We consider the class of constant depth AND/OR circuits augmented with a layer of modular counting gates at the bottom layer, i.e AC◦MODm circuits. We show that the following holds for several types of gates G: by adding a gate of type G at the output, it is possible to obtain an equivalent probabilistic depth 2 circuit of quasipolynomial size consisting of a gate of type G at the output and a ...

Reversible Peres gates with more than two all over binary-valued control signals are discussed. Methods are disclosed for the low cost realization of this kind of Peres gates without requiring ancillary lines. It is shown that Peres gates with n control signals may be obtained with a quantum cost of 2n+1 – n – 2, using Feynman gates and controlled gates realizing the κ-th root of NOT, where κ =...

We address the problem of constructing quantum circuits to implement an arbitrary two-qubit quantum computation. We pursue circuits without ancilla qubits and as small a number of elementary quantum gates as possible. Our lower bound for worst-case optimal two-qubit circuits calls for at least 17 gates: 15 one-qubit rotations and 2 controlled-NOT ~CNOT! gates. We also constructively prove a wor...

We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values (x; y) to (x; xy)) is universal in the sense that all unitary operations on arbitrarily many bits n (U(2 n)) can be expressed as compositions of these gates. We investigate the number of the above gates required to implement other gates, such as generalized D...

Three-input TOFFOLI gates are heavily used when performing classical logic operations on quantum data, e.g., in reversible arithmetic circuits. However, in physical implementations TOFFOLI gates are decomposed into six CNOT gates and several one-qubit gates. Though this decomposition has been known for at least 10 years, we provide here the first demonstration of its CNOT-optimality. We first p...

The intrinsic idea of superdense coding is to find as many gates as possible such that they can be perfectly discriminated. In this paper, we consider a new scheme of discrimination of quantum gates, called ancillaassisted discrimination, in which a set of quantum gates on a d−dimensional system are perfectly discriminated with assistance from an r−dimensional ancilla system. The main contribut...

We present a new algorithm for classical simulation of quantum circuits over the Clifford+T gate set. The runtime of the algorithm is polynomial in the number of qubits and the number of Clifford gates in the circuit but exponential in the number of T gates. The exponential scaling is sufficiently mild that the algorithm can be used in practice to simulate medium-sized quantum circuits dominate...

Clustered voltage scaling is a power reducing method which does not affect the overall system performance. The main idea is to run gates on a non-critical path by a low-voltage supply. Since low-voltage gates are not able to drive high-voltage gates, level-converters are needed. In order to reduce the number of level-converters, which may cancel out the power savings, they are arranged in a clu...