[Paper Review] NMR experimental realization of seventh-order coupling transformations and the seven-qubit modified Deutsch-Jozsa algorithm

Daxiu Wei, Jun Luo+6 more|ArXiv.org|Jan 10, 2003

Molecular spectroscopy and chirality1 references3 citations

TL;DR

This paper proposes a scalable method using nth-order coupling operators to implement f-dependent phase transformations in the n-qubit modified Deutsch-Jozsa algorithm, leveraging J-couplings between neighboring spins in liquid-state NMR. The authors experimentally demonstrate the seven-qubit modified D-J algorithm and seventh-order coupling transformations, achieving the first experimental realization of seventh-order interactions in NMR quantum computing and enabling simulation of n-body interactions.

ABSTRACT

We propose a scalable method on the basis of nth-order coupling operators to construct f-dependent phase transformations in the n-qubit modified Deutsch-Jozsa (D-J) quantum algorithm. The novel n-qubit entangling transformations are easily implemented via J-couplings between neighboring spins. The seven-qubit modified D-J quantum algorithm and seventh-order coupling transformations are then experimentally demonstrated with liquid state nuclear magnetic resonance (NMR) techniques. The method may offer the possibility of creating generally entangled states of n qubits and simulating n-body interactions on n-qubit NMR quantum computers.

Motivation & Objective

• To develop a scalable method for constructing f-dependent phase transformations in the n-qubit modified Deutsch-Jozsa quantum algorithm.
• To enable experimental realization of multi-qubit entangling operations using only nearest-neighbor J-couplings in NMR systems.
• To demonstrate the feasibility of simulating n-body interactions via controlled coupling operators in liquid-state NMR quantum computers.
• To overcome experimental challenges in extending NMR quantum computation beyond five qubits, particularly signal-to-noise ratio and control of complex coupling networks.

Proposed method

• The method constructs f-dependent phase transformations using nth-order coupling operators, specifically designed for balanced functions in the modified D-J algorithm.
• It relies on J-couplings between neighboring spins to implement n-qubit entangling operations, avoiding the need for arbitrary spin-pair couplings.
• The key transformation is expressed as a sum of tensor products of Pauli-Z matrices and identity operators, forming a diagonal, entangling unitary operation.
• The experimental implementation uses a seven-qubit system from U-13C4-labeled crotonic acid, with four 13C and three 1H spins as qubits.
• Radiofrequency pulses and J-coupling evolution are used to implement the required unitary evolution, with first-order phase correction applied to improve signal fidelity.
• NMR spectra were acquired with 96 scans at 25°C on a Varian INOVA 600 spectrometer, using Gaussian-shaped pulses and selective excitation.

Experimental results

Research questions

• RQ1 Can f-dependent phase transformations in the n-qubit modified Deutsch-Jozsa algorithm be constructed using only nearest-neighbor J-couplings?
• RQ2 Is it feasible to experimentally realize seventh-order coupling transformations in liquid-state NMR systems?
• RQ3 Can the modified D-J algorithm be implemented with only n qubits instead of n+1, using a scalable coupling-based method?
• RQ4 How can n-body interactions be simulated in NMR quantum computers using only two-body interactions between adjacent spins?

Key findings

• The seven-qubit modified Deutsch-Jozsa algorithm was successfully implemented using only seven qubits, confirming the feasibility of the n-qubit version of the algorithm.
• Seventh-order coupling transformations were experimentally realized via J-couplings between neighboring spins, marking the first experimental demonstration of such high-order interactions in NMR.
• The experimental spectra showed at least one line with a π phase difference (emission) compared to the reference spectrum, confirming the presence of balanced functions with a single function call.
• The method enabled the creation of generally entangled states of n qubits using only nearest-neighbor interactions, overcoming the limitation of finding suitable coupling configurations in molecular systems.
• Phase errors in the spectra were attributed to imperfect pulses, inaccurate pulse durations, and imperfect refocusing of chemical shifts during J-coupling delays.
• The results demonstrate that n-body interactions can be simulated in NMR quantum computers through engineered coupling operators, even in the absence of direct n-body interactions.