Prospects and limitations of algorithmic cooling

Abstract

Heat-bath algorithmic cooling (AC) of spins is a theoretically powerful effective cooling approach, that (ideally) cools spins with low polarization exponentially better than cooling by reversible entropy manipulations alone. Here, we investigate the limitations and prospects of AC. For non-ideal and semioptimal AC, we study the impact of finite relaxation times of reset and computation spins on the achievable effective cooling. We derive, via simulations, the attainable cooling levels for given ratios of relaxation times using two semioptimal practicable algorithms. We expect this analysis to be valuable for the planning of future experiments. For ideal and optimal AC, we make use of lower bounds on the number of required reset steps, based on entropy considerations, to present important consequences of using AC as a tool for improving signal-to-noise ratio in liquid-state magnetic resonance spectroscopy. We discuss the potential use of AC for noninvasive clinical diagnosis and drug monitoring, where it may have significantly lower specific absorption rate (SAR) with respect to currently used methods.

Achievable Polarization for Heat-Bath Algorithmic Cooling

“…Based on this work, many cooling algorithms have been designed [6][7][8][9][10][11]. HBAC is not only of theoretical interest, experiments have already demonstrated an improvement in polarization using this protocol with a few qubits [12][13][14][15][16][17][18], where a few rounds of HBAC were reached; and some studies have even included the impact of noise [19].…”

“…Based on this work, many cooling algorithms have been designed [6][7][8][9][10][11]. HBAC is not only of theoretical interest, experiments have already demonstrated an improvement in polarization using this protocol with a few qubits [12][13][14][15][16][17][18], where a few rounds of HBAC were reached; and some studies have even included the impact of noise [19].Through numerical simulations, Moussa [7] and Schulman et al [8] observed that if the polarization of the bath ( b ) is much smaller than 2 −n , where n is the number of qubits used, the asymptotic polarization reached will be ∼ 2 n−2 b ; but when b is greater than 2 −n , a polarization of order one can be reached. Inspired also by the work of Patange [20], who investigated the use of algorithmic cooling on spins bigger than 1 2 (using NV center where the defect has an effective spin 1), we investigate the case of cooling a qubit using a general spin l, and extra qubits which get contact with a bath.…”

Algorithmic cooling in liquid-state nuclear magnetic resonance

“…We bypassed Shannon's bound in three different processes. The current optimal control methods (GRAPE), and better ones such as a second order GRAPE [42] and Krotov based optimization [43] could enable various applications of AC in magnetic resonance spectroscopy [13,14,44] and maybe also other potential applications [45][46][47][48][49][50][51][52][53][54]. ln (4) (see [23]), where ε C,eq is the carbons' equilibrium polarization.…”

Experimental heat-bath cooling of spins

“…[36,59]. The duration of each reset step is T WAIT = τ d, where in liquid state NMR τ is T 1 (reset), while in the solid state [31,32] τ was the characteristic time for spin diffusion.…”

“…In ref. [59], we analyze various cooling algorithms for several values of R. Ideally, T 1 (comp) T run T WAIT τ , where T run = N T WAIT is the runtime of the algorithm and N is the number of reset steps. A partial analysis is given in ref.…”