Signal processing techniques for efficient compilation of controlled rotations in trapped ions

Quantum logic gates with many control qubits are essential in many quantum algorithms, but remain challenging to perform in current experiments. Trapped ion quantum computers natively feature a different type of entangling operation, namely the Molmer-Sorensen (MS) gate which effectively applies an Ising interaction to all qubits at the same time. We consider a sequence of equal all-to-all MS operations, interleaved with single qubit gates that act only on one special qubit. Using a connection with quantum signal processing techniques, we find that it is possible to perform an arbitray SU(2) rotation on the special qubit if and only if all other qubits are in the state |1>. Such controlled rotation gates with N-1 control qubits require 2N applications of the MS gate, and can be mapped to a conventional Toffoli gate by demoting a single qubit to ancilla.Comment: 14 pages, 3 figures, comments welcome. v3 includes several fixes and adds an appendix with explicit angle

Constructing quantum circuits with global gates

There are various gate sets that can be used to describe a quantum computation. A particularly popular gate set in the literature on quantum computing consists of arbitrary single-qubit gates and 2-qubit CNOT gates. A CNOT gate is however not always the natural multi-qubit interaction that can be implemented on a given physical quantum computer, necessitating a compilation step that transforms these CNOT gates to the native gate set. A particularly interesting case where compilation is necessary is for ion trap quantum computers, where the natural entangling operation can act on more than 2 qubits and can even act globally on all qubits at once. This calls for an entirely different approach to constructing efficient circuits. In this paper we study the problem of converting a given circuit that uses 2-qubit gates to one that uses global gates. Our three main contributions are as follows. First, we find an efficient algorithm for transforming an arbitrary circuit consisting of Clifford gates and arbitrary phase gates into a circuit consisting of single-qubit gates and a number of global interactions proportional to the number of non-Clifford phases present in the original circuit. Second, we find a general strategy to transform a global gate that targets all qubits into one that targets only a subset of the qubits. This approach scales linearly with the number of qubits that are not targeted, in contrast to the exponential scaling reported in (Maslov & Nam, N. J. Phys. 2018). Third, we improve on the number of global gates required to synthesise an arbitrary n-qubit Clifford circuit from the 12n-18 reported in (Maslov & Nam, N. J. Phys. 2018) to 6n-8.Comment: 13 pages. v2: added some more figures and fixed a number of (mathematical) typo

tqix.pis: A toolbox for large-scale quantum simulation platforms

We introduce tqix.pis, a library of tqix for executing various algorithms in large-scale quantum simulation platforms. The program emulates basic functions of a quantum circuit, including initialization qubits, quantum gates, and measurements. It utilizes the collective processes in ensembles of two-level systems to reduce the dimension, and facilitates the simulation time with multi-core processors and Graphics Processing Units. The library is thus programmable for different large-scale quantum simulation platforms, such as trapped ions, ultracold atoms in optical lattices, Rydberg atom arrays in optical tweezers, and nitrogen-vacancy centers. It is applicable for examining spin squeezing, variational quantum squeezing, quantum phase transition, many-body quantum dynamics, and other quantum algorithms.Comment: 17 pages, 8 figure