Algorithmic cooling and scalable NMR quantum computers

doi:10.1073/pnas.241641898

Algorithmic cooling and scalable NMR quantum computers

^*Electrical Engineering Department, University of California, Los Angeles, CA 90095; ^†Electrical Engineering Department, College of Judea and Samaria, Ariel 44837, Israel; ^‡Computer Science Department, Technion, Technion City, Haifa 32000, Israel; ^¶Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109; and ^‖RAS Computer Analysis Laboratory, Sun Microsystems, Menlo Park, CA 94025

Communicated by N. David Mermin, Cornell University, Ithaca, NY (received for review June 19, 2001)

Abstract

We present here algorithmic cooling (via polarization heat bath)—a powerful method for obtaining a large number of highly polarized spins in liquid nuclear-spin systems at finite temperature. Given that spin-half states represent (quantum) bits, algorithmic cooling cleans dirty bits beyond the Shannon's bound on data compression, by using a set of rapidly thermal-relaxing bits. Such auxiliary bits could be implemented by using spins that rapidly get into thermal equilibrium with the environment, e.g., electron spins. Interestingly, the interaction with the environment, usually a most undesired interaction, is used here to our benefit, allowing a cooling mechanism. Cooling spins to a very low temperature without cooling the environment could lead to a breakthrough in NMR experiments, and our “spin-refrigerating” method suggests that this is possible. The scaling of NMR ensemble computers is currently one of the main obstacles to building larger-scale quantum computing devices, and our spin-refrigerating method suggests that this problem can be resolved.

Footnotes

↵ § To whom correspondence should be addressed. E-mail: talmo{at}cs.technion.ac.il.
↵ ** Individual addressing of qubits requires a slightly different bias for each one, which is easily achievable in practice.
↵ †† We refer to these qubits as bits, because no quantum effects are used in the cooling process.
↵ §§ Actually, adjusted bits that failed to purify are always dirtier than the RRTR bits, but supervisor bits are dirtier only as long as ɛ $\text{[math]}$ < ɛ₀. Therefore the CUT of the adjusted bits that failed to purify, 𝒞 (which is explained in the next subsection) is the main “engine” that cools the NMR system at all stages of the protocol.
↵ ¶¶ An algorithm with ℓ replaced by ℓ_j (different numbers of repetitions, depending on the bias-level j) could have some advantages but will not be as easy to analyze.
↵ ‡‡ Actually, the important contribution of ref. 10 is the result that in some neighborhood of the totally mixed state, all states are separable; hence, some pseudo-entangled state (a state for which the pseudo pure part is entangled) contains no entanglement. But ref. 10 does not prove (and does not claim to prove) that current NMR quantum computers do not perform quantum computation. We, in contrast, conjecture that the PPS technique and the work of ref. 10 form the first step in proving that quantum computing without entanglement is possible.
Abbreviations:

PPS,

pseudo-pure state;

RRTR,

rapidly reaching thermal relaxation;

BCS,

basic compression subroutine;

qubit,

quantum bit