• Journal of Advanced Navigation Technology
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• v.14 no.5
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• pp.710-717
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• 2010

Even though there are 256 possible 1-qudit(1-variable quantum digit) functions in quaternary logic, the most useful functions are 4!=24 ones capable of representing in QGFSOP expressions by possible permuting of 0,1,2, and 3. In this paper, we propose a permutational literal(PL) representation and a QPL(Quaternary PL) gate which use the operands of a multiplicand A and an augend D in $Ax^C$+D(GF4) operation as a control variable of multi-cascaded PLs. And we also present new PL synthesis algorithms to synthesize QGFSOP expressed 24 (1-qudit) functions by applying three PL operators as ab(mutual permutation), + D(addition), and XA (multiplication). Finally architectures, circuits, and a CMOS implementation to realize proposed PL synthesis algorithms for $Ax^C$+D(GF4) functions are presented.

• The Journal of the Korea institute of electronic communication sciences
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• v.11 no.2
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• pp.165-170
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• 2016

The characteristic and application of a new duality structure in the $NCV-{\mid}v_1$ > library is studied in this paper. All unitary operations on arbitrarily many qudit's n can be expressed as composition of one- and two-qudit $NCV-{\mid}v_1$ > libraries if their state vectors are eigenvectors. This research provides an extended realization from Barenco's many bits n operator(U(2n)) which is applicable to only all positive polarity statevectors to whole polarity ones. At the control gate synthesis of a unitary operator, such an enhanced expansion is possible due to their symmetric duality property in the case of using both $NCV-{\mid}v_1$ > and $NCV^{\dag}-{\mid}v_1$ > libraries which make the AND predominantly dependent cascade synthesis possible.

• The Journal of the Korea institute of electronic communication sciences
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• v.11 no.1
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• pp.29-36
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• 2016

Recently a new class of quantum gate called $NCV-{\mid}v_1$ > library with low cost realizable potentialities is being watched with keen interest. The $NCV-{\mid}v_1$ > MCT gate is composed of AND cascaded-$CV-{\mid}v_1$ > gates to control the target qudit and its adjoint gates to erase junk ones. This paper presents a new symmetrical duality library named $NCV^{\dag}-{\mid}v_1$ > library corresponding to $NCV-{\mid}v_1$ > library. The new $NCV^{\dag}-{\mid}v_1$ > library can be operated on OR logic under certain conditions. By using both the $NCV-{\mid}v_1$ > and $NCV^{\dag}-{\mid}v_1$ > libraries it is possible to realize MPMCT gates, SOP and POS type synthesis of quantum logic circuits with extremely low cost, and expect dual gate property caused by different operational attributes with respect to forward and backward operations.