Single qubit operations with base squeezed coherent states

In quantum computing with base either coherent or squeezed coherent states, information is encoded into coherent states with opposite amplitudes. To exploit the base states in quantum computation, we need arbitrary qubit rotations plus a two-qubit gate such as controlled-Z gate to simulate any multiqubit unitary transformations. We develop an approach to realize single qubit operations with the base squeezed coherent states. The optical setup requires a resource of the base squeezed coherent states, unbalanced beam splitter whose transmittance tends to unity and photon counters in auxiliary modes. A successful two-photon subtraction from transmitted beam is heralded by two-photon click in auxiliary modes where tiny part of the initial beam is detected. The thrust of the method is that it achieves a high fidelity without photodetectors with a high efficiency or a single-photon resolution. We observe that there is wide diapason of values of the parameters that provide performance of single qubit operations with the base states. The problem is resolved in Wigner representation to take into account imperfections of the optical devices.