243,731 research outputs found
Introducing a Research Program for Quantum Humanities: Theoretical Implications
Quantum computing is a new form of computing that is based on the principles
of quantum mechanics. It has the potential to revolutionize many fields,
including the humanities and social sciences. The idea behind quantum
humanities is to explore the potential of quantum computing to answer new
questions in these fields, as well as to consider the potential societal
impacts of this technology. This paper proposes a research program for quantum
humanities, which includes the application of quantum algorithms to humanities
and social science research, the reflection on the methods and techniques of
quantum computing, and the evaluation of its potential societal implications.
This research program aims to define the field of quantum humanities and to
establish it as a meaningful part of the humanities and social sciences.Comment: 21 pages, 2 figure
Four-level and two-qubit systems, sub-algebras, and unitary integration
Four-level systems in quantum optics, and for representing two qubits in
quantum computing, are difficult to solve for general time-dependent
Hamiltonians. A systematic procedure is presented which combines analytical
handling of the algebraic operator aspects with simple solutions of classical,
first-order differential equations. In particular, by exploiting and sub-algebras of the full SU(4)
dynamical group of the system, the non-trivial part of the final calculation is
reduced to a single Riccati (first order, quadratically nonlinear) equation,
itself simply solved. Examples are provided of two-qubit problems from the
recent literature, including implementation of two-qubit gates with Josephson
junctions.Comment: 1 gzip file with 1 tex and 9 eps figure files. Unpack with command:
gunzip RSU05.tar.g
Quantum vs. Classical Read-once Branching Programs
The paper presents the first nontrivial upper and lower bounds for
(non-oblivious) quantum read-once branching programs. It is shown that the
computational power of quantum and classical read-once branching programs is
incomparable in the following sense: (i) A simple, explicit boolean function on
2n input bits is presented that is computable by error-free quantum read-once
branching programs of size O(n^3), while each classical randomized read-once
branching program and each quantum OBDD for this function with bounded
two-sided error requires size 2^{\Omega(n)}. (ii) Quantum branching programs
reading each input variable exactly once are shown to require size
2^{\Omega(n)} for computing the set-disjointness function DISJ_n from
communication complexity theory with two-sided error bounded by a constant
smaller than 1/2-2\sqrt{3}/7. This function is trivially computable even by
deterministic OBDDs of linear size. The technically most involved part is the
proof of the lower bound in (ii). For this, a new model of quantum
multi-partition communication protocols is introduced and a suitable extension
of the information cost technique of Jain, Radhakrishnan, and Sen (2003) to
this model is presented.Comment: 35 pages. Lower bound for disjointness: Error in application of info
theory corrected and regularity of quantum read-once BPs (each variable at
least once) added as additional assumption of the theorem. Some more informal
explanations adde
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