Generalising Unitary Time Evolution

F. Alberto Grünbaum, L. Velázquez, Albert H. Werner +1 more

Dimpi Thakuria, Abhay Srivastav, Brij Mohan +2 more

Abstract The quantum speed limit describes how quickly a quantum system can evolve in time from an initial state to a final state under a given dynamics. Here, we derive a generalised quantum speed limit (GQSL) for arbitrary time-continuous evolution using the geometrical approach of quantum mechanics. The GQSL is applicable for quantum systems undergoing unitary, non-unitary, completely positive, non-completely positive and relativistic quantum dynamics. This reduces to the well known standard quantum speed limit (QSL), i.e. the Mandelstam-Tamm bound when the quantum system undergoes unitary time evolution. Using our formalism, we then obtain a quantum speed limit for non-Hermitian quantum systems. To illustrate our findings, we have estimated the quantum speed limit for a time-independent non-Hermitian system as well as for a time-dependent non-Hermitian system namely the Bethe-Lamb Hamiltonian for general two-level system.

Stephen Mark Barnett, Anthony Chefles, David Thomas Pegg +1 more

We develop and discuss noveltypes of generalisedquantum measurement. The associated non-unitary time evolution enables the manipulation of quantum states in ways that are not achievable by unitary operations. Particular emphasis is given to quantum optical realisations. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Tatsuhiko N. Ikeda

Bálint Koczor, Simon C. Benjamin

Variational quantum circuits are promising tools whose efficacy depends on their optimisation method. For noise-free unitary circuits, the quantum generalisation of natural gradient descent was recently introduced. The method can be shown to be equivalent to imaginary time evolution, and is highly effective due to a metric tensor reconciling the classical parameter space to the device's Hilbert space. Here we generalise quantum natural gradient to consider arbitrary quantum states (both mixed and pure) via completely positive maps; thus our circuits can incorporate both imperfect unitary gates and fundamentally non-unitary operations such as measurements. Whereas the unitary variant relates to classical Fisher information, here we find that quantum Fisher information defines the core metric in the space of density operators. Numerical simulations indicate that our approach can outperform other variational techniques when circuit noise is present. We finally assess the practical feasibility of our implementation and argue that its scalability is only limited by the number and quality of imperfect gates and not by the number of qubits.