Algorithmic cooling in liquid-state nuclear magnetic resonance

Abstract

Algorithmic cooling is a method that employs thermalization to increase qubit purification level, namely it reduces the qubit-system's entropy. We utilized gradient ascent pulse engineering (GRAPE), an optimal control algorithm, to implement algorithmic cooling in liquid state nuclear magnetic resonance. Various cooling algorithms were applied onto the three qubits of 13 C2-trichloroethylene, cooling the system beyond Shannon's entropy bound in several different ways. In particular, in one experiment a carbon qubit was cooled by a factor of 4.61. This work is a step towards potentially integrating tools of NMR quantum computing into in vivo magnetic resonance spectroscopy.

Algorithmic quantum heat engines

“…One of the computational qubits operated as target qubit which is going to be cooled by applying PPA while other computational qubits play a role in entropy compression [33]. This cooling process can be implemented arXiv:1901.01166v1 [quant-ph] 4 Jan 2019 with a minimal system composed of just 3-qubit [32][33][34][35]. For the four-stroke engine, we consider the target qubit as the working fluid (see Fig.…”

“…We used parameters of 13 C 2 -trichloroethylene (TCE) (see Table I) with paramagnetic reagent Cr(acac) 3 in cloroform-d solution (CDCl 3 ) in our numerical calculations, which are also experimentally used for HBAC in Refs. [34,35]. Carbon-1 and Carbon-2 qubits are classified as the target and the compression qubits.…”

“…Here we, propose to replace adiabatic steps by SWAP operations while the cooling step by an algorithmic cooling [32][33][34][35][36][37][38][39][40][41][42][43][44][45]. By this way, NMR thermal device operation would closely resemble an NMR quantum computer [46][47][48][49] albeit processing a completely noisy input.…”

Heat Bath Algorithmic Cooling with Spins: Review and Prospects

“…Meanwhile, Chang et al implemented cooling solely by the final compression gate on three fluorines in C 2 F 3 BR using LSNMR. Full implementation of HBAC in LSNMR was accomplished much later in [21].…”

Strong algorithmic cooling in large star-topology quantum registers

“…Here, the reset qubits periodically release their excess entropy to a heat-bath so that higher cooling of the computation qubit can be achieved by constructive iterations of AC. Since then, several HBAC algorithms have been proposed [10][11][12][13][14] and numerous experimental studies have also been reported [15][16][17][18][19][20][21] which use three or five qubit entropy compression circuits as the building block for AC. More recently asymptotic bounds for HBAC algorithms have been estimated numerically by Raeisi et * mahesh.ts@iiserpune.ac.in al.…”