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In this tutorial we review the basic building blocks of Quantum Information Processing with cold trapped atomic-ions. We mainly focus on methods to implement single-qubit rotations and two-qubit entangling gates, which form a universal set…
The performance of a quantum information processor depends on the precise control of phases introduced into the system during quantum gate operations. As the number of operations increases with the complexity of a computation, the phases of…
An efficient implementation of the Toffoli gate is of conceptual importance for running various quantum algorithms, including Grover's search and Shor's integer factorization. However, direct implementation of the Toffoli gate either…
Two-qubit gates are a fundamental constituent of a quantum computer and typically its most challenging operation. In a trapped-ion quantum computer, this is typically implemented with laser beams which are modulated in amplitude, frequency,…
Fast entangling gate operations are a fundamental prerequisite for quantum simulation and computation. We propose an entangling scheme for arbitrary pairs of ions in a linear crystal, harnessing the high electric polarizability of highly…
Oscillating magnetic fields and field gradients can be used to implement single-qubit rotations and entangling multi-qubit quantum gates for trapped-ion quantum information processing (QIP). With fields generated by currents in…
We demonstrate high fidelity entangling quantum gates within a chain of five trapped ion qubits by optimally shaping optical fields that couple to multiple collective modes of motion. We individually address qubits with segmented optical…
Quantum algorithms on near-term quantum processors are typically executed using shallow quantum circuits composed of one- and two-qubit gates. However, as circuit depth and gate number increase, gate imperfections and qubit decoherence…
Control over physical systems at the quantum level is a goal shared by scientists in fields as diverse as metrology, information processing, simulation and chemistry. For trapped atomic ions, the quantized motional and internal degrees of…
A crucial building block for quantum information processing with trapped ions is a controlled-NOT quantum gate. In this paper, two different sequences of laser pulses implementing such a gate operation are analyzed using quantum process…
Quantum computing using two-dimensional NMR has recently been described using scalar coupling evolution technique [J. Chem. Phys.,109,10603 (1998)]. In the present paper, we describe two-dimensional NMR quantum computing with the help of…
Constructing a large scale ion trap quantum processor will require entangling gate operations that are robust in the presence of noise and experimental imperfection. We experimentally demonstrate how a new type of M{\o}lmer-S{\o}rensen gate…
We present a qutrit quantum computer design using trapped ions in the presence of a magnetic field gradient. The magnetic field gradient induces a "spin-spin" type coupling, similar to the J-coupling observed in molecules, between the…
Single-mode squeezing and Fourier transformation operations are two essential logical gates in continuous-variable quantum computation, which have been experimentally implemented by means of an optical four-mode cluster state. In this…
Two-qubit gate performance is vital for scaling up ion-trap quantum computing. Optimized quantum control is needed to achieve reductions in gate-time and gate error-rate. We describe two-qubit gates with addressed Raman beams within a…
Ion trap systems are a leading platform for large scale quantum computers. Trapped ion qubit crystals are fully-connected and reconfigurable, owing to their long range Coulomb interaction that can be modulated with external optical forces.…
Trapped-ion systems are a promising route toward the realization of both near-term and universal quantum computers. However, one of the pressing challenges is improving the fidelity of two-qubit entangling gates. These operations are often…
Trapped-ion systems are a leading platform for quantum computing. The M{\o}lmer-S{\o}rensen (MS) gate is a widely used method for implementing controlled interactions in multipartite systems. However, due to unavoidable interactions with…
Dual-type qubits have become a promising way to suppress the crosstalk error of auxiliary operations in large-scale ion trap quantum computation. Here we demonstrate a direct entangling gate between dual-type qubits encoded in the $S_{1/2}$…
A global race towards developing a gate-based, universal quantum computer that one day promises to unlock the never before seen computational power has begun and the biggest challenge in achieving this goal arguably is the quality…