Realizing Exactly Solvable SU(N) Magnets with Thermal Atoms

We show that $n$ thermal fermionic alkaline-earth atoms in a flat-bottom trap allow one to robustly implement a spin model displaying two symmetries: the $S_n$ symmetry that permutes atoms occupying different vibrational levels of the trap and the SU($N$) symmetry associated with $N$ nuclear spin states. The high symmetry makes the model exactly solvable, which, in turn, enables the analytic study of dynamical processes such as spin diffusion in this SU($N$) system. We also show how to use this system to generate entangled states that allow for Heisenberg-limited metrology. This highly symmetric spin model should be experimentally realizable even when the vibrational levels are occupied according to a high-temperature thermal or an arbitrary non-thermal distribution.Comment: 12 pages, 5 figures (including supplemental materials

Spectrum Estimation of Density Operators with Alkaline-Earth Atoms

We show that Ramsey spectroscopy of fermionic alkaline-earth atoms in a square-well trap provides an efficient and accurate estimate for the eigenspectrum of a density matrix whose n copies are stored in the nuclear spins of n such atoms. This spectrum estimation is enabled by the high symmetry of the interaction Hamiltonian, dictated, in turn, by the decoupling of the nuclear spin from the electrons and by the shape of the square-well trap. Practical performance of this procedure and its potential applications to quantum computing and time keeping with alkaline-earth atoms are discussed

Spectrum Estimation of Density Operators with Alkaline-Earth Atoms

We show that Ramsey spectroscopy of fermionic alkaline-earth atoms in a square-well trap provides an efficient and accurate estimate for the eigenspectrum of a density matrix whose n copies are stored in the nuclear spins of n such atoms. This spectrum estimation is enabled by the high symmetry of the interaction Hamiltonian, dictated, in turn, by the decoupling of the nuclear spin from the electrons and by the shape of the square-well trap. Practical performance of this procedure and its potential applications to quantum computing and time keeping with alkaline-earth atoms are discussed

Quantum algorithms for algebraic problems

Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges in the theory of quantum computation, and such algorithms motivate the formidable task of building a large-scale quantum computer. This article reviews the current state of quantum algorithms, focusing on algorithms with superpolynomial speedup over classical computation, and in particular, on problems with an algebraic flavor.Comment: 52 pages, 3 figures, to appear in Reviews of Modern Physic

Breaking Symmetric Cryptosystems Using Quantum Period Finding

Due to Shor's algorithm, quantum computers are a severe threat for public key cryptography. This motivated the cryptographic community to search for quantum-safe solutions. On the other hand, the impact of quantum computing on secret key cryptography is much less understood. In this paper, we consider attacks where an adversary can query an oracle implementing a cryptographic primitive in a quantum superposition of different states. This model gives a lot of power to the adversary, but recent results show that it is nonetheless possible to build secure cryptosystems in it. We study applications of a quantum procedure called Simon's algorithm (the simplest quantum period finding algorithm) in order to attack symmetric cryptosystems in this model. Following previous works in this direction, we show that several classical attacks based on finding collisions can be dramatically sped up using Simon's algorithm: finding a collision requires $\Omega(2^{n/2})$ queries in the classical setting, but when collisions happen with some hidden periodicity, they can be found with only $O(n)$ queries in the quantum model. We obtain attacks with very strong implications. First, we show that the most widely used modes of operation for authentication and authenticated encryption e.g. CBC-MAC, PMAC, GMAC, GCM, and OCB) are completely broken in this security model. Our attacks are also applicable to many CAESAR candidates: CLOC, AEZ, COPA, OTR, POET, OMD, and Minalpher. This is quite surprising compared to the situation with encryption modes: Anand et al. show that standard modes are secure with a quantum-secure PRF. Second, we show that Simon's algorithm can also be applied to slide attacks, leading to an exponential speed-up of a classical symmetric cryptanalysis technique in the quantum model.Comment: 31 pages, 14 figure

Capital and Income Breeding in Male Ungulates: Causes and Consequences of Strategy Differences Among Species

The capital and income breeding concept links energy resources used during reproduction to the timing of their acquisition. During reproduction, capital breeders rely on resources gained previously and accumulated for reproductive investment. By contrast, income breeders use mainly resources collected during the period of reproductive activity. Most commonly, this concept is applied to females; relatively few studies have considered males. Moreover, there has been little attention to the link between the capital-income divide and other aspects of mating strategy. We studied adult males of three wild ungulates with different levels of polygyny. A large dataset (4,264 red deer, 53,619 roe deer, and 13,537 Alpine chamois, respectively) was obtained during 2007–2017 in the whole territory of Slovenia and in the Trento province, Italy. During the rut, body mass loss of males in highly polygynous species was more than twice that of weakly polygynous species: on average, red deer stags lost 19.5%; chamois bucks 16.0%; and roe deer bucks 7.5% of their body mass. This indicates potential for a hitherto unrecognised link between the degree of intrasexual competition and the degree of capital mating. The variability in body mass at the end of the rut was clearly reduced in both highly polygynous species (from 15.1 to 9.4% in red deer, and from 12.5 to 10.5% in chamois), but did not change in roe deer. Finally, roe deer bucks had recovered body mass to that of the pre-rut period by just 2 months after the rut, while red deer stags did not manage to compensate the loss of weight until the end of the year. We suggest that, at least in ungulates, there is a link between the degree of polygyny and that of capital breeding. Males of capital and income breeders underwent body mass changes resulting from different reproductive investment during the rut. Capital breeders lost considerably more weight, and invested a variable amount of energy among individuals or among years, possibly to cope with different environmental or body conditions. In so doing, they ended the rut with poorer but more even condition among individuals

Framework-Based Applications: From Incremental Development to Incremental Reasoning

Object-oriented frameworks provide a powerful technique for developing groups of related applications. The framework includes one or more template methods that at appropriate points call various hook methods. Each application built on a framework reuses the template methods provided by the framework; the application developer provides definitions, tailored to the needs of the particular application, for only the hook methods. Our goal is to develop a technique for reasoning in which we reason about the framework behavior just once; whenever a new application A is developed, we arrive at its behavior by composing the behavior of hook methods defined in A with the behavior of the framework. Just as the template methods allow the application developers to reuse the code of the framework, our technique allows them to reuse the effort involved in reasoning about the framework in understanding each application built on the framework. We illustrate the technique by applying it to a simple example, and contrast our approach with a more standard approach based on behavioral subtyping