Generation of high-fidelity quantum control methods for multilevel systems

Abstract

In recent decades there has been a rapid development of methods to experimentally control individual quantum systems. A broad range of quantum control methods has been developed for two-level systems, however the complexity of multi-level quantum systems make the development of analogous control methods extremely challenging. Here, we exploit the equivalence between multilevel systems with SU(2) symmetry and spin-1/2 systems to develop a technique for generating new robust, high-fidelity, multi-level control methods. As a demonstration of this technique, we develop new adiabatic and composite multi-level quantum control methods and experimentally realise these methods using an 171 Yb + ion system. We measure the average infidelity of the process in both cases to be around 10 −4 , demonstrating that this technique can be used to develop high-fidelity multi-level quantum control methods and can, for example, be applied to a wide range of quantum computing protocols including implementations below the fault-tolerant threshold in trapped ions.

Asymptotic improvements to quantum circuits via qutrits

“…We focus on the 171 Yb + ion, which has been experimentally demonstrated as both a qubit and qutrit [10,11]. Trapped ions are often favored in QC schemes due to their long T 1 times.…”

Topological Uhlmann phase transitions for a spin-jparticle in a magnetic field

“…More recently, a generalization of the solid angle formula for arbitrary spin-j states has been found in terms of the state's Majorana constellation [23,24] which also gives insight on their entanglement properties [25]. From a more practical standpoint, the study of the geometric phase for a spin-1/2 is the workhorse to build 1-qubit holonomic quantum gates [9,26], with a possible extension to SU (2) qudit gates for higher spins [27]. This makes the study of the geometric phase for spin-j particles of vital importance.…”

Resource-Efficient Quantum Computing by Breaking Abstractions

“…Although qutrits incur higher per-operation error rates than qubits, this is compensated by dramatic reductions in runtimes and quantum gate counts. Moreover, our approach only applies qutrit operations in an intermediary stage: the input and output are still qubits, which is important for initialization and measurement on practical quantum devices [50], [51].…”