Logics between classical reversible logic and quantum logic

Classical reversible logic and quantum computing share the common feature that all computations are reversible, each result of a computation can be brought back to the initial state without loss of information

On two subgroups of U(n), useful for quantum computing

As two basic building blocks for any quantum circuit, we consider the 1-qubit PHASOR circuit Phi(theta) and the 1-qubit NEGATOR circuit N(theta). Both are roots of the IDENTITY circuit. Indeed: both (NO) and N(0) equal the 2 x 2 unit matrix. Additionally, the NEGATOR is a root of the classical NOT gate. Quantum circuits (acting on w qubits) consisting of controlled PHASORs are represented by matrices from ZU(2(w)); quantum circuits consisting of controlled NEGATORs are represented by matrices from XU(2(w)). Here, ZU(n) and XU(n) are subgroups of the unitary group U(n): the group XU(n) consists of all n x n unitary matrices with all 2n line sums (i.e. all n row sums and all n column sums) equal to 1 and the group ZU(n) consists of all n x n unitary diagonal matrices with first entry equal to 1. Any U(n) matrix can be decomposed into four parts: U = exp(i alpha) Z(1)XZ(2), where both Z(1) and Z(2) are ZU(n) matrices and X is an XU(n) matrix. We give an algorithm to find the decomposition. For n = 2(w) it leads to a four-block synthesis of an arbitrary quantum computer

Design and synthesis of reversible logic

Energy lost during computation is an important issue for digital design. Today, all electronics devices suffer from energy lost due to the conventional logic system used. The amount of energy loss in the form of heat leads to immense challenges in nowadays circuit design. To overcome that, reversible logic has been invented. Since properties of reversible logic differ greatly than conventional logic, synthesis methods used for conventional logic cannot be used in reversible logic. In this dissertation, we proposed new synthesis algorithms and several circuit designs using reversible logic