arXiv subjects

A. Spoerl

Publications and source records attributed to A. Spoerl.

3 recordsLinked to original sources

arXiv2009

Optimal Control for Generating Quantum Gates in Open Dissipative Systems

Optimal control methods for implementing quantum modules with least amount of relaxative loss are devised to give best approximations to unitary gates under relaxation. The potential gain by optimal control using relaxation parameters against time-optimal control is explored and exemplified in numerical and in algebraic terms: it is the method of choice to govern quantum systems within subspaces of weak relaxation whenever the drift Hamiltonian would otherwise drive the system through fast decaying modes. In a standard model system generalising decoherence-free subspaces to more realistic scenarios, openGRAPE-derived controls realise a CNOT with fidelities beyond 95% instead of at most 15% for a standard Trotter expansion. As additional benefit it requires control fields orders of magnitude lower than the bang-bang decouplings in the latter.

quant-ph↗

arXiv2008

Quantum CISC Compilation by Optimal Control and Scalable Assembly of Complex Instruction Sets beyond Two-Qubit Gates

We present a quantum CISC compiler and show how to assemble complex instruction sets in a scalable way. Enlarging the toolbox of universal gates by optimised complex multi-qubit instruction sets thus paves the way to fight decoherence for realistic settings. Compiling a quantum module into the machine code for steering a concrete quantum hardware device lends itself to be tackled by means of optimal quantum control. To this end, there are two opposite approaches: (i) one may use a decomposition into the restricted instruction set (RISC) of universal one- and two-qubit gates, which in turn have prefabricated translations into the machine code or (ii) one may prefer to generate the entire target module directly by a complex instruction set (CISC) of available controls. Here we advocate direct compilation up to the limit of system size a classical high-performance parallel computer cluster can reasonably handle. For going beyond these limits, i.e. for large systems we propose a combined way, namely (iii) to make recursive use of medium-sized building blocks generated by optimal control in the sense of a quantum CISC compiler. The advantage of the method over standard RISC compilations into one- and two-qubit universal gates is explored on the parallel cluster HLRB-II (with a total LINPACK performance of 63.3 TFlops/s) for the quantum Fourier transform, the indirect SWAP gate as well as for multiply-controlled CNOT gates. Implications for upper limits to time complexities are also derived.

quant-ph↗

arXiv2006

Which Quantum Evolutions Can Be Reversed by Local Unitary Operations? Algebraic Classification and Gradient-Flow-Based Numerical Checks

Generalising in the sense of Hahn's spin echo, we completely characterise those unitary propagators of effective multi-qubit interactions that can be inverted solely by {\em local} unitary operations on $n$ qubits (spins-$\tfrac{1}{2}$). The subset of $U\in \mathbf{SU}(2^n)$ satisfying $U^{-1}=K_1 U K_2$ with pairs of local unitaries $K_1, K_2\in\mathbf{SU}(2)^{\otimes n}$ comprises two classes: in type-I, $K_1$ and $K_2$ are inverse to one another, while in type-II they are not. {Type-I} consists of one-parameter groups that can jointly be inverted for all times $t\in\R{}$ because their Hamiltonian generators satisfy $K H K^{-1} = \Ad K (H) = -H$. As all the Hamiltonians generating locally invertible unitaries of type-I are spanned by the eigenspace associated to the eigenvalue -1 of the {\em local} conjugation map $\Ad K$, this eigenspace can be given in closed algebraic form. The relation to the root space decomposition of $\mathfrak{sl}(N,\C{})$ is pointed out. Special cases of type-I invertible Hamiltonians are of $p$-quantum order and are analysed by the transformation properties of spherical tensors of order $p$. Effective multi-qubit interaction Hamiltonians are characterised via the graphs of their coupling topology. {Type-II} consists of pointwise locally invertible propagators, part of which can be classified according to the symmetries of their matrix representations. Moreover, we show gradient flows for numerically solving the decision problem whether a propagator is type-I or type-II invertible or not by driving the least-squares distance $\norm{K_1 e^{-itH} K_2 - e^{+itH}}^2_2$ to zero.

quant-ph↗