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Page 6947 of Mathematical Reviews Vol. , Issue 95k [page]

1995 Mathematical Reviews  
Melkman (IL-BGUN; Be‘ér Sheva‘) 95k:68077 68Q25 Iwamoto, Chuzo (J-K YUS-C; Fukuoka); Toussaint, Godfried T. (3-MGL-C; Montreal, PQ) Finding Hamiltonian circuits in arrangements of Jordan curves is NP-complete  ...  It is shown that the Hamiltonian circuit (a circuit that passes through every vertex of the graph exactly once) prob-  ... 

Term Grouping and Travelling Salesperson for Digital Quantum Simulation [article]

Kaiwen Gui, Teague Tomesh, Pranav Gokhale, Yunong Shi, Frederic T. Chong, Margaret Martonosi, Martin Suchara
2021 arXiv   pre-print
Digital simulation of quantum dynamics by evaluating the time evolution of a Hamiltonian is the initially proposed application of quantum computing.  ...  The large number of quantum gates required for emulating the complete second quantization form of the Hamiltonian, however, makes such an approach unsuitable for near-term devices with limited gate fidelities  ...  The exact solution of TSP is is NP-hard and we cannot find a solution in polynomial time (unless P = NP) [19] .  ... 
arXiv:2001.05983v3 fatcat:fjbeop7obvazzjyths33w7t364

SFCDecomp: Multicriteria Optimized Tool Path Planning in 3D Printing using Space-Filling Curve Based Domain Decomposition [article]

Prashant Gupta, Yiran Guo, Narasimha Boddeti, Bala Krishnamoorthy
2021 arXiv   pre-print
We first show that the minimum turn cost 3d printing problem is NP-hard, even when the region is a simple polygon.  ...  Strength testing of a tensile test specimen printed with tool paths that maximize or minimize adjacent layer edge overlaps reveal significant differences in tensile strength between the two classes of  ...  [17] showed that the Hamiltonian circuit problem in grid graphs is NP-complete.  ... 
arXiv:2109.01769v1 fatcat:dyuw5xrgkrheffaoqipj4u2yzu

Reconstruction of Weakly Simple Polygons from Their Edges

Hugo A. Akitaya, Csaba D. Tóth
2018 International journal of computational geometry and applications  
While the analogous question for simple polygons can easily be answered in O(n n) time, we show that it is NP-complete for weakly simple polygons.  ...  Given n line segments in the plane, do they form the edge set of a weakly simple polygon; that is, can the segment endpoints be perturbed by at most ε, for any ε>0, to obtain a simple polygon?  ...  It follows that the decision version of the problems in Section 5 are also NP-complete: It is NP-complete to find up to k subdivision points to form a weakly simple polygon, or to find an edge set with  ... 
doi:10.1142/s021819591860004x fatcat:ymytb34sczgepbssamsjutqtay

On Lagrangian Formalism of Quantum Computation [article]

Jue Xu
2021 arXiv   pre-print
We reformulate quantum computation in terms of Lagrangian (sum-over-path) formalism, in contrast to the widely used Hamiltonian (unitary gate) formulation.  ...  The meanings of Lagrangian (action) are interpreted in various contexts of quantum computation, such as complexity analysis.  ...  Despite these efforts, finding the ground state of 2-local Hamiltonian is proved to be hard in general even for quantum computers, i.e., this problem is QMA-complete (quantum analogue of NP-complete).  ... 
arXiv:2112.04892v1 fatcat:uijgocnxxje4bjsnbapn4uqj7a

On the linear stability of the inviscid Kármán vortex street

Javier Jimenez
1987 Journal of Fluid Mechanics  
It is shown here that it is a consequence of the Hamiltonian structure of the model, related to the codimension of the set of matrices with a particular Jordan block structure in the space of Hamiltonian  ...  matrices, and that it can be expected to hold generically for any two-dimensional inviscid array of vortices that has back-to-fore symmetry, and that is 'close enough' to the point-vortex model.  ...  circuit per vortex patch).  ... 
doi:10.1017/s0022112087001174 fatcat:trefjwwvvfhwzlky7qqfctywqm

Non-stretchable pseudo-visibility graphs

Ileana Streinu
2005 Computational geometry  
The example is based on the characterization of vertex-edge pseudo-visibility graphs of O'Rourke and Streinu [Proc. ACM Symp. Comput.  ...  The construction is then extended to an infinite family.  ...  A preliminary version appeared in [16] .  ... 
doi:10.1016/j.comgeo.2004.12.003 fatcat:4xr2xfb7yvdexlss2y7p6mrznq

Optimizing quantum heuristics with meta-learning

Max Wilson, Rachel Stromswold, Filip Wudarski, Stuart Hadfield, Norm M. Tubman, Eleanor G. Rieffel
2021 Quantum Machine Intelligence  
Finding the best way to amplify the performance of these methods on hardware is an important task.  ...  We also find that the meta-learner is generally more resistant to noise, for example, seeing a smaller reduction in performance in Noisy and Sampling environments, and performs better on average by a "  ...  Government is authorized to reproduce and distribute reprints for Governmental purpose notwithstanding any copyright annotation thereon.  ... 
doi:10.1007/s42484-020-00022-w fatcat:xoqjlh5phndx3itiosrq4dheti

Bravyi-Kitaev Superfast simulation of electronic structure on a quantum computer

Kanav Setia, James D. Whitfield
2018 Journal of Chemical Physics  
In order to simulate indistinguishable fermionic particles, it is first required to map the fermionic state to the state of the qubits.  ...  In this initial study of the hydrogen molecule, we have compared BKSF, Jordan-Wigner and Bravyi-Kitaev transforms under the Trotter approximation.  ...  This is illustrated in Figure 5 , where the Trotter error of all three algorithms collapse onto the same curve.  ... 
doi:10.1063/1.5019371 pmid:29716211 fatcat:nscj7f66mje3tiqydamgelwu7e

Quantum Computation Beyond the Circuit Model [article]

Stephen P. Jordan
2008 arXiv   pre-print
The quantum circuit model is the most widely used model of quantum computation.  ...  a proof that a certain problem of estimating Jones polynomials is complete for the one clean qubit complexity class, and a generalization of perturbative gadgets which allows k-body interactions to be  ...  Boolean satisfiability has the property that it is both contained in NP and it is NP-hard. Such problems are called NP-complete.  ... 
arXiv:0809.2307v1 fatcat:2j7vl7hmprge7oqyalfoipboum

Hardware-Tailored Diagonalization Circuits [article]

Daniel Miller, Laurin E. Fischer, Igor O. Sokolov, Panagiotis Kl. Barkoutsos, Ivano Tavernelli
2022 arXiv   pre-print
We apply our framework to group the Pauli operators occurring in the decomposition of a given Hamiltonian into jointly-HT-diagonalizable sets.  ...  Although it is always possible to construct a quantum circuit that simultaneously diagonalizes a given set of commuting Pauli operators, only resource-efficient circuits are reliably executable on near-term  ...  This research is part of two projects that have received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreements No. 847471 and  ... 
arXiv:2203.03646v1 fatcat:4335nik2kncv7hhbtksi2qpwqa

Solving strongly correlated electron models on a quantum computer

Dave Wecker, Matthew B. Hastings, Nathan Wiebe, Bryan K. Clark, Chetan Nayak, Matthias Troyer
2015 Physical Review A. Atomic, Molecular, and Optical Physics  
of its phases is more involved.  ...  While the evolution of a quantum state under a Hamiltonian is straightforward (if sometimes expensive), using quantum computers to determine the ground state phase diagram of a quantum model and the properties  ...  The authors acknowledge hospitality of the Aspen Center for Physics, supported by NSF grant # 1066293.  ... 
doi:10.1103/physreva.92.062318 fatcat:i7x754qbd5erbpcg54e56chj3m

The Variational Quantum Eigensolver: a review of methods and best practices [article]

Jules Tilly, Hongxiang Chen, Shuxiang Cao, Dario Picozzi, Kanav Setia, Ying Li, Edward Grant, Leonard Wossnig, Ivan Rungger, George H. Booth, Jonathan Tennyson
2022 arXiv   pre-print
The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics  ...  All the different components of the algorithm are reviewed in detail including representation of Hamiltonians and wavefunctions on a quantum computer, the optimization process, the post-processing mitigation  ...  In fact, the VQE optimization is shown to be NP-hard [93] , which means that in the worst possible case, finding the optimal solution to the problem is intractable.  ... 
arXiv:2111.05176v2 fatcat:7f2t7cqjwvhxnlvfvjqk7o37ha

An entanglement perspective on the quantum approximate optimization algorithm [article]

Maxime Dupont, Nicolas Didier, Mark J. Hodson, Joel E. Moore, Matthew J. Reagor
2022 arXiv   pre-print
It is the case for the quantum approximate optimization algorithm (QAOA) in the limit of large circuit depth, which aims to solve quadratic unconstrained binary optimization problems.  ...  We study the entanglement growth and spread resulting from randomized and optimized QAOA circuits and find that there is a volume-law entanglement barrier between the initial and final states.  ...  by a Jordan-Wigner transformation.  ... 
arXiv:2206.07024v1 fatcat:ns7mdh4wbrgwfcigh6srrudqc4

Prelude to Simulations of Loop Quantum Gravity on Adiabatic Quantum Computers

Jakub Mielczarek
2021 Frontiers in Astronomy and Space Sciences  
A possibility of simulating loop quantum gravity is discussed, and a method of solving a graph non-changing scalar (Hamiltonian) constraint with the use of adiabatic quantum computations is proposed.  ...  The article addresses the possibility of implementing spin network states, used in the loop quantum gravity approach to Planck scale physics on an adiabatic quantum computer.  ...  ACKNOWLEDGMENTS The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation.  ... 
doi:10.3389/fspas.2021.571282 fatcat:koc2kl25grabpb5umycqr4oms4
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