We prove exponentially small upper bounds on the correlation between parity and quadratic polynomials mod 3. One corollary of this is that in order to compute parity, circuits consisting of a threshold gate at the top, mod 3 gates in the middle, and AND gates of fan-in two at the inputs must be of size 2. This is the first result of this type for general mod 3 subcircuits with ANDs of fan-in gr...

We prove exponentially small upper bounds on the correlation between parity and quadratic polynomials mod 3: One corollary of this is that in order to compute parity, circuits consisting of a threshold gate at the top, mod 3 gates in the middle, and AND gates of fan-in two at the inputs must be of size 2OðnÞ: This is the first result of this type for general mod 3 subcircuits with ANDs of fan-i...

Advanced Encryption Standard (AES) is the symmetric key standard for encryption and decryption. In this work, a 128-bit AES encryption and decryption using Rijndael Algorithm is designed and synthesized using verilog code. The fault detection scheme for their hardware implementation plays an important role in making the AES robust to the internal and malicious faults. In the proposed AES, a com...

Reversible logic is becoming an important research area which aims mainly to reduce power dissipation during computing. In this paper we introduce a new parity preserving reversible gate PPPG (a 5x5 gate). This gate is universal in the sense it can synthesize any arbitrary Boolean function. It is also a parity preserving gate in which the parity of input matches the parity of the output. This p...

We consider the resource bounded quantum circuit model with circuits restricted by the number of qubits they act upon and by their depth. Focusing on natural universal sets of gates which are familiar from classical circuit theory, several new lower bounds for constant depth quantum circuits are proved. The main result is that parity (and hence fanout) requires log depth quantum circuits, when ...

We investigate a class QNC(ADD) that is QNC with gates for addition of two binary numbers, where QNC is a class consisting of quantum operations computed by constant-depth quantum circuits. We show that QNC(ADD) = QAC(PAR) = QAC(MUL), where QAC(PAR) and QAC(MUL) are QAC with gates for parity and multiplication respectively, and where QAC is QNC with Toffoli gates of arbitrary fan-in. In the cla...

In this paper, we present a parity-preserving QED3 with spontaneous breaking of a local U(1)-symmetry. The breaking is accomplished by a potential of the φ6type. It is shown that a net attractive interaction appears in the Møller scattering (s and p-wave scattering between two electrons) as mediated by the gauge field and a Higgs scalar. This might favour a pair-condensation mechanism.

Recently, Bravyi and König have shown that there is a trade-off between fault-tolerantly implementable logical gates and geometric locality of stabilizer codes. They consider locality-preserving operations which are implemented by a constant-depth geometrically-local circuit and are thus fault-tolerant by construction. In particular, they shown that, for local stabilizer codes in D spatial dime...