Spectral Analysis Program (SAP)

Program eliminates or reduces time-consuming aspects of computation of power spectrum for high-frequency communication system. This program was written in FORTRAN IV for UNIVAC 1230 or 1108 computer

Two-message quantum interactive proofs and the quantum separability problem

Suppose that a polynomial-time mixed-state quantum circuit, described as a sequence of local unitary interactions followed by a partial trace, generates a quantum state shared between two parties. One might then wonder, does this quantum circuit produce a state that is separable or entangled? Here, we give evidence that it is computationally hard to decide the answer to this question, even if one has access to the power of quantum computation. We begin by exhibiting a two-message quantum interactive proof system that can decide the answer to a promise version of the question. We then prove that the promise problem is hard for the class of promise problems with "quantum statistical zero knowledge" (QSZK) proof systems by demonstrating a polynomial-time Karp reduction from the QSZK-complete promise problem "quantum state distinguishability" to our quantum separability problem. By exploiting Knill's efficient encoding of a matrix description of a state into a description of a circuit to generate the state, we can show that our promise problem is NP-hard with respect to Cook reductions. Thus, the quantum separability problem (as phrased above) constitutes the first nontrivial promise problem decidable by a two-message quantum interactive proof system while being hard for both NP and QSZK. We also consider a variant of the problem, in which a given polynomial-time mixed-state quantum circuit accepts a quantum state as input, and the question is to decide if there is an input to this circuit which makes its output separable across some bipartite cut. We prove that this problem is a complete promise problem for the class QIP of problems decidable by quantum interactive proof systems. Finally, we show that a two-message quantum interactive proof system can also decide a multipartite generalization of the quantum separability problem.Comment: 34 pages, 6 figures; v2: technical improvements and new result for the multipartite quantum separability problem; v3: minor changes to address referee comments, accepted for presentation at the 2013 IEEE Conference on Computational Complexity; v4: changed problem names; v5: updated references and added a paragraph to the conclusion to connect with prior work on separability testin

Leggett-Garg inequalities and the geometry of the cut polytope

The Bell and Leggett-Garg tests offer operational ways to demonstrate that non-classical behavior manifests itself in quantum systems, and experimentalists have implemented these protocols to show that classical worldviews such as local realism and macrorealism are false, respectively. Previous theoretical research has exposed important connections between more general Bell inequalities and polyhedral combinatorics. We show here that general Leggett-Garg inequalities are closely related to the cut polytope of the complete graph, a geometric object well-studied in combinatorics. Building on that connection, we offer a family of Leggett-Garg inequalities that are not trivial combinations of the most basic Leggett-Garg inequalities. We then show that violations of macrorealism can occur in surprising ways, by giving an example of a quantum system that violates the new "pentagon" Leggett-Garg inequality but does not violate any of the basic "triangle" Leggett-Garg inequalities.Comment: 5 pages, 1 figur

A Signal Distribution Network for Sequential Quantum-dot Cellular Automata Systems

The authors describe a signal distribution network for sequential systems constructed using the Quantum-dot Cellular Automata (QCA) computing paradigm. This network promises to enable the construction of arbitrarily complex QCA sequential systems in which all wire crossings are performed using nearest neighbor interactions, which will improve the thermal behavior of QCA systems as well as their resistance to stray charge and fabrication imperfections. The new sequential signal distribution network is demonstrated by the complete design and simulation of a two-bit counter, a three-bit counter, and a pattern detection circuit

Towards efficient decoding of classical-quantum polar codes

Known strategies for sending bits at the capacity rate over a general channel with classical input and quantum output (a cq channel) require the decoder to implement impractically complicated collective measurements. Here, we show that a fully collective strategy is not necessary in order to recover all of the information bits. In fact, when coding for a large number N uses of a cq channel W, N I(W_acc) of the bits can be recovered by a non-collective strategy which amounts to coherent quantum processing of the results of product measurements, where I(W_acc) is the accessible information of the channel W. In order to decode the other N (I(W) - I(W_acc)) bits, where I(W) is the Holevo rate, our conclusion is that the receiver should employ collective measurements. We also present two other results: 1) collective Fuchs-Caves measurements (quantum likelihood ratio measurements) can be used at the receiver to achieve the Holevo rate and 2) we give an explicit form of the Helstrom measurements used in small-size polar codes. The main approach used to demonstrate these results is a quantum extension of Arikan's polar codes.Comment: 21 pages, 2 figures, submission to the 8th Conference on the Theory of Quantum Computation, Communication, and Cryptograph

Towards musical interaction : 'Schismatics' for e-violin and computer.

This paper discusses the evolution of the Max/MSP patch used in schismatics (2007, rev. 2010) for electric violin (Violectra) and computer, by composer Sam Hayden in collaboration with violinist Mieko Kanno. schismatics involves a standard performance paradigm of a fixed notated part for the e-violin with sonically unfixed live computer processing. Hayden was unsatisfied with the early version of the piece: the use of attack detection on the live e-violin playing to trigger stochastic processes led to an essentially reactive behaviour in the computer, resulting in a somewhat predictable one-toone sonic relationship between them. It demonstrated little internal relationship between the two beyond an initial e-violin ‘action’ causing a computer ‘event’. The revisions in 2010, enabled by an AHRC Practice-Led research award, aimed to achieve 1) a more interactive performance situation and 2) a subtler and more ‘musical’ relationship between live and processed sounds. This was realised through the introduction of sound analysis objects, in particular machine listening and learning techniques developed by Nick Collins. One aspect of the programming was the mapping of analysis data to synthesis parameters, enabling the computer transformations of the e-violin to be directly related to Kanno’s interpretation of the piece in performance

Time dependent spin-dressing using a 3^3He atomic beam

We have performed high precision experimental measurements of spin precession using a dressed $^3$He atomic beam. Spin-dressing uses an oscillating magnetic field detuned to high frequency which is orthogonal to a static magnetic field to effectively change the gyromagnetic ratio of a spin. We verify the validity of the spin-dressing Hamiltonian in regions beyond the limiting solution in which the Larmor frequency is much smaller than the frequency of the dressing field. We also evaluate the effect of magnetic field misalignment, e.g. if the oscillating magnetic field is not orthogonal to the static magnetic field. Modulation of the dressing field parameters is also discussed, with a focus on whether such a modulation can be approximated merely as a time dependent, dressed gyromagnetic ratio. Furthermore, we discuss implications for a proposed search for the neutron electric dipole moment, which would employ spin-dressing to make the effective $^3$He and neutron magnetic moments equal.Comment: 10 pages, 7 figure