Cooling the qubit into a pure initial state is crucial for realizing fault-tolerant quantum information processing. Here we envisage a star-topology arrangement of reset and computation qubits for this purpose. The reset qubits cool or purify the computation qubit by transferring its entropy to a heat-bath with the help of a heat-bath algorithmic cooling procedure. By combining standard NMR methods with powerful quantum control techniques, we cool central qubits of two large startopology systems, with 13 and 37 spins respectively. We obtain polarization enhancements by a factor of over 24, and an associated reduction in the spin temperature from 298 K down to 12 K. Exploiting the enhanced polarization of computation qubit, we prepare combination-coherences of orders up to 15. By benchmarking the decay of these coherences we investigate the underlying noise process. Further, we also cool a pair of computation qubits and subsequently prepare them in an effective pure-state.

Weak measurements done on a subsystem of a bipartite system having both classical and nonClassical correlations between its components can potentially reveal information about the other subsystem with minimal disturbance to the overall state. We use weak quantum discord and the fidelity between the initial bipartite state and the state after measurement to construct a cost function that accounts for both the amount of information revealed about the other system as well as the disturbance to the overall state. We investigate the behaviour of the cost function for families of two qubit states and show that there is an optimal choice that can be made for the strength of the weak measurement.NonClassical correlations in quantum states including, but not limited to, entanglement has been a topic of significant interest in the recent past because of the potential and promise held forth by quantum information processing and quantum technologies [1][2][3]. Ollivier and Zurek [4] and independently, Henderson and Vedral [5], noted that mixed quantum states allowed for the possibility of having nonClassical correlations other than entanglement and quantified the same in terms of the quantum discord. A variety of alternate measures of nonClassical correlations in a bipartite quantum state were subsequently proposed [2,6,7]. A general strategy followed in constructing measures of nonClassical correlations is to subtract the 'classical' correlations in a bipartite state from the 'total' correlations; treating what remains as a quantifier of the nonClassical or quantum correlations in the state [8].Typically, entropic measures like the mutual information and relative entropy are used to quantify the correlations in constructing the various measures. Quantifying the total correlations in a bipartite quantum state is straightforward, for instance, using the quantum mutual information. However, defining the 'classical' part of the total correlations is often a relatively ambiguous task. One strategy is to posit classical observers measuring one or both of the subsystems so as to quantify the correlations in the resultant measurement statistics. To achieve this, the classical observers utilize the classical counterpart of the same entropic measure of quantum correlations that was used to quantify the total correlations. Significantly though, in the quantum case, the measurement statistics depend on the measurement done. This necessitates a further maximisation of the measure of classical correlations over all measurement strategies in order to disambiguate the discord-like measure to the maximum extent possible. In the ensuing treatment, quantum discord is considered as the example of nonClassical correlations. The total correlations in a bipartite state ρ AB are measured in terms of the quantum mutual information defined aswhere

Global unitary transformations (optswaps) that optimally increase the bias of any mixed computation qubit in a quantum system -represented by a diagonal density matrix -towards a particular state of the computational basis which, in effect, increases its purity are presented. Quantum circuits that achieve this by implementing the above data compression technique -a generalization of the 3B-Comp [Fernandez, Lloyd, Mor, Roychowdhury (2004); arXiv: quant-ph/0401135] used before -are described. These circuits enable purity increment in the computation qubit by maximally transferring part of its von Neumann or Shannon entropy to any number of surrounding qubits and are valid for the complete range of initial biases. Using the optswaps, a practicable new method that algorithmically achieves hierarchy-dependent cooling of qubits to their respective limits in an engineered quantum register opened to the heat-bath is delineated. In addition to multi-qubit purification and satisfying two of DiVincenzo's criteria for quantum computation in some architectures, the implications of this work for quantum data compression are discussed.

with citation errors in the eleventh sentence in Section I. The eleventh sentence in Section I has been replaced with "Over the years, the existence of a bound for HBAC [11], followed by its numerical estimate [14] and analytical proof [22], as well as the achievable limiting polarization [23] have been investigated." The sentence has been replaced as of 16 December 2019. The sentence is incorrect in the printed version of the journal.

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