2,036 research outputs found
Enumeration of reversible functions and its application to circuit complexity
We review combinational results to enumerate and classify reversible functions and investigate the application to circuit complexity. In particularly, we consider the effect of negating and permuting input and output variables and the effect of applying linear and affine transformations to inputs and outputs. We apply the results to reversible circuits and prove that minimum circuit realizations of functions in the same equivalence class differ at most in a linear number of gates in pres- ence of negation and permutation and at most in a quadratic number of gates in presence of linear and affine transformations
Techniques for the Synthesis of Reversible Toffoli Networks
This paper presents novel techniques for the synthesis of reversible networks
of Toffoli gates, as well as improvements to previous methods. Gate count and
technology oriented cost metrics are used. Our synthesis techniques are
independent of the cost metrics. Two new iterative synthesis procedure
employing Reed-Muller spectra are introduced and shown to complement earlier
synthesis approaches. The template simplification suggested in earlier work is
enhanced through introduction of a faster and more efficient template
application algorithm, updated (shorter) classification of the templates, and
presentation of the new templates of sizes 7 and 9. A novel ``resynthesis''
approach is introduced wherein a sequence of gates is chosen from a network,
and the reversible specification it realizes is resynthesized as an independent
problem in hopes of reducing the network cost. Empirical results are presented
to show that the methods are effective both in terms of the realization of all
3x3 reversible functions and larger reversible benchmark specifications.Comment: 20 pages, 5 figure
Visualizing Quantum Circuit Probability -- estimating computational action for quantum program synthesis
This research applies concepts from algorithmic probability to Boolean and
quantum combinatorial logic circuits. A tutorial-style introduction to states
and various notions of the complexity of states are presented. Thereafter, the
probability of states in the circuit model of computation is defined. Classical
and quantum gate sets are compared to select some characteristic sets. The
reachability and expressibility in a space-time-bounded setting for these gate
sets are enumerated and visualized. These results are studied in terms of
computational resources, universality and quantum behavior. The article
suggests how applications like geometric quantum machine learning, novel
quantum algorithm synthesis and quantum artificial general intelligence can
benefit by studying circuit probabilities.Comment: 17 page
Speed-up via Quantum Sampling
The Markov Chain Monte Carlo method is at the heart of efficient
approximation schemes for a wide range of problems in combinatorial enumeration
and statistical physics. It is therefore very natural and important to
determine whether quantum computers can speed-up classical mixing processes
based on Markov chains. To this end, we present a new quantum algorithm, making
it possible to prepare a quantum sample, i.e., a coherent version of the
stationary distribution of a reversible Markov chain. Our algorithm has a
significantly better running time than that of a previous algorithm based on
adiabatic state generation. We also show that our methods provide a speed-up
over a recently proposed method for obtaining ground states of (classical)
Hamiltonians.Comment: 8 pages, fixed some minor typo
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