We introduce Fibonacci gates as a polynomial time computable primitive, and develop a theory of holographic algorithms based on these gates. The Fibonacci gates play the role of matchgates in Valiant’s theory [16]. We develop a signature theory and characterize all realizable signatures for Fibonacci gates. For bases of arbitrary dimensions we prove a universal bases collapse theorem. We apply ...

The quantum circuit is generalized to include non-unitary gates operated by quantum measurement, in order to reduce the number of the overhead of qubits required to ensure fault tolerance. A specific type of one-qubit non-unitary gates, together with the controlled-not gate and all one-qubit unitary gates, is shown to constitute a universal set of gates for the non-unitary quantum circuit. A re...

The versatile control of graphene's plasmonic modes via an external gate-voltage inspires us to design efficient electro-optical graphene plasmonic logic gates at the midinfrared wavelengths. We show that these devices are superior to the conventional optical logic gates because the former possess cut-off states and interferometric effects. Moreover, the designed six basic logic gates (i.e., NO...

Evans and Pippenger showed in 1998 that -noisy gates with 2 inputs are universal for arbitrary computation (i.e. can compute any function with bounded error), if all gates fail independently with probability and < 0 = (3 − √ 7)/4 ≈ 8.856%. We show that formulas built from gates with 2 inputs, in which each gate fails with probability at least 0 cannot be universal. Hence, there is a threshold o...

Quantum computing using two-dimensional NMR has recently been described using scalar coupling evolution technique [J. Chem. Phys., 109, 10603 (1998)]. In the present paper, we describe two-dimensional NMR quantum computing with the help of selective pulses. A number of logic gates are implemented using two and three qubits with one extra observer spin. Some many-in-one gates (or Portmanteau gat...

We are interested in speeding up approximate inference in Markov Random Fields (MRFs). We present a new method that uses gates—binary random variables that determine which factors of the MRF to use. Which gates are open depends on the observed evidence; when many gates are closed, the MRF takes on a sparser and faster structure that omits “unnecessary” factors. We train parameters that control ...

Abstract: In this paper we present ultra low-voltage and high speed CMOS domino Carry gates. For supply voltages below 325mV the delay for the proposed ultra low-voltage Carry gates are approximately 5% relative to a complementary CMOS Carry gate. Furthermore, the Energy Delay Product is less than 1% relative to complementary CMOS Carry gate at the same supply voltage. Different domino Carry ga...

In this paper we investigate single electron tunneling (SET) devices from the logic design perspective, using the SET tunnel junction’s ability to control the transport of individual electrons. More in particular, we present the implementation of a Full Adder using SET threshold gates. First, we augment the threshold gates with an active buffer in order to overcome feedback effects which can ap...

We present a collection of results concerning the structure of reversible gate classes over non-binary alphabets, including (1) a reversible gate class over non-binary alphabets that is not finitely generated (2) an explicit set of generators for the class of all gates, the class of all conservative gates, and a class of generalizations of the two (3) an embedding of the poset of reversible gat...

Galois Field Sum of Products (GFSOP) leads to efficient multi-valued reversible circuit synthesis using quantum gates. In this paper, we propose a new generalization of ternary Toffoli gate and another new generalized reversible ternary gate with discussion of their quantum realizations. Algorithms for synthesizing ternary GFSOP using quantum cascades of these gates are proposed. In both the sy...