Session S09: Focus Session: Advances in Quantum Computing

Fast Entangling Gates with Trapped-Ion Qubits

Trapped ion qubits are one of the most promising candidates for scalable quantum computing. Entangling gates with trapped ions achieve higher fidelities than in any other system, but are typically performed in an adiabatic regime, where the motional frequencies of the ions in the trap limit the gate speed. Many schemes have been proposed to overcome these limitations, but have only now been successfully implemented[1,2]. Following [3] we use amplitude-shaped cw-pulses to perform entangling gates significantly faster than the speed limit for conventional gate mechanisms. At these gate speeds, the motional modes are not spectrally isolated, leading to entanglement with both motional modes sensitively depending on the optical phase of the control fields.\newline We perform gates with fidelity $99.8 \%$ in $1.6\,\mathrm{\mu s}$[2] - over an order of magnitude faster than previous trapped ion gates of similar fidelity. We also demonstrate entanglement generation for gate times as short as $480\,\mathrm{ns}$ - this is below a single motional period of the ions. \newline [1] J.D. Wong-Campos et al., Phys. Rev. Lett. 117, 230501 (2017)\newline [2] V.M. Sch\"afer et al., arXiv:1709.06952 (2017), to be published in Nature\newline [3] A.M. Steane et al., New J. Phys. 16, 053049 (2014)   

Quantum Control & Quantum Error Correction with Superconducting Circuits.

We have developed an efficient quantum control scheme that allows for arbitrary operations on a cavity mode using strongly dispersive qubit-cavity interaction and time-dependent drives. In addition, we have discovered a new class of bosonic quantum error correcting codes, which can correct both cavity loss and dephasing errors. Our control scheme can readily be implemented using circuit QED systems and extended for quantum error correction to protect information encoded in bosonic codes. Moreover, engineered dissipation can also implement holonomic quantum computation using superconducting circuits.   

Quantum algorithms to simulate many-body physics of correlated fermions

Simulating strongly correlated fermionic systems is notoriously hard on classical computers. An alternative approach, as proposed by Feynman, is to use a quantum computer. Here, we discuss quantum simulation of strongly correlated fermionic systems. We focus specifically on 2-dimensional (2D) and linear geometry with nearest neighbor qubit-qubit couplings. We improve an existing algorithm to prepare an arbitrary Slater determinant by exploiting a unitary symmetry. We also present a quantum algorithm to prepare an arbitrary fermionic Gaussian state. Both algorithms are optimal in the sense that the numbers of parameters in the quantum circuits are equal to those to describe the quantum states. Furthermore, we propose an algorithm to implement the 2D fermionic Fourier transformation on a 2D qubit array with only $O(N^{1.5})$ gates and $O(\sqrt N)$ circuit depth, which is the minimum depth required for quantum information to travel across the qubit array. We also present methods to simulate each time step in the evolution of the 2D Fermi-Hubbard model. Finally, we discuss how these algorithms can be used to determine the ground state properties and phase diagrams of strongly correlated quantum systems the Hubbard model as an example.   

$^{133}$Ba$^+$: A radioactive trapped ion qubit

$^{133}\text{Ba}^+$ has been identified as an attractive trapped ion qubit due to its unique combination of spin-1/2 nucleus, visible-wavelength electronic transitions, and the longest $^{2}\text{D}_{5/2}$ lifetime of any alkaline-earth-like atomic ion. This nearly ideal system hosts hyperfine and optical qubit clock-states (long coherence times), enables fast high fidelity state preparation, and allows high fidelity readout via state selective electron shelving or direct optical qubit manipulation. Due to the 10.5yr half-life and unknown spectroscopic features required for laser cooling and qubit manipulations, $^{133}\text{Ba}^+$ had not been previously used as a host for quantum information. By using efficient loading and in-situ laser heating for isotopic purification, we can trap and laser cool a single $^{133}\text{Ba}^+$. We present recent work with $^{133}\text{Ba}^+$, including hyperfine qubit manipulations, the first demonstration of state selective electron shelving in $^{133}\text{Ba}^+$, and new spectroscopic measurements of the $^{2}\text{P}_{3/2}$ states. These measurements, along with continued efforts, will allow this optimal trapped ion qubit to be implemented across a wide range of current and future quantum information experiments.   

Cloud-Based Trapped-Ion Quantum Computing

In this talk I will cover the progress made on developing a scalable system of trapped-ion qubits to perform arbitrary quantum algorithms. Trapped ions are fundamentally identical units with long coherence times, and thus ideally suited for scalable quantum computation. Our current system allows for loading and preparing long chains of ${}^{171}{Yb}^{+}$ ions in a microfabricated chip trap. The hardware is linked to a cloud-based interface that allows users to build and request particular algorithms of their choosing. I will provide a review of this system, with a focus on hardware design for effective algorithm execution. Additionally, I will provide a glimpse into how lessons learned from the current system will lead us to more robust and scalable quantum information processors in the future.   

Using quantum mechanics to find your way through a maze

A quantum walk is a quantum version of a classical random walk. It can take place on a line or on a more complicated graph. Quantum walks can be used to find a distinguished vertex of a graph or anomalous structural elements, such as an extra edge or loop, with a quantum speedup. In recent work we have shown they can also find paths. We discuss two kinds of graphs, linked stars and trees, and show that a quantum walk can find a path between a vertex labeled START and one labeled FINISH with a quantum speedup.   

Sorting individual atoms in 3D: an omniscient Maxwell's demon

Combining site-resolved imaging, site-selective state flips and state-dependent motions, we have sorted atoms in randomly half filled 5x5x5 3D optical lattices into 96{\%} filled 5x5x2 or 4x4x3 sub-lattices. The sub-lattice ends up perfectly filled \textasciitilde 30{\%} of the time. Our experiment realizes the full essence of a Maxwell demon [Phys. Rev. A \textbf{70}, 040302(R) (2004)]. The sorting reduces the apparent configurational entropy by a factor of 8 and the total entropy by a factor of 2.4. The resulting manifestly low entropy state would be comfortably below the quantum degeneracy threshold if the lattice were adiabatically shut off and the atoms left in a 3D box trap [Phys. Rev. Lett. \textbf{89}, 090404 (2002)]. We will use the result of our Maxwell demon as the initial state of a neutral atom quantum computer.