Fully quantum coherent control

Richard J. Nelson, Yaakov S. Weinstein, David G. Cory +1 more

In the conventional picture of quantum feedback, control sensors make measurements on a quantum system, a classical controller processes the results of the measurements, and semiclassical actuators act back on the system to alter its behavior. We describe and provide an experimental demonstration of an alternative method for quantum feedback control, in which the sensors, controller, and actuators of conventional feedback control are replaced with quantum systems that interact coherently with the system to be controlled. The resulting control system represents a fully coherent quantum feedback loop.

Warren S. Warren

Thomas Feurer

Kathleen Barsse, Romain Péchoux, Simon Perdrix

Coherent control, aka quantum control, is a central concept in quantum computing that is attracting increasing attention from both the quantum foundations and quantum software communities. Defining coherent control in the presence of recursion and measurement has long been known to be a major challenge. In particular, no-go results have been established for standard semantical domains like completely positive maps. We address this problem by introducing the first quantum programming language with recursion that allows for the coherent control of arbitrary quantum operations. We equip this language with both an operational and a denotational semantics that we prove to be adequate. To design these semantics, we show that combining coherent control, recursion, and measurement crucially requires describing the evolution of subprograms in the absence of input. To address this, the operational semantics takes into account a default evolution branch, while the denotational semantics uses the concept of coherent quantum operation, based on vacuum extensions. We strengthen the validity of our approach by developing an observational equivalence: two programs are equivalent if their probability of termination is the same in any context. The denotational semantics is shown to be fully abstract with respect to this observational equivalence.

Jeffrey L. Krause

Stefano Pasini, Götz Silvester Uhrig

We generalize the problem of the coherent control of small quantum systems to the case where the quantum bit (qubit) is subject to a fully general rotation. Following the ideas developed in Pasini et al (2008 Phys. Rev. A 77, 032315), the systematic expansion in the shortness of the pulse is extended to the case where the pulse acts on the qubit as a general rotation around an axis of rotation varying in time. The leading and the next-leading corrections are computed. For certain pulses we prove that the general rotation does not improve on the simpler rotation with fixed axis.