnetic field. }, doi = {10.1209/0295-5075/86/27002}, url = {http://arxiv.org/abs/0809.2289v2}, author = {Michael Foss-Feig and Jonathan R. Friedman} } @article {1421, title = {Gibbs States and the Consistency of Local Density Matrices}, year = {2006}, month = {2006/03/02}, abstract = { Suppose we have an n-qubit system, and we are given a collection of local density matrices rho_1,...,rho_m, where each rho_i describes some subset of the qubits. We say that rho_1,...,rho_m are "consistent" if there exists a global state sigma (on all n qubits) whose reduced density matrices match rho_1,...,rho_m. We prove the following result: if rho_1,...,rho_m are consistent with some state sigma > 0, then they are also consistent with a state sigma{\textquoteright} of the form sigma{\textquoteright} = (1/Z) exp(M_1+...+M_m), where each M_i is a Hermitian matrix acting on the same qubits as rho_i, and Z is a normalizing factor. (This is known as a Gibbs state.) Actually, we show a more general result, on the consistency of a set of expectation values ,...,, where the observables T_1,...,T_r need not commute. This result was previously proved by Jaynes (1957) in the context of the maximum-entropy principle; here we provide a somewhat different proof, using properties of the partition function. }, url = {http://arxiv.org/abs/quant-ph/0603012v1}, author = {Yi-Kai Liu} } @article {lackey2002gauss, title = {On the Gauss{\textendash}Bonnet Formula in Riemann{\textendash}Finsler Geometry}, journal = {Bulletin of the London Mathematical Society}, volume = {34}, number = {03}, year = {2002}, month = {2002/04/01}, pages = {329{\textendash}340}, publisher = {Cambridge Univ Press}, abstract = {Using Chern{\textquoteright}s method of transgression, the Euler class of a compact orientable Riemann{\textendash}Finsler space is represented by polynomials in the connection and curvature matrices of a torsion-free connection. When using the Chern connection (and hence the Christoffel{\textendash}Levi{\textendash}Civita connection in the Riemannian case), this result extends the Gauss{\textendash}Bonnet formula of Bao and Chern to Finsler spaces whose indicatrices need not have constant volume.}, author = {Brad Lackey} } @article {1266, title = {On Galilean connections and the first jet bundle}, year = {1999}, month = {1999/09/24}, abstract = { We express the first jet bundle of curves in Euclidean space as homogeneous spaces associated to a Galilean-type group. Certain Cartan connections on a manifold with values in the Lie algebra of the Galilean group are characterized as geometries associated to systems of second order ordinary differential equations. We show these Cartan connections admit a form of normal coordinates, and that in these normal coordinates the geodesic equations of the connection are second order ordinary differential equations. We then classify such connections by some of their torsions, extending a classical theorem of Chern involving the geometry associated to a system of second order differential equations. }, url = {http://arxiv.org/abs/math/9909148v1}, author = {James D. E. Grant and Brad Lackey} } @inbook {1776, title = {A geometric inequality and a Weitzenboeck formula for Finsler surfaces}, booktitle = {The Theory of Finslerian Laplacians and Applications}, year = {1998}, pages = {245{\textendash}275}, publisher = {Springer}, organization = {Springer}, author = {Bao, David and Lackey, Brad} }