Integrated software package STAMP for minor planets

The integrated software package STAMP allowed for rapid and exact reproduction of the tables of the year-book 'Ephemerides of Minor Planets.' Additionally, STAMP solved the typical problems connected with the use of the year-book. STAMP is described. The year-book 'Ephemerides of Minor Planets' (EMP) is a publication used in many astronomical institutions around the world. It contains all the necessary information on the orbits of the numbered minor planets. Also, the astronomical coordinates are provided for each planet during its suitable observation period

Qubit Entanglement Breaking Channels

This paper continues the study of stochastic maps, or channels, which break entanglement. We give a detailed description of entanglement-breaking qubit channels, and show that such maps are precisely the convex hull of those known as classical-quantum channels. We also review the complete positivity conditions in a canonical parameterization and show how they lead to entanglement-breaking conditions.Comment: Contains main results from section 2 of quant-ph/0207100 Version 2 corrects minor typos. Final version to appear in Rev. Math. Phy

The Equivalence of Sampling and Searching

In a sampling problem, we are given an input x, and asked to sample approximately from a probability distribution D_x. In a search problem, we are given an input x, and asked to find a member of a nonempty set A_x with high probability. (An example is finding a Nash equilibrium.) In this paper, we use tools from Kolmogorov complexity and algorithmic information theory to show that sampling and search problems are essentially equivalent. More precisely, for any sampling problem S, there exists a search problem R_S such that, if C is any "reasonable" complexity class, then R_S is in the search version of C if and only if S is in the sampling version. As one application, we show that SampP=SampBQP if and only if FBPP=FBQP: in other words, classical computers can efficiently sample the output distribution of every quantum circuit, if and only if they can efficiently solve every search problem that quantum computers can solve. A second application is that, assuming a plausible conjecture, there exists a search problem R that can be solved using a simple linear-optics experiment, but that cannot be solved efficiently by a classical computer unless the polynomial hierarchy collapses. That application will be described in a forthcoming paper with Alex Arkhipov on the computational complexity of linear optics.Comment: 16 page

Magnetic qubits as hardware for quantum computers

We propose two potential realisations for quantum bits based on nanometre scale magnetic particles of large spin S and high anisotropy molecular clusters. In case (1) the bit-value basis states |0> and |1> are the ground and first excited spin states Sz = S and S-1, separated by an energy gap given by the ferromagnetic resonance (FMR) frequency. In case (2), when there is significant tunnelling through the anisotropy barrier, the qubit states correspond to the symmetric, |0>, and antisymmetric, |1>, combinations of the two-fold degenerate ground state Sz = +- S. In each case the temperature of operation must be low compared to the energy gap, \Delta, between the states |0> and |1>. The gap \Delta in case (2) can be controlled with an external magnetic field perpendicular to the easy axis of the molecular cluster. The states of different molecular clusters and magnetic particles may be entangled by connecting them by superconducting lines with Josephson switches, leading to the potential for quantum computing hardware.Comment: 17 pages, 3 figure

Restrictions on Transversal Encoded Quantum Gate Sets

Transversal gates play an important role in the theory of fault-tolerant quantum computation due to their simplicity and robustness to noise. By definition, transversal operators do not couple physical subsystems within the same code block. Consequently, such operators do not spread errors within code blocks and are, therefore, fault tolerant. Nonetheless, other methods of ensuring fault tolerance are required, as it is invariably the case that some encoded gates cannot be implemented transversally. This observation has led to a long-standing conjecture that transversal encoded gate sets cannot be universal. Here we show that the ability of a quantum code to detect an arbitrary error on any single physical subsystem is incompatible with the existence of a universal, transversal encoded gate set for the code.Comment: 4 pages, v2: minor change

Quantum divisibility test and its application in mesoscopic physics

We present a quantum algorithm to transform the cardinality of a set of charged particles flowing along a quantum wire into a binary number. The setup performing this task (for at most N particles) involves log_2 N quantum bits serving as counters and a sequential read out. Applications include a divisibility check to experimentally test the size of a finite train of particles in a quantum wire with a one-shot measurement and a scheme allowing to entangle multi-particle wave functions and generating Bell states, Greenberger-Horne-Zeilinger states, or Dicke states in a Mach-Zehnder interferometer.Comment: 9 pages, 5 figure

On the role of entanglement and correlations in mixed-state quantum computation

In a quantum computation with pure states, the generation of large amounts of entanglement is known to be necessary for a speedup with respect to classical computations. However, examples of quantum computations with mixed states are known, such as the deterministic computation with one quantum qubit (DQC1) model [Knill and Laflamme, Phys. Rev. Lett. 81, 5672 (1998)], in which entanglement is at most marginally present, and yet a computational speedup is believed to occur. Correlations, and not entanglement, have been identified as a necessary ingredient for mixed-state quantum computation speedups. Here we show that correlations, as measured through the operator Schmidt rank, are indeed present in large amounts in the DQC1 circuit. This provides evidence for the preclusion of efficient classical simulation of DQC1 by means of a whole class of classical simulation algorithms, thereby reinforcing the conjecture that DQC1 leads to a genuine quantum computational speedup

Topological Quantum Error Correction with Optimal Encoding Rate

We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of arbitrary genus. We find a class of regular toric codes that are optimal. For physical implementations, we present planar topological codes.Comment: REVTEX4 file, 5 figure

An Universal Quantum Network - Quantum CPU

An universal quantum network which can implement a general quantum computing is proposed. In this sense, it can be called the quantum central processing unit (QCPU). For a given quantum computing, its realization of QCPU is just its quantum network. QCPU is standard and easy-assemble because it only has two kinds of basic elements and two auxiliary elements. QCPU and its realizations are scalable, that is, they can be connected together, and so they can construct the whole quantum network to implement the general quantum algorithm and quantum simulating procedure.Comment: 8 pages, Revised versio

Inequalities for quantum channels assisted by limited resources

The information capacities and ``distillability'' of a quantum channel are studied in the presence of auxiliary resources. These include prior entanglement shared between the sender and receiver and free classical bits of forward and backward communication. Inequalities and trade-off curves are derived. In particular an alternative proof is given that in the absence of feedback and shared entanglement, forward classical communication does not increase the quantum capacity of a channel.Comment: 8 pages, 4 figures (references updated, minor changes