3 research outputs found
Graph test of controllability in qubit arrays: A systematic way to determine the minimum number of external controls
The ability to implement any desired quantum logic gate on a quantum
processing unit is equivalent to evolution-operator controllability of the
qubits. Conversely, controllability analysis can be used to minimize the
resources, i.e., the number of external controls and qubit-qubit couplings,
required for universal quantum computing. Standard controllability analysis,
consisting in the construction of the dynamical Lie algebra, is, however,
impractical already for a comparatively small number of qubits. Here, we show
how to leverage an alternative approach, based on a graph representation of the
Hamiltonian, to determine controllability of arrays of coupled qubits. We
provide a complete computational framework and exemplify it for arrays of five
qubits, inspired by the ibmq_quito architecture. We find that the number of
controls can be reduced from five to one for complex qubit-qubit couplings and
to two for standard qubit-qubit couplings.Comment: 18 pages, 7 figures, 3 tables, 3 algorithm
Krotov: A Python implementation of Krotov's method for quantum optimal control
We present a new open-source Python package, krotov, implementing the quantum optimal control method of that name. It allows to determine time-dependent external fields for a wide range of quantum control problems, including state-to-state transfer, quantum gate implementation and optimization towards an arbitrary perfect entangler. Krotov's method compares to other gradient-based optimization methods such as gradient-ascent and guarantees monotonic convergence for approximately time-continuous control fields. The user-friendly interface allows for combination with other Python packages, and thus high-level customization
Determining the ability for universal quantum computing: Testing controllability via dimensional expressivity
Operator controllability refers to the ability to implement an arbitrary unitary in SU(N) and is a prerequisite for universal quantum computing. Controllability tests can be used in the design of quantum devices to reduce the number of external controls. Their practical use is hampered, however, by the exponential scaling of their numerical effort with the number of qubits. Here, we devise a hybrid quantum-classical algorithm based on a parametrized quantum circuit. We show that controllability is linked to the number of independent parameters, which can be obtained by dimensional expressivity analysis. We exemplify the application of the algorithm to qubit arrays with nearest-neighbour couplings and local controls. Our work provides a systematic approach to the resource-efficient design of quantum chips