“Spectral implementation” for creating a labeled pseudo-pure state and the Bernstein–Vazirani algorithm in a four-qubit nuclear magnetic resonance quantum processor

Abstract

A quantum circuit is introduced to describe the preparation of a labeled pseudo-pure state by multiplet-component excitation scheme which has been experimentally implemented on a 4-qubit nuclear magnetic resonance quantum processor. Meanwhile, we theoretically analyze and numerically investigate the low-power selective single-pulse implementation of a controlled-rotation gate, which manifests its validity in our experiment. Based on the labeled pseudo-pure state prepared, a 3-qubit Bernstein-Vazirani algorithm has been experimentally demonstrated by spectral implementation. The ''answers'' of the computations are identified from the split peak positions in the spectra of the observer spin, which are equivalent to projective measurements required by the algorithms.

Experimental demonstration of the Deutsch-Jozsa algorithm in homonuclear multispin systems

“…In early experiments, the DJ algorithm is realized in homonuclear or heteronuclear spin systems by using traditional high-power (hard) pulses and/or low-power (soft) spin (and/or transition) selective pulses with the refocusing schemes [5,6,16,18,20]. The low-power and long-duration selective pulses are, however, only for an approximation of the logic gate and involve inevitably an unwanted evolution under the internal Hamiltonian, which leads to additional conditional phases [29]. At the same time, a long duration also introduces errors due to relaxation or decoherence.…”

Spectral implementation of some quantum algorithms by one- and two-dimensional nuclear magnetic resonance

“…For this purpose, the oracle has to compute a function f a (x) = a.x . The scheme proposed by Berstein and Vazirani required an ancillary qubit and determined a n-qubit string with n+1 qubits, which has been demonstrated by NMR recently [36]. However, Du and his co-workers had simplified the scheme such that the ancillary qubit was not required [46].…”

“…Such a "spectral implementation" of a quantum computer was demonstrated by implementation of some logic gates by one-and two-dimensional NMR [33]. Later, "spectral implementation" of a complete set of logic gates and DJ-algorithm [34], Berstein-Vazirani problem [35] and quantum Fourier transform [36] has also been implemented by NMR. In this work we extend this range by spectrally implementing Grover's search algorithm, approximate quantum counting, a modified version of Berstein-Vazirani problem, and Hogg's algorithm.…”