Part I. Fundamental Concepts: 1. Introduction and overview 2. Introduction to quantum mechanics 3. Introduction to computer science Part II. Quantum Computation: 4. Quantum circuits 5. The quantum Fourier transform and its application 6. Quantum search algorithms 7. Quantum computers: physical realization Part III. Quantum Information: 8. Quantum noise and quantum operations 9. Distance measures for quantum information 10. Quantum error-correction 11. Entropy and information 12. Quantum information theory Appendices References Index.

Quantum Computation and Quantum Information

A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and which have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored.

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

Rechargeable solid-state batteries have long been considered an attractive power source for a wide variety of applications, and in particular, lithium-ion batteries are emerging as the technology of choice for portable electronics. One of the main challenges in the design of these batteries is to ensure that the electrodes maintain their integrity over many discharge-recharge cycles. Although promising electrode systems have recently been proposed, their lifespans are limited by Li-alloying agglomeration or the growth of passivation layers, which prevent the fully reversible insertion of Li ions into the negative electrodes. Here we report that electrodes made of nanoparticles of transition-metal oxides (MO, where M is Co, Ni, Cu or Fe) demonstrate electrochemical capacities of 700 mA h g(-1), with 100% capacity retention for up to 100 cycles and high recharging rates. The mechanism of Li reactivity differs from the classical Li insertion/deinsertion or Li-alloying processes, and involves the formation and decomposition of Li2O, accompanying the reduction and oxidation of metal nanoparticles (in the range 1-5 nanometres) respectively. We expect that the use of transition-metal nanoparticles to enhance surface electrochemical reactivity will lead to further improvements in the performance of lithium-ion batteries.

Nano-sized transition-metal oxides as negative-electrode materials for lithium-ion batteries

Cryptosystem designers frequently assume that secrets will be manipulated in closed, reliable computing environments. Unfortunately, actual computers and microchips leak information about the operations they process. This paper examines specific methods for analyzing power consumption measurements to find secret keys from tamper resistant devices. We also discuss approaches for building cryptosystems that can operate securely in existing hardware that leaks information.

/pdf/differential-power-analysis-4t7fjmuc7b.pdf

Differential Power Analysis

'Bottom-up fabrication', which exploits the intrinsic properties of atoms and molecules to direct their self-organization, is widely used to make relatively simple nanostructures. A key goal for this approach is to create nanostructures of high complexity, matching that routinely achieved by 'top-down' methods. The self-assembly of DNA molecules provides an attractive route towards this goal. Here I describe a simple method for folding long, single-stranded DNA molecules into arbitrary two-dimensional shapes. The design for a desired shape is made by raster-filling the shape with a 7-kilobase single-stranded scaffold and by choosing over 200 short oligonucleotide 'staple strands' to hold the scaffold in place. Once synthesized and mixed, the staple and scaffold strands self-assemble in a single step. The resulting DNA structures are roughly 100 nm in diameter and approximate desired shapes such as squares, disks and five-pointed stars with a spatial resolution of 6 nm. Because each oligonucleotide can serve as a 6-nm pixel, the structures can be programmed to bear complex patterns such as words and images on their surfaces. Finally, individual DNA structures can be programmed to form larger assemblies, including extended periodic lattices and a hexamer of triangles (which constitutes a 30-megadalton molecular complex).

/pdf/folding-dna-to-create-nanoscale-shapes-and-patterns-1liv7u73y0.pdf

Folding DNA to create nanoscale shapes and patterns

In many cases tests of a program that uncover simple errors are also effective in uncovering much more complex errors. This so-called coupling effect can be used to save work during the testing process.

Hints on Test Data Selection: Help for the Practicing Programmer

A sound pressure level meter adapted for use in monitoring noise levels, particularly for use by law enforcement agencies wherein the device includes means for providing a logarithmic indication of the root mean square value of ambient sound pressure levels and wherein means are provided for holding and displaying a maximum sound pressure level detected over a given period of time and for providing an alarm when a detected level exceeds a predetermined threshold level.

On the Importance of Checking Cryptographic Protocols for Faults (Extended Abstract).

DNA experiments are proposed to solve the famous "SAT" problem of computer science. This is a special case of a more general method that can solve NP-complete problems. The advantage of these results is the huge parallelism inherent in DNA-based computing. It has the potential to yield vast speedups over conventional electronic-based computers for such search problems.

https://science.sciencemag.org/content/sci/268/5210/542.full.pdf

DNA solution of hard computational problems

It is well known that the reachability problem for directed graphs is logspace-complete for the complexity class NSPACE(log n) , and thus holds the key to the open question of whether DSPACE(logn)= NSPACE(logn) ([3,4,5,6]). Here as usual OSPACE(logn) is the class of languages that are accepted in logn space by deterministic Turing Ma chi nes, wh i 1eNSPACE( log n) i s the c1ass 0 f 1anguages that are accepted in log n space by nondeterministic ones. The reachability problem for undirected graphs has also been considered ([5]), but it has remained an open question whether undirected graph reachability is logspace-complete for NSPACE(logn). Here we derive results suggesting that the undirected reachability problem is structurally different from, and easier than, the directed version. These results are an affirmative answer to a question of S. Cook.

Random walks, universal traversal sequences, and the complexity of maze problems

It is well known that every set in P has small circuits [13]. Adleman [1] has recently proved the stronger result that every set accepted in polynomial time by a randomized Turing machine has small circuits. Both these results are typical of the known relationships between uniform and nonuniform complexity bounds. They obtain a nonuniform upper bound as a consequence of a uniform upper bound. The central theme here is an attempt to explore the converse direction. That is, we wish to understand when nonuniform upper bounds can be used to obtain uniform upper bounds. In this section we will define our basic notion of nonuniform complexity. Then we will show how to relate it to more common notions.

Richard J. Lipton

Papers

Hints on Test Data Selection: Help for the Practicing Programmer

On the Importance of Checking Cryptographic Protocols for Faults (Extended Abstract).

DNA solution of hard computational problems

Random walks, universal traversal sequences, and the complexity of maze problems

Some connections between nonuniform and uniform complexity classes