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arXiv 2022年

作者： Leditzky, Felix Leung, Debbie Siddhu, Vikesh Smith, Graeme Smolin, John A. Department of Mathematics IQUIST University of Illinois at Urbana-Champaign UrbanaIL61801 United States Institute for Quantum Computing Department of Combinatorics & Optimization University of Waterloo WaterlooONN2L 3G1 Canada Perimeter Institute for Theoretical Physics WaterlooONN2L 2Y5 Canada JILA University of Colorado NIST 440 UCB BoulderCO80309 United States Department of Physics and Quantum Computing Group Carnegie Mellon University PittsburghPA15213 United States Department of Physics Center for Theory of Quantum Matter University of Colorado BoulderCO80309 United States IBM Quantum IBM T.J. Watson Research Center Yorktown HeightsNY10598 United States

Determining capacities of quantum channels is a fundamental question in quantum information theory. Despite having rigorous coding theorems quantifying the flow of information across quantum channels, their capacities are poorly understood due to super-additivity effects. Studying these phenomena is important for deepening our understanding of quantum information, yet simple and clean examples of super-additive channels are scarce. Here we study a family of channels called platypus channels. Its simplest member, a qutrit channel, is shown to display super-additivity of coherent information when used jointly with a variety of qubit channels. Higher-dimensional family members display super-additivity of quantum capacity together with an erasure channel. Subject to the "spin-alignment conjecture" introduced in the companion paper [1], our results on superadditivity of quantum capacity extend to lower-dimensional channels as well as larger parameter ranges. In particular, super-additivity occurs between two weakly additive channels each with large capacity on their own, in stark contrast to previous results. Remarkably, a single, novel transmission strategy achieves super-additivity in all examples. Our results show that super-additivity is much more prevalent than previously thought. It can occur across a wide variety of channels, even when both participating channels have large quantum capacity. Copyright © 2022, The Authors. All rights reserved.

关键词： Additives

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Robust Interior Point Method for quantum Key Distribution Rate Computation

arXiv

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arXiv 2021年

作者： Hu, Hao Im, Jiyoung Lin, Jie Lütkenhaus, Norbert Wolkowicz, Henry Department of Combinatorics and Optimization Faculty of Mathematics University of Waterloo WaterlooONN2L 3G1 Canada Department of Mathematical Sciences Clemson University ClemsonSC29634 United States Institute for Quantum Computing Department of Physics and Astronomy University of Waterloo WaterlooONN2L 3G1 Canada Department of Electrical & Computer Engineering University of Toronto TorontoONM5S 3G4 Canada

Security proof methods for quantum key distribution, QKD, that are based on the numerical key rate calculation problem, are powerful in principle. However, the practicality of the methods are limited by computational resources and the efficiency and accuracy of the underlying algorithms for convex optimization. We derive a stable reformulation of the convex nonlinear semidefinite programming, SDP, model for the key rate calculation problems. We use this to develop an efficient, accurate algorithm. The stable reformulation is based on novel forms of facial reduction, FR, for both the linear constraints and nonlinear quantum relative entropy objective function. This allows for a Gauss-Newton type interior-point approach that avoids the need for perturbations to obtain strict feasibility, a technique currently used in the literature. The result is high accuracy solutions with theoretically proven lower bounds for the original QKD from the FR stable reformulation. This provides novel contributions for FR for general SDP. We report on empirical results that dramatically improve on speed and accuracy, as well as solving previously intractable problems. © 2021, CC BY.

关键词： Convex optimization

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Performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs

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Physical Review A 2012年第5期86卷 052334-052334页

作者： Edward Farhi David Gosset Itay Hen A. W. Sandvik Peter Shor A. P. Young Francesco Zamponi Center for Theoretical Physics Massachusetts Institute of Technology 77 Massachusetts Avenue 6-304 Cambridge Massachusetts 02139 USA Department of Combinatorics & Optimization and Institute for Quantum Computing University of Waterloo 200 University Avenue West Waterloo Ontario Canada N2L 3G1 Department of Physics University of California Santa Cruz California 95064 USA Department of Physics Boston University Boston Massachusetts 02215 USA Department of Mathematics Center for Theoretical Physics and CSAIL Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Laboratoire de Physique Théorique UMR 8549 CNRS and Ecole Normale Supérieure 24 Rue Lhomond FR-75231 Paris Cedex 05 France

In this paper we study the performance of the quantum adiabatic algorithm on random instances of two combinatorial optimization problems, 3-regular 3-XORSAT and 3-regular max-cut. The cost functions associated with these two clause-based optimization problems are similar as they are both defined on 3-regular hypergraphs. For 3-regular 3-XORSAT the clauses contain three variables and for 3-regular max-cut the clauses contain two variables. The quantum adiabatic algorithms we study for these two problems use interpolating Hamiltonians which are amenable to sign-problem free quantum Monte Carlo and quantum cavity methods. Using these techniques we find that the quantum adiabatic algorithm fails to solve either of these problems efficiently, although for different reasons.

关键词： Cost functions Random quanta Adiabatic

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Novel Technique for Robust Optimal Algorithmic Cooling

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Physical Review Letters 2019年第22期122卷 220501-220501页

作者： Sadegh Raeisi Mária Kieferová Michele Mosca Department of Physics Sharif University of Technology Tehran *** Iran Institute for Quantum Computing University of Waterloo Ontario N2L 3G1 Canada Department of Physics and Astronomy University of Waterloo Ontario N2L 3G1 Canada Department of Physics and Astronomy Macquarie University Sydney New South Wales 2109 Australia Department of Combinatorics and Optimization University of Waterloo Ontario N2L 3G1 Canada Perimeter Institute for Theoretical Physics Waterloo Ontario N2L 2Y5 Canada Canadian Institute for Advanced Research Toronto Ontario M5G 1Z8 Canada

Heat-bath algorithmic cooling provides algorithmic ways to improve the purity of quantum states. These techniques are complex iterative processes that change from each iteration to the next and this poses a significant challenge to implementing these algorithms. Here, we introduce a new technique that on a fundamental level, shows that it is possible to do algorithmic cooling and even reach the cooling limit without any knowledge of the state and using only a single fixed operation, and on a practical level, presents a more feasible and robust alternative for implementing heat-bath algorithmic cooling. We also show that our new technique converges to the asymptotic state of heat-bath algorithmic cooling and that the cooling algorithm can be efficiently implemented; however, the saturation could require exponentially many iterations and remains impractical. This brings heat-bath algorithmic cooling to the realm of feasibility and makes it a viable option for realistic application in quantum technologies.

关键词： Cooling & trapping quantum control quantum error correction quantum information architectures & platforms quantum sensing Nitrogen vacancy centers in diamond Nuclear magnetic resonance

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quantum circuit optimizations for NISQ architectures

arXiv

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arXiv 2019年

作者： Nash, Beatrice Gheorghiu, Vlad Mosca, Michele Department of Physics Massachusetts Institute of Technology CambridgeMA United States Institute for Quantum Computing University of Waterloo WaterlooONN2L 3G1 Canada Department of Combinatorics and Optimization University of Waterloo WaterlooONN2L 3G1 Canada SoftwareQ Inc. KitchenerON Perimeter Institute for Theoretical Physics WaterlooONN2L 6B9 Canada Canadian Institute for Advanced Research TorontoONM5G 1Z8 Canada

Currently available quantum computing hardware platforms have limited 2-qubit connectivity among their addressable qubits. In order to run a generic quantum algorithm on such a platform, one has to transform the initial logical quantum circuit describing the algorithm into an equivalent one that obeys the connectivity restrictions. In this work we construct a circuit synthesis scheme that takes as input the qubit connectivity graph and a quantum circuit over the gate set generated by {CNOT, RZ} and outputs a circuit that respects the connectivity of the device. As a concrete application, we apply our techniques to Google's Bristlecone 72-qubit quantum chip connectivity, IBM's Tokyo 20-qubit quantum chip connectivity, and Rigetti's Acorn 19-qubit quantum chip connectivity. In addition, we also compare the performance of our scheme as a function of sparseness of randomly generated quantum circuits. Copyright © 2019, The Authors. All rights reserved.

关键词： Timing circuits

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One-shot quantum state redistribution and quantum Markov chains

arXiv

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arXiv 2021年

作者： Anshu, Anurag Hadiashar, Shima Bab Jain, Rahul Nayak, Ashwin Touchette, Dave School of Engineering and Applied Sciences Harvard University CambridgeMA United States Department of Combinatorics and Optimization Institute for Quantum Computing University of Waterloo 200 University Ave. W. WaterlooONN2L 3G1 Canada Department of Computer Science Center for Quantum Technologies National University of Singapore 21 Lower Kent Ridge Rd Singapore119077 Singapore Department of Computer Science Institut Quantique Université de Sherbrooke 2500 Boulevard de l’Université SherbrookeQCJ1K 2R1 Canada

We revisit the task of quantum state redistribution in the one-shot setting, and design a protocol for this task with communication cost in terms of a measure of distance from quantum Markov chains. More precisely, the distance is defined in terms of quantum max-relative entropy and quantum hypothesis testing entropy. Our result is the first to operationally connect quantum state redistribution and quantum Markov chains, and can be interpreted as an operational interpretation for a possible one-shot analogue of quantum conditional mutual information. The communication cost of our protocol is lower than all previously known ones and asymptotically achieves the well-known rate of quantum conditional mutual information. Thus, our work takes a step towards an optimal characterization of the resources required for one-shot quantum state redistribution, an important open problem in quantum Shannon theory. © 2021, CC BY.

关键词： Entropy

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A quantum central path algorithm for linear optimization

arXiv

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arXiv 2023年

作者： Augustino, Brandon Leng, Jiaqi Nannicini, Giacomo Terlaky, Tamás Wu, Xiaodi Sloan School of Management Massachusetts Institute of Technology United States Simons Institute for the Theory of Computing Department of Mathematics University of California Berkeley United States Department of Industrial and Systems Engineering University of Southern California United States Department of Industrial and Systems Engineering Lehigh University United States Quantum Computing and Optimization Lab Lehigh University United States Department of Mathematics University of Maryland College Park United States Department of Computer Science University of Maryland College Park United States Joint Center for Quantum Information and Computer Science University of Maryland United States

We propose a novel quantum algorithm for solving linear optimization problems by quantum-mechanical simulation of the central path. While interior point methods follow the central path with an iterative algorithm that works with successive linearizations of the perturbed KKT conditions, we perform a single simulation working directly with the nonlinear complementarity equations. This approach yields an algorithm for solving linear optimization problems involving m constraints and n variables to Ε-optimality using O (√m + n · RΕ1) queries to an oracle that evaluates a potential function, where R1 is an 1-norm upper bound on the size of the optimal solution. In the standard gate model (i.e., without access to quantum RAM) our algorithm can obtain highly-precise solutions to LO problems using at most O (√m + n · nnz(A)RΕ1) elementary gates, where nnz(A) is the total number of non-zero elements found in the constraint matrix. © 2023, CC BY.

关键词： optimization algorithms

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Simulating Hamiltonian Dynamics with a Truncated Taylor Series

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Physical Review Letters 2015年第9期114卷 090502-090502页

作者： Dominic W. Berry Andrew M. Childs Richard Cleve Robin Kothari Rolando D. Somma Department of Physics and Astronomy Macquarie University Sydney New South Wales 2109 Australia Institute for Quantum Computing University of Waterloo Ontario N2L 3G1 Canada Department of Combinatorics and Optimization University of Waterloo Ontario N2L 3G1 Canada Department of Computer Science Institute for Advanced Computer Studies and Joint Center for Quantum Information and Computer Science University of Maryland College Park Maryland 20910 USA Canadian Institute for Advanced Research Toronto Ontario M5G 1Z8 Canada School of Computer Science University of Waterloo Ontario N2L 3G1 Canada Center for Theoretical Physics Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Theoretical Division Los Alamos National Laboratory Los Alamos New Mexico 87545 USA

We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of physical systems. As in another recent algorithm, the cost of our method depends only logarithmically on the inverse of the desired precision, which is optimal. However, we simplify the algorithm and its analysis by using a method for implementing linear combinations of unitary operations together with a robust form of oblivious amplitude amplification.

关键词： HAMILTONIAN systems TAYLOR'S series quantum theory quantum computers LOGARITHMIC functions

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Towards simulating 2D effects in lattice gauge theories on a quantum computer

arXiv

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arXiv 2020年

作者： Paulson, Danny Dellantonio, Luca Haase, Jan F. Celi, Alessio Kan, Angus Jena, Andrew Kokail, Christian van Bijnen, Rick Jansen, Karl Zoller, Peter Muschik, Christine A. Institute for Quantum Computing University of Waterloo WaterlooONN2L 3G1 Canada Department of Physics & Astronomy University of Waterloo WaterlooONN2L 3G1 Canada Departament de Física Universitat Autònoma de Barcelona BellaterraE-08193 Spain Center of Quantum Physics University of Innsbruck InnsbruckA-6020 Austria Institute for Quantum Optics and Quantum Information Austrian Academy of Sciences InnsbruckA-6020 Austria Department of Combinatorics & Optimization University of Waterloo WaterlooONN2L 3G1 Canada NIC DESY Zeuthen Platanenallee 6 Zeuthen15738 Germany Perimeter Institute for Theoretical Physics WaterlooONN2L 2Y5 Canada

quantum computing is in its greatest upswing, with so-called Noisy-Intermediate-Scale-quantum devices heralding the computational power to be expected in the near future. While the field is progressing towards quantum advantage, quantum computers already have the potential to tackle classically intractable problems. Here, we consider gauge theories describing fundamental particle interactions. On the way to their full-fledged quantum simulations, the challenge of limited resources on near-term quantum devices has to be overcome. We propose an experimental quantum simulation scheme to study ground state properties in two-dimensional quantum electrodynamics (2D QED) using existing quantum technology. Our protocols can be adapted to larger lattices and offer the perspective to connect the lattice simulation to low energy observable quantities, e.g. the hadron spectrum, in the continuum theory. By including both dynamical matter and a non-minimal gauge field truncation, we provide the novel opportunity to observe 2D effects on present-day quantum hardware. More specifically, we present two Variational quantum Eigensolver (VQE) based protocols for the study of magnetic field effects, and for taking an important first step towards computing the running coupling of QED. For both instances, we include variational quantum circuits for qubit-based hardware. We simulate the proposed VQE experiments classically to calculate the required measurement budget under realistic conditions. While this feasibility analysis is done for trapped ions, our approach can be directly adapted to other platforms. The techniques presented here, combined with advancements in quantum hardware, pave the way for reaching beyond the capabilities of classical simulations. Copyright © 2020, The Authors. All rights reserved.

关键词： quantum chemistry

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Benchmarking the quantum cryptanalysis of symmetric, public-key and hash-based cryptographic schemes

arXiv

引用

arXiv 2019年

作者： Gheorghiu, Vlad Mosca, Michele Institute for Quantum Computing University of Waterloo WaterlooONN2L 3G1 Canada Department of Combinatorics & Optimization University of Waterloo WaterlooONN2L 3G1 Canada evolutionQ Inc. WaterlooON Canada softwareQ Inc. KitchenerON Canada Perimeter Institute for Theoretical Physics WaterlooONN2L 6B9 Canada Canadian Institute for Advanced Research TorontoONM5G 1Z8 Canada

quantum algorithms can break factoring and discrete logarithm based cryptography and weaken symmetric cryptography and hash functions. In order to estimate the real-world impact of these attacks, apart from tracking the development of fault-tolerant quantum computers it is important to have an estimate of the resources needed to implement these quantum attacks. For attacking symmetric cryptography and hash functions, generic quantum attacks are substantially less powerful than they are for today’s public-key cryptography. So security will degrade gradually as quantum computing resources increase. At present, there is a substantial resource overhead due to the cost of fault-tolerant quantum error correction. We provide estimates of this overhead using state-of-the-art methods in quantum fault-tolerance. For example, recent lattice surgery methods reduced memory costs by roughly a factor of 5 over previous methods. Future advances in fault-tolerance and in the quality of quantum hardware may reduce this overhead further. Another part of the cost of implementing generic quantum attacks is the cost of implementing the cryptographic functions. We use state-of-the-art optimized circuits, though further improvements in their implementation would also reduce the resources needed to implement these attacks. To bound the potential impact of further circuit optimizations we provide cost estimates assuming trivial-cost implementations of these functions. These figures indicate the effective bit-strength of the various symmetric schemes and hash functions based on what we know today (and with various assumptions on the quantum hardware), and frame the various potential improvements that should continue to be tracked. As an example, we also look at the implications for Bitcoin’s proof-of-work system. For many of the currently used asymmetric (public-key) cryptographic schemes based on RSA and elliptic curve discrete logarithms, we again provide cost estimates based on the latest

关键词： Fault tolerance

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