We present new examples of the use of the quantum computer (QC) emulator. For educational purposes we describe the implementation of the CNOT and Toffoli gate, two basic building blocks of a QC, on a three qubit NMR-like QC.
The Quantum Computer Emulator (QCE) described in this paper consists of a simulator of a generic, general purpose quantum computer and a graphical user interface. The latter is used to control the simulator, to define the hardware of the quantum computer and to debug and execute quantum algorithms. QCE runs in a Windows 98/NT/2000/ME/XP environment. It can be used to validate designs of physically realizable quantum processors and as an interactive educational tool to learn about quantum computers and quantum algorithms. A detailed exposition is given of the implementation of the CNOT and the Toffoli gate, the quantum Fourier transform, Grover's database search algorithm, an order finding algorithm, Shor's algorithm, a three-input adder and a number partitioning algorithm. We also review the results of simulations of an NMR-like quantum computer.
Abstract It is shown theoretically how to use the EPR (electron paramagnetic resonance) technique, using electron spins as qubits, coupled with each other by the exchange interaction, to set the configuration of n qubits ( n = 1–4) at resonance, in conjunction with pulses, to construct the NOT (one qubit), CNOT (two qubits), CCNOT (three qubits), and CCCNOT (four qubits) Toffoli gates, which can be exploited to build a quantum computer. This is unique to EPR, wherein exchange‐coupled electron spins are used. This is different from NMR (Nuclear Magnetic Resonance), which uses nuclear spins as qubits, that do not couple with each other by the exchange interaction.
Abstract Universal quantum entangling gates are a crucial building block in the large‐scale quantum computation and quantum communication, and it is an important task to find simple ways to implement them. Here an effective quantum circuit for the implementation of a controlled‐NOT (CNOT) gate is constructed by introducing a non‐computational quantum state in the auxiliary space. Furthermore, the method is extended to the construction of a general n ‐control‐qubit Toffoli gate with qubit–qudit gates and single‐qudit gates. Based on the presented quantum circuits, the polarization CNOT and Toffoli gates with linear optics are designed by operating on the spatial‐mode degree of freedom of photons. The proposed optical schemes can be achieved with a higher success probability and no extra auxiliary photons are needed.