# Quantum Computation and Information Seminar

### Spin chain probe for quantum refrigeration and thermometry

We investigate the prospects for using a spin chain of length $N$ as a probe for refrigeration and thermometry on a collection of identical qubits, all prepared in a thermal state $\chi(T)$ with temperature $T$. This requires a minimal degree of control -– one need only perform a swap operation between a single spin of the probe and the thermal qubits. Each swap operation either cools the thermal qubit, or leaves it the same, and the state of the probe incrementally gets closer to $\chi(T)\otimes N$. It is this latter property, which we call pseudo-thermalisation, that allows the probe to be used for thermometry. By measuring each spin with the observable for the thermal qubits' Hamiltonian, the statistics can be used to infer $T$ up to some arbitrary accuracy. We then propose an algorithm which, provided prior knowledge of $T$ and the dynamics of the probe, will allow for optimising the cooling process. We show that the presence of local dephasing on the spins, or an imperfection of the swap operation, reduces the entropy reduction possible and slows the rate of pseudo-thermalisation. However, the thermal qubits always remain thermal, with a temperature no greater than $T$.

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Supported by: Phys-Info (IT), SQIG (IT), CeFEMA and CAMGSD, with funding from FCT, FEDER and EU FP7, specifically through the Doctoral Programme in the Physics and Mathematics of Information (DP-PMI), FCT strategic projects PEst-OE/EEI/LA0008/2013 and UID/EEA/50008/2013, IT project QuSim, project CRUP-CPU CQVibes, the FP7 Coordination Action QUTE-EUROPE (600788), and the FP7 projects Landauer (GA 318287) and PAPETS (323901).