![]() Accompanied by numerical examples, this paper presents an overview on existing theoretical developments for open optimal quantum control realizing state-to-state transfer, unitary gate optimization as well as state-preparation, and presents the numerical tools and implementation aspect as realized in Quandary, for deployment on modern high-performance computing platforms. Implemented in C++, Quandary uses the message passing paradigm for distributed memory computers that enables scalability to large numbers of compute cores. This paper gives an overview of the open-source code Quandary, which is designed to solve quantum control problems in larger open quantum systems modelled by Lindblad's master equation. Qutip or Krotov) is restricted to run on shared memory platforms, limiting their applicability to smaller quantum systems, in particular if interactions with the environment are taken into account. Most current software for quantum optimal control (e.g. These control pulses provide the fundamental interface between the quantum compiler and the quantum hardware. Quantum optimal control can be used to shape the control pulses for realizing unitary and non-unitary transformations of quantum states. More precisely, we upper-bound this number in terms of hypothesis-testing channel divergence between E and its fully dephased version, and we also relate it to the robustness of coherence of E. Finally, we analyze the effect that dephasing noise can have on a quantum channel E by investigating the number of distinguishable channels that E can be mapped to by a family of dephasing superchannels. Moreover, we prove that the coherence-generating power of a general quantum channel is a monotone under dephasing superchannels. We also find physical realizations of general ΞC through pre- and postprocessing employing dephasing channels with memory, and we show that memory plays a nontrivial role for quantum systems of dimension d>2. We prove that such superchannels ΞC form a particular subclass of Schur-product supermaps that act on the Jamiołkowski state J(E) of a channel E via a Schur product, J′=J∘C. These are defined as superchannels that affect only nonclassical properties of a quantum channel E, i.e., they leave invariant the transition probabilities induced by E in the distinguished basis. We characterize a class of environmental noises that decrease the coherent properties of quantum channels by introducing and analyzing the properties of dephasing superchannels. Although the calculations needed to extend our proofs to less symmetric codes seem to be extremely complicated, we nevertheless think that the results obtained for the 5−qubit quantum code reveal a general behavior pattern of quantum error correcting codes against qubit independent errors. We have been able to obtain these results thanks to the high symmetry of the 5−qubit quantum code. We also prove, for qubit independent errors, that if the correction circuit of the 5−qubit quantum code detects an error, then the corrected state has central symmetry and, as a consequence, its variance is maximal. We show that this code does not fix qubit independent errors, even assuming that the correction circuit does not introduce new errors. ![]() We restrict our study to the classical 5−qubit quantum error correcting code (proposed by Laflamme and some collaborators), which is able to correct arbitrary errors in a single qubit and is also fault-tolerant. We say that a quantum code does not fix a quantum computing error if its application does not reduce the variance of the error. The goal of this work is to analyse the performance of quantum error correction codes in regard to fixing independent errors in several qubits.
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