Quantum and classical resources for unitary design of open-system evolutions

Abstract

Abstract. A variety of tasks in quantum control, ranging from purification and cooling, to quantum stabilization and open-system simulation, rely on the ability to implement a target quantum channel over a specified time interval within prescribed accuracy. This can be achieved by engineering a suitable unitary dynamics of the system of interest along with its environment -which, depending on the available level of control, is fully or partly exploited as a coherent quantum controller. After formalizing a controllability framework for completely positive trace-preserving quantum dynamics, we provide sufficient conditions on the environment state and dimension that allow for the realization of relevant classes of quantum channelsincluding extreme channels, stochastic unitaries, or simply any channel. The results hinge on generalizations of Stinespring's dilation via a subsystem principle. In the process, we show that a conjecture by Lloyd on the minimal dimension of the environment required for arbitrary open-system simulation, albeit formally disproved, can in fact be salvaged -provided that classical randomization is included among the available resources. Existing measurement-based feedback protocols for universal simulation, dynamical decoupling, and dissipative state preparation are recast within the proposed coherent framework as concrete applications, and the resources they employ discussed in the light of the general results.

Nonconservative Forces via Quantum Reservoir Engineering

“…In particular, it has been shown that it is possible to preserve and even enhance the quantum dynamical features of a system by judiciously coupling the system to a dissipative environment. Applications of quantum reservoir engineering include amplification [8], nonreciprocal photon transmission [9,10], photon blockade [11], efficient photoinduced charge separation in solar energy conversion [12], binding of atoms [13,14], inducing phase transitions [15][16][17], implementation of quantum gates [18][19][20][21], and the generation of entangled [22][23][24][25][26][27], squeezed [28][29][30], and other exotic [31][32][33][34] quantum states.…”

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

“…(a) Thermodynamical consistency restricts the structure of the open system control GKLS master equation [20,163,164,169,596]. (b) Certain control task require a change of entropy, such as reset or thermalization [52,56,166,168,227,558,559]. Tasks that do not require a change of entropy may still benefit from it, for example by reaching the target while actively cooling [316,415].…”

“…An elementary and universal task is the reset transformation. The control objective is a fast reset to a desired state with high fidelity [52,56,227,558,559]. The fidelity is restricted by the third law of thermodynamics: Very high fidelity requires infinite resources [550].…”

Five-Spin Supramolecule for Simulating Quantum Decoherence of Bell States

“…However, simulating the effect of decoherence is very hard because it originates from the interaction of a relatively small subset of qubits with a huge number of environmental degrees of freedom. The resulting dissipative dynamics on the system qubits can be computed along different lines − based in general on adding to the system qubits with additional qubits modeling a (weak) coupling to the environment. Here, we show that such a quantum simulation can be performed on a 5-qubit supramolecule with tailored interactions.…”