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As we approach the era of quantum advantage, when quantum computers (QCs) can outperform any classical computer on particular tasks, there remains the difficult challenge of how to validate their performance. While algorithmic success can be easily verified in some instances such as number factoring or oracular algorithms, these approaches only provide pass/fail information for a single QC. On the other hand, a comparison between different QCs on the same arbitrary circuit provides a lower-bound for generic validation: a quantum computation is only as valid as the agreement between the results produced on different QCs. Such an approach is also at the heart of evaluating metrological standards such as disparate atomic clocks. In this paper, we report a cross-platform QC comparison using randomized and correlated measurements that results in a wealth of information on the QC systems. We execute several quantum circuits on widely different physical QC platforms and analyze the cross-platform fidelities.

Quantum computers can study thermodynamics by finding zeros of functions in the complex plane., Partition functions are ubiquitous in physics: They are important in determining the thermodynamic properties of many-body systems and in understanding their phase transitions. As shown by Lee and Yang, analytically continuing the partition function to the complex plane allows us to obtain its zeros and thus the entire function. Moreover, the scaling and nature of these zeros can elucidate phase transitions. Here, we show how to find partition function zeros on noisy intermediate-scale trapped-ion quantum computers in a scalable manner, using the XXZ spin chain model as a prototype, and observe their transition from XY-like behavior to Ising-like behavior as a function of the anisotropy. While quantum computers cannot yet scale to the thermodynamic limit, our work provides a pathway to do so as hardware improves, allowing the future calculation of critical phenomena for systems beyond classical computing limits.

Quantum simulations provide a useful tool to study a broad range of problems in physics, chemistry, and biology. Trapped ions are a versatile quantum simulator and a main contender for a universal circuit model quantum computer. They provide a highly controllable quantum environment, which grants access to measure phenomena in regimes that are not otherwise accessible in nature. Here, our aim is to show particular examples of quantum physics simulations with a trapped ion quantum computer/simulator. On one hand, we will focus on the simulation of para-particle oscillators; that is, a parity-deformed harmonic oscillator characterized by an order parameter. These oscillators generalize the standard Fermi-Dirac and Bose-Einstein statistics associated with fermions and bosons to para-particles. We realize a method for simulating and characterizing these alternative particles using a trapped-ion experiment. The combination of the Jaynes-Cummings and anti-Jaynes Cummings dynamics present in a trapped ion coupled to multiple modes of motion simultaneously allows us to recover effective Hamiltonians which create a system analogous to para-Fermi or para-Bose oscillators. Trapped ions are a versatile quantum simulator and a main contender for a universal circuit model quantum computer. We use both of these flavors in this project, simulating para-Bosons digitally and para-Fermions directly by tailoring the native ion-mode couplings. We discuss the mapping steps and the latest experimental results. On the other hand, quantum walks provide a powerful framework for quantum simulation of physical systems. As a result, the community has been keen to see first implementations demonstrated, including single-particle relativistic quantum mechanics governed by the Dirac equation. Then, continuing with quantum circuit applications, our work presents a first programmable circuit implementation of quantum walks in one-dimensional space on a trapped-ion processor and its time-evolution up to five steps. The connection between quantum walks and Dirac cellular automata, a modeling framework for complex systems made up of simpler units, allows us to recover the characteristic spreading probability of an initially localized relativistic Dirac particle for different values of its mass. Due to a resource-efficient mapping of qubit states to walker positions, we achieve a high simulation performance despite going to deep quantum circuits (of up to 32 entangling gates).

In recent years, Quantum Computing (QC) has progressed to the point where small working prototypes are available for use. Termed Noisy Intermediate-Scale Quantum (NISQ) computers, these prototypes are too small for large benchmarks or even for Quantum Error Correction, but they do have sufficient resources to run small benchmarks, particularly if compiled with optimizations to make use of scarce qubits and limited operation counts and coherence times. QC has not yet, however, settled on a particular preferred device implementation technology, and indeed different NISQ prototypes implement qubits with very different physical approaches and therefore widely-varying device and machine characteristics. Our work performs a full-stack, benchmark-driven hardware-software analysis of QC systems. We evaluate QC architectural possibilities, software-visible gates, and software optimizations to tackle fundamental design questions about gate set choices, communication topology, the factors affecting benchmark performance and compiler optimizations. In order to answer key cross-technology and cross-platform design questions, our work has built the first top-to-bottom toolflow to target different qubit device technologies, including superconducting and trapped ion qubits which are the current QC front-runners. We use our toolflow, TriQ, to conduct {\em real-system} measurements on 7 running QC prototypes from 3 different groups, IBM, Rigetti, and University of Maryland. From these real-system experiences at QC's hardware-software interface, we make observations about native and software-visible gates for different QC technologies, communication topologies, and the value of noise-aware compilation even on lower-noise platforms. This is the largest cross-platform real-system QC study performed thus far; its results have the potential to inform both QC device and compiler design going forward., Comment: Preprint of a publication in ISCA 2019

We train generative modeling circuits on a quantum hybrid computer showing an optimization strategy and a resource trade-off., Generative modeling is a flavor of machine learning with applications ranging from computer vision to chemical design. It is expected to be one of the techniques most suited to take advantage of the additional resources provided by near-term quantum computers. Here, we implement a data-driven quantum circuit training algorithm on the canonical Bars-and-Stripes dataset using a quantum-classical hybrid machine. The training proceeds by running parameterized circuits on a trapped ion quantum computer and feeding the results to a classical optimizer. We apply two separate strategies, Particle Swarm and Bayesian optimization to this task. We show that the convergence of the quantum circuit to the target distribution depends critically on both the quantum hardware and classical optimization strategy. Our study represents the first successful training of a high-dimensional universal quantum circuit and highlights the promise and challenges associated with hybrid learning schemes.

We introduce the cross-cavity quantum Rabi model describing the interaction of a single two-level system with two orthogonal boson fields and propose its quantum simulation by two-dimensional, bichromatic, first-sideband driving of a single trapped ion. Like a first try of provide an analytical solution to our model, we solved the model in the weak coupling regime with Schwinger two-boson representation of SU(2). We introduce the Fulton-Gouterman approach to diagonalize the CCQRM in the two-level system basis, we provide an introductory survey of the model, including its diagonalization in the two-level system basis, numerical spectra and its characteristics in the weak, ultra strong and deep strong coupling regimes are included. We also show that the particular case of degenerate field frequencies and balanced couplings allows us to cast the model as two parity deformed oscillators in any given coupling regime. Presentamos el modelo de Rabi cuántico en cavidades cruzadas que describe un único sistema de dos niveles que interactúa con dos campos ortogonales de bosones y proponemos su simulación cuántica utilizando dos pares de campos biocromáticos ortogonales, sintonizados en la primera banda de transición de un sólo ion atrapado. Como primer intento para dar una solución analítica a nuestro modelo, estudiamos el régimen de acoplamiento débil en la representación de Schwinger de SU(2) de dos bosones. Y, para el caso más general, introducimos el formalismo de Fulton-Gouterman para diagonalizar el Hamiltoniano en la base del qubit, lo que nos permite estudiar numéricamente espectro y sus características en los regímenes de acoplamiento débil, ultra-fuerte y fuerte-profundo. También mostramos que el caso particular de campos degenerados en frecuencia y acoplamientos iguales nos permite ver el modelo como dos osciladores con paridad deformada en cualquier régimen de acoplamiento.