Implementing Logic Gates and the Deutsch–Jozsa Quantum Algorithm by Two-Dimensional NMR Using Spin- and Transition-Selective Pulses

Abstract

Quantum logical operations using two-dimensional NMR have recently been described using the scalar coupling evolution technique [J. Chem. Phys. 109, 10603 (1998)]. In the present paper, we describe the implementation of quantum logical operations using two-dimensional NMR, with the help of spin-and transitionselective pulses. A number of logic gates are implemented using two and three qubits with one extra observer spin. Some manyin-one gates (or Portmanteau gates) are also implemented. Toffoli gate (or AND/NAND gate) and OR/NOR gates are implemented on three qubits. The Deutsch-Jozsa quantum algorithm for one and two qubits, using one extra work qubit, has also been implemented using spin-and transition-selective pulses after creating a coherent superposition state in the two-dimensional methodology.

Singlet-state creation and universal quantum computation in NMR using a genetic algorithm

“…SQR and C-NOT gates using hard pulses (Sec. III A 1 and III A 2) is valid for higher spin systems with homonuclear spin pairs (for example 1 H − 1 H − 19 F − 19 F system in 2,3-Difluro-6-nitrophenol [22]). …”

“…For single qubit rotation (SQR) in the above system, one can use spin selective pulses (low power, long R.F pulses) which will excite a small spectral region around the spin to be selected [22]. On the other hand, by using the natural chemical shift difference between two spins, we show here how to implement SQR with global hard (non-selective) pulses.…”

Implementation of a Deutsch-like quantum algorithm utilizing entanglement at the two-qubit level on an NMR quantum-information processor

“…Thus far, NMR has been the most successful method employed to physically implement small quantum information processors and to test the power of intrinsically quantum algorithms [6,7]. The visualisation of a spin-1/2 particle as a qubit, combined with existing multi-dimensional NMR methods has led to breakthroughs in pseudopure state preparation [7][8][9][10], the demonstration of universal quantum logic gates [11][12][13][14][15], and the implementation of various quantum algorithms [16][17][18][19][20][21][22][23][24].…”

Programmable quantum-state discriminator by nuclear magnetic resonance

“…Nuclear magnetic resonance (NMR) has played a leading role for practical demonstration of quantum algorithms and gates [12,13,14,15,16,17,18,19]. .…”

“…. The unitary operators needed for implementation of these quantum circuits have mostly been realized using spin selective as well as transition selective radio frequency pulses and coupling evolution, utilizing spin-spin (J) or dipolar couplings among the spins [12,13,14,15,16,17,18,19] . In this paper we demonstrate the implementation of quantum state discriminator which discriminates the pair of non orthogonal states as well as orthogonal states which are symmetric about a particular state, conditioned on the state of the ancilla qubit.…”