Nuclear magnetic resonance quantum computing using liquid crystal solvents

Abstract

Liquid crystals offer several advantages as solvents for molecules used for nuclear magnetic resonance quantum computing (NMRQC). The dipolar coupling between nuclear spins manifest in the NMR spectra of molecules oriented by a liquid crystal permits a significant increase in clock frequency, while short spin-lattice relaxation times permit fast recycling of algorithms, and save time in calibration and signal-enhancement experiments. Furthermore, the use of liquid crystal solvents offers scalability in the form of an expanded library of spin-bearing molecules suitable for NMRQC. These ideas are demonstrated with the successful execution of a 2-qubit Grover search using a molecule ( 13 C 1 HCl 3 ) oriented in a liquid crystal and a clock speed eight times greater than in an isotropic solvent. Perhaps more importantly, five times as many logic operations can be executed within the coherence time using the liquid crystal solvent.

NMR Quantum Information Processing

“…Since spin is inherently a discrete quantum property which exists inside a finite Hilbert space, spin-1/2 systems are excellent quantum bits. Nuclear spins used in NMR QIP are typically the spin-1/2 nuclei of 1 H, 13 C, 19 F, 15 N, 31 P, or 29 Si atoms, but higher order spins such as spin-3/2 and 5/2 have also been experimentally investigated. In liquid-state NMR, these atoms are parts of molecules dissolved in a solvent, such that the system is typically extremely well approximated as being O (10 18 ) independent molecules.…”

“…While dipolar interactions are rapidly averaged away in a liquid, they play a significant role in liquid crystal [19,20] and solid state NMR QIP experiments.…”

Implementation of conditional phase-shift gate for quantum information processing by NMR, using transition-selective pulses

“…For example, the C 11ǫ type gates (Eqs. [24]- [26]) require one spin selective and two transition selective pulses.…”

“…The pulse sequence of C 11ǫ , C 1ǫ1 and C ǫ11 gates are given in Eqs. [24]- [26]. The SW AP 13 gate performs a swap between qubits 1 and 3, and is realized by a cascade of transition selective π pulses [12].…”

NMR Based Quantum Information Processing: Achievements and Prospects

“…It is the realization that NMR studies of dipolarly coupled spins provides a test bed for complex quantum dynamics that has led Chuang [133] and us to propose next generation QIP devices built from liquid crystals and solids, respectively. The solid state also offers an ideal test bed for larger studies of multi-body dynamics and of the transition from quantum to classical behavior [136].…”