Time-optimal polarization transfer from an electron spin to a nuclear spin

Polarization transfers from an electron spin to a nuclear spin are essential for various physical tasks, such as dynamic nuclear polarization in nuclear magnetic resonance and quantum state transformations on hybrid electron-nuclear spin systems. We present time-optimal schemes for electron-nuclear polarization transfers which improve on conventional approaches and will have wide applications.Comment: 11 pages, 8 figure

Large Scale Simulation of Ideal Quantum Computers on SMP-Clusters

Quantum processing of information has become a rapidly evolving field of research in physics, mathematics, computer science, and engineering [1] and has led to substantial progress in quantum computation, quantum communication and control of quantum systems. Quantum computers have become of great interest primarily due to their potential of solving certain computationally hard problems such as factoring integers [2] and searching databases faster than a conventional computer [3]. Candidate technologies for realizing quantum computers include trapped ions, atoms in QED cavities, Josephson junctions, nuclear or electronic spins, quantum dots, and molecular magnets. Grover’s quantum search [3] and Shor’s quantum prime factorization algorithm [2] have been successfully implemented on systems of up to 7 qubits using liquid NMR techniques [4], experimentally demonstrating the viability of the concept of quantum computation. In spite of this impressive development, a demonstration that quantum computation can solve a non-trivial problem is still lacking. To be of practical use, quantum computers will need error correction, which requires at least several tens of qubits and the ability to perform hundreds of gate operations. This imposes a number of strict requirements [5], and narrows down the list of candidate physical systems. Simulating numbers of qubits in this range is important to numericall

Quantum Shift Scheduling - A Comparison to Classical Approaches

Solving discrete optimization problems with constraints is a very common task in industry and research as it is fundamental in solving many planning tasks. In this paper we will look at an instance of a time table problem for generating shift schedules at the German Space Operation Center (GSOC). We describe the implementation of a quantum approach and compare the differences to classical optimization strategies, knowing that the problem sizes given to the quantum systems are not competitive yet. By doing so we are establishing a software chain that is able to map our problem to different physical systems which paves the way to problem solving as a hybrid solution where sub-problems are distributed among classical and quantum hardware. In this study we included three approaches to tackle the described problem. For the quantum part, we included a programmatically generated quantum circuit that yields a solution to a (sub) problem using Grovers algorithm, able to be run on any general quantum computer with sufficiently many qubits of sufficiently high quality. On the classical side, as a validation and benchmark reference, we use a heuristic search method, implemented by GSOCs own planning tool set Plato and PINTA (Lenzen et al. 2012; Nibler et al. 2021) as well as a constraint integer programming formulation solved by an external software framework, such as e. g. GLPK or SCIP (Gamrath et al. 2020). This paper builds on and extends results from (Scherer et al. 2021)

OnCall Operator Scheduling for Satellites with Grover's Algorithm

The application of quantum algorithms on some problems in NP promises a significant reduction of time complexity. This work uses Grover's Algorithm, designed to search an unstructured database with quadratic speedup, to find valid a solution for an instance of the on-call operator scheduling problem at the German Space Operation Center. We explore new approaches in encoding the problem and construct the Grover oracle automatically from the given constraints and independent of the problem size. Our solution is not designed for currently available quantum chips but aims to scale with their growth in the next years

Nuclear-magnetic-resonance quantum calculations of the Jones polynomial

The repertoire of problems theoretically solvable by a quantum computer recently expanded to include the approximate evaluation of knot invariants, specifically the Jones polynomial. The experimental implementation of this evaluation, however, involves many known experimental challenges. Here we present experimental results for a small-scale approximate evaluation of the Jones polynomial by nuclear magnetic resonance (NMR); in addition, we show how to escape from the limitations of NMR approaches that employ pseudopure states. Specifically, we use two spin-1/2 nuclei of natural abundance chloroform and apply a sequence of unitary transforms representing the trefoil knot, the figure-eight knot, and the Borromean rings. After measuring the nuclear spin state of the molecule in each case, we are able to estimate the value of the Jones polynomial for each of the knots

des John von Neumann-Instituts für Computing

Computing (NIC) und hiermit des ZAM als wesentlicher Säule des NIC. Um den akademischen Nachwuch