Dynamic Cooling on Contemporary Quantum Computers

Abstract

We study the problem of dynamic cooling whereby a target qubit is cooled at the expense of heating up <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:mi>N</a:mi><a:mo>−</a:mo><a:mn>1</a:mn></a:math> further identical qubits by means of a global unitary operation. A standard back-of-the-envelope high-temperature estimate establishes that the target qubit temperature can be dynamically cooled by at most a factor of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><d:mn>1</d:mn><d:mo>/</d:mo><d:msqrt><d:mi>N</d:mi></d:msqrt></d:math>. Here we provide the exact expression for the minimum temperature to which the target qubit can be cooled and reveal that there is a crossover from the high initial temperature regime, where the scaling is <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><g:mn>1</g:mn><g:mo>/</g:mo><g:msqrt><g:mi>N</g:mi></g:msqrt></g:math>, to a low initial temperature regime, where a much faster scaling of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><j:mn>1</j:mn><j:mo>/</j:mo><j:mi>N</j:mi></j:math> occurs. This slow, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><m:mn>1</m:mn><m:mo>/</m:mo><m:msqrt><m:mi>N</m:mi></m:msqrt></m:math> scaling, which was relevant for early high-temperature NMR quantum computers, is the reason dynamic cooling was dismissed as ineffectual around 20 years ago; the fact that current low-temperature quantum computers fall in the fast, <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><p:mn>1</p:mn><p:mo>/</p:mo><p:mi>N</p:mi></p:math> scaling regime, reinstates the appeal of dynamic cooling today. We further show that the associated work cost of cooling is exponentially more advantageous in the low-temperature regime. We discuss the implementation of dynamic cooling in terms of quantum circuits and examine the effects of hardware noise. We successfully demonstrate dynamic cooling in a three-qubit system on a real quantum processor. Since the circuit size grows quickly with <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><s:mi>N</s:mi></s:math>, scaling dynamic cooling to larger systems on noisy devices poses a challenge. We therefore propose a suboptimal cooling algorithm, whereby relinquishing a small amount of cooling capability results in a drastically reduced circuit complexity, greatly facilitating the implementation of dynamic cooling on near-future quantum computers. Published by the American Physical Society 2024

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