Abstract
Heat-Bath Algorithmic Cooling is a set of techniques for producing highly pure quantum systems by utilizing a surrounding heat-bath and unitary interactions. These techniques originally used the thermal environment only to fully thermalize ancillas at the environment temperature. Here we extend HBAC protocols by optimizing over the thermalization strategy. We find, for any d-dimensional system in an arbitrary initial state, provably optimal cooling protocols with surprisingly simple structure and exponential convergence to the ground state. Compared to the standard ones, these schemes can use fewer or no ancillas and exploit memory effects to enhance cooling. We verify that the optimal protocols are robusts to various deviations from the ideal scenario. For a single target qubit, the optimal protocol can be well approximated with a Jaynes-Cummings interaction between the system and a single thermal bosonic mode for a wide range of environmental temperatures. This admits an experimental implementation close to the setup of a micromaser, with a performance competitive with leading proposals in the literature. The proposed protocol provides an experimental setup that illustrates how non-Markovianity can be harnessed to improve cooling. On the technical side we 1. introduce a new class of states called maximallyactivestates and discuss their thermodynamic significance in terms of optimal unitary control, 2. introduce a new set of thermodynamic processes, called β-permutations, whose access is sufficient to simulate a generic thermalization process, 3. show how to use abstract toolbox developed within the resource theory approach to thermodynamics to perform challenging optimizations, while combining it with open quantum system dynamics tools to approximate optimal solutions within physically realistic setups.
Highlights
Cooling is a central problem in quantum physics and in realizing technologies for quantum information processing
We use powerful techniques, developed within the resource theory approach to thermodynamics [7], to greatly extend an important class of cooling algorithms known as Heat-Bath Algorithmic Cooling (HBAC) [3, 4]
The asymptotically optimal protocol of this form is the Partner Pairing Algorithm (PPA), introduced in [8], whose asymptotic performance has been recently derived for a single target qubit starting in a maximally mixed state [9]
Summary
A general xHBAC will consist of a number of rounds and manipulate two types of systems, the target system. A important β-permutation, denoted by βopt, is the one that maximizes the ground state population of S among all dephasing thermalizations and, achieves the largest partial sums l i=0 p(ik). The optimal xHBAC protocol that uses no auxiliary systems A still has p(0k) → 1 exponentially in k Such protocol has the further advantage that the cooling operations do not change with the round k.
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