Three and Four-Body Interactions in Spin-Based Quantum Computers

In the effort to design and to construct a quantum computer, several leading proposals make use of spin-based qubits. These designs generally assume that spins undergo pairwise interactions. We point out that, when several spins are engaged mutually in pairwise interactions, the quantitative strengths of the interactions can change and qualitatively new terms can arise in the Hamiltonian, including four-body interactions. In parameter regimes of experimental interest, these coherent effects are large enough to interfere with computation, and may require new error correction or avoidance techniques.Comment: 5 pages incl. 4 figures. To appear in Phys. Rev. Lett. For an expanded version including detailed calculations see http://xxx.lanl.gov/abs/cond-mat/030201

Some New Insights and a Note Regarding Alexander Jannaeus Anchor/Star (TJC Group L) Coins

Dieser Artikel untersucht einen spezifischen Münztyp, der von Alexander Jannaeus und wahrscheinlich von seinen Nachfolgern im 1. Jh. v. Chr. geprägt wurde. Neue Varianten und unpublizierte Exemplare werden diskutiert, einhergehend mit dem Vorschlag, diesen Münztyp in vier Untertypen aufzugliedern. Daneben wird die Herstellung der Stempel berücksichtigt, mit denen die kleinsten Exemplare dieses Typs geprägt wurden. Schließlich machen die Autoren einen Vorschlag, welches  Nominal diese Münzen im judäischen Zahlungsverkehr einnahmen.The article examines one specific type of coin that was minted by Alexander Jannaeus and probably by his successors, during the first century BCE. New variants and unpublished specimens are discussed along with a proposal that this coin type may be divided into four subtypes. The article also considers the preparation of the dies used to mint the smallest of this type of coin. Finally, the article proposes the denomination that these coins had in the ancient Judean marketplace

On the least common multiple of qq-binomial coefficients

In this paper, we prove the following identity \lcm({n\brack 0}_q,{n\brack 1}_q,...,{n\brack n}_q) =\frac{\lcm([1]_q,[2]_q,...,[n+1]_q)}{[n+1]_q}, where ${n\brack k}_q$ denotes the $q$-binomial coefficient and $[n]_q=\frac{1-q^n}{1-q}$. This result is a $q$-analogue of an identity of Farhi [Amer. Math. Monthly, November (2009)].Comment: 5 page

Using Classical Probability To Guarantee Properties of Infinite Quantum Sequences

We consider the product of infinitely many copies of a spin-$1\over 2$ system. We construct projection operators on the corresponding nonseparable Hilbert space which measure whether the outcome of an infinite sequence of $\sigma^x$ measurements has any specified property. In many cases, product states are eigenstates of the projections, and therefore the result of measuring the property is determined. Thus we obtain a nonprobabilistic quantum analogue to the law of large numbers, the randomness property, and all other familiar almost-sure theorems of classical probability.Comment: 7 pages in LaTe

Quantum entangling power of adiabatically connected hamiltonians

The space of quantum Hamiltonians has a natural partition in classes of operators that can be adiabatically deformed into each other. We consider parametric families of Hamiltonians acting on a bi-partite quantum state-space. When the different Hamiltonians in the family fall in the same adiabatic class one can manipulate entanglement by moving through energy eigenstates corresponding to different value of the control parameters. We introduce an associated notion of adiabatic entangling power. This novel measure is analyzed for general $d\times d$ quantum systems and specific two-qubits examples are studiedComment: 5 pages, LaTeX, 2 eps figures included. Several non minor changes made (thanks referee) Version to appear in the PR

Adiabatic Quantum Computation in Open Systems

We analyze the performance of adiabatic quantum computation (AQC) under the effect of decoherence. To this end, we introduce an inherently open-systems approach, based on a recent generalization of the adiabatic approximation. In contrast to closed systems, we show that a system may initially be in an adiabatic regime, but then undergo a transition to a regime where adiabaticity breaks down. As a consequence, the success of AQC depends sensitively on the competition between various pertinent rates, giving rise to optimality criteria.Comment: v2: 4 pages, 1 figure. Published versio

Adiabatic quantum computation and quantum phase transitions

We analyze the ground state entanglement in a quantum adiabatic evolution algorithm designed to solve the NP-complete Exact Cover problem. The entropy of entanglement seems to obey linear and universal scaling at the point where the mass gap becomes small, suggesting that the system passes near a quantum phase transition. Such a large scaling of entanglement suggests that the effective connectivity of the system diverges as the number of qubits goes to infinity and that this algorithm cannot be efficiently simulated by classical means. On the other hand, entanglement in Grover's algorithm is bounded by a constant.Comment: 5 pages, 4 figures, accepted for publication in PR

Robustness of adiabatic quantum computation

We study the fault tolerance of quantum computation by adiabatic evolution, a quantum algorithm for solving various combinatorial search problems. We describe an inherent robustness of adiabatic computation against two kinds of errors, unitary control errors and decoherence, and we study this robustness using numerical simulations of the algorithm.Comment: 11 pages, 5 figures, REVTe