3,505 research outputs found
Quantum Circuits for Incompletely Specified Two-Qubit Operators
While the question ``how many CNOT gates are needed to simulate an arbitrary
two-qubit operator'' has been conclusively answered -- three are necessary and
sufficient -- previous work on this topic assumes that one wants to simulate a
given unitary operator up to global phase. However, in many practical cases
additional degrees of freedom are allowed. For example, if the computation is
to be followed by a given projective measurement, many dissimilar operators
achieve the same output distributions on all input states. Alternatively, if it
is known that the input state is |0>, the action of the given operator on all
orthogonal states is immaterial. In such cases, we say that the unitary
operator is incompletely specified; in this work, we take up the practical
challenge of satisfying a given specification with the smallest possible
circuit. In particular, we identify cases in which such operators can be
implemented using fewer quantum gates than are required for generic completely
specified operators.Comment: 15 page
Quantum Multiplexers, Parrondo Games, and Proper Quantization
A quantum logic gate of particular interest to both electrical engineers and
game theorists is the quantum multiplexer. This shared interest is due to the
facts that an arbitrary quantum logic gate may be expressed, up to arbitrary
accuracy, via a circuit consisting entirely of variations of the quantum
multiplexer, and that certain one player games, the history dependent Parrondo
games, can be quantized as games via a particular variation of the quantum
multiplexer. However, to date all such quantizations have lacked a certain
fundamental game theoretic property.
The main result in this dissertation is the development of quantizations of
history dependent quantum Parrondo games that satisfy this fundamental game
theoretic property. Our approach also yields fresh insight as to what should be
considered as the proper quantum analogue of a classical Markov process and
gives the first game theoretic measures of multiplexer behavior.Comment: Doctoral dissertation, Portland State University, 138 pages, 22
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Non-unitary probabilistic quantum computing circuit and method
A quantum circuit performing quantum computation in a quantum computer. A chosen transformation of an initial n-qubit state is probabilistically obtained. The circuit comprises a unitary quantum operator obtained from a non-unitary quantum operator, operating on an n-qubit state and an ancilla state. When operation on the ancilla state provides a success condition, computation is stopped. When operation on the ancilla state provides a failure condition, computation is performed again on the ancilla state and the n-qubit state obtained in the previous computation, until a success condition is obtained
Bidirectional imperfect quantum teleportation with a single Bell state
We present a bidirectional modification of the standard one-qubit
teleportation protocol, where both Alice and Bob transfer noisy versions of
their qubit states to each other by using single Bell state and auxiliary
(trigger) qubits. Three schemes are considered: the first where the actions of
parties are governed by two independent quantum random triggers, the second
with single random trigger, and the third as a mixture of the first two. We
calculate the fidelities of teleportation for all schemes and find a condition
on correlation between trigger qubits in the mixed scheme which allows us to
overcome the classical fidelity boundary of 2/3. We apply the Choi-Jamiolkowski
isomorphism to the quantum channels obtained in order to investigate an
interplay between their ability to transfer the information,
entanglement-breaking property, and auxiliary classical communication needed to
form correlations between trigger qubits. The suggested scheme for
bidirectional teleportation can be realized by using current experimental
tools.Comment: 8 pages, 4 figures; published versio
Eigenlogic: a Quantum View for Multiple-Valued and Fuzzy Systems
We propose a matrix model for two- and many-valued logic using families of
observables in Hilbert space, the eigenvalues give the truth values of logical
propositions where the atomic input proposition cases are represented by the
respective eigenvectors. For binary logic using the truth values {0,1} logical
observables are pairwise commuting projectors. For the truth values {+1,-1} the
operator system is formally equivalent to that of a composite spin 1/2 system,
the logical observables being isometries belonging to the Pauli group. Also in
this approach fuzzy logic arises naturally when considering non-eigenvectors.
The fuzzy membership function is obtained by the quantum mean value of the
logical projector observable and turns out to be a probability measure in
agreement with recent quantum cognition models. The analogy of many-valued
logic with quantum angular momentum is then established. Logical observables
for three-value logic are formulated as functions of the Lz observable of the
orbital angular momentum l=1. The representative 3-valued 2-argument logical
observables for the Min and Max connectives are explicitly obtained.Comment: 11 pages, 2 table
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