Efficient qubit routing for a globally connected trapped ion quantum computer

The cost of enabling connectivity in noisy intermediate‐scale quantum (NISQ) devices is an important factor in determining computational power. A qubit routing algorithm is created, which enables efficient global connectivity in a previously proposed trapped ion quantum computing architecture. The routing algorithm is characterized by comparison against both a strict lower bound, and a positional swap based routing algorithm. An error model is proposed, which can be used to estimate the achievable circuit depth and quantum volume of the device as a function of experimental parameters. A new metric based on quantum volume, but with native two‐qubit gates, is used to assess the cost of connectivity relative to the upper bound of free, all to all connectivity. The metric is also used to assess a square‐grid superconducting device. These two architectures are compared and it is found that for the shuttling parameters used, the trapped ion design has a substantially lower cost associated with connectivity

Optimisation of two-dimensional ion trap arrays for quantum simulation

The optimisation of two-dimensional (2D) lattice ion trap geometries for trapped ion quantum simulation is investigated. The geometry is optimised for the highest ratio of ion-ion interaction rate to decoherence rate. To calculate the electric field of such array geometries a numerical simulation based on a "Biot-Savart like law" method is used. In this article we will focus on square, hexagonal and centre rectangular lattices for optimisation. A method for maximising the homogeneity of trapping site properties over an array is presented for arrays of a range of sizes. We show how both the polygon radii and separations scale to optimise the ratio between the interaction and decoherence rate. The optimal polygon radius and separation for a 2D lattice is found to be a function of the ratio between rf voltage and drive frequency applied to the array. We then provide a case study for 171Yb+ ions to show how a two-dimensional quantum simulator array could be designed

Doppler-free Yb Spectroscopy with Fluorescence Spot Technique

We demonstrate a simple technique to measure the resonant frequency of the 398.9 nm 1S0 - 1P1 transition for the different Yb isotopes. The technique, that works by observing and aligning fluorescence spots, has enabled us to measure transition frequencies and isotope shifts with an accuracy of 60 MHz. We provide wavelength measurements for the transition that differ from previously published work. Our technique also allows for the determination of Doppler shifted transition frequencies for photoionisation experiments when the atomic beam and laser beam are not perpendicular and furthermore allows us to determine the average velocity of the atoms along the direction of atomic beam

The impact of hardware specifications on reaching quantum advantage in the fault tolerant regime

We investigate how hardware specifications can impact the final run time and the required number of physical qubits to achieve a quantum advantage in the fault tolerant regime. Within a particular time frame, both the code cycle time and the number of achievable physical qubits may vary by orders of magnitude between different quantum hardware designs. We start with logical resource requirements corresponding to a quantum advantage for a particular chemistry application, simulating the FeMoco molecule, and explore to what extent slower code cycle times can be mitigated by using additional qubits. We show that in certain situations architectures with considerably slower code cycle times will still be able to reach desirable run times, provided enough physical qubits are available. We utilize various space and time optimization strategies that have been previously considered within the field of error-correcting surface codes. In particular, we compare two distinct methods of parallelization, Game of Surface Code's Units, and AutoCCZ factories, both of which enable one to incrementally speed up the computation until the reaction limited rate is reached. Finally we calculate the number of physical qubits which would be required to break the 256 bit elliptic curve encryption of keys in the Bitcoin network, within the small available time frame in which it would actually pose a threat to do so. It would require approximately 317 million physical qubits to break the encryption within one hour using the surface code, a code cycle time of 1 $\mu s$, a reaction time of 10 $\mu s$, and physical gate error of $10^{-3}$. To break the encryption instead within one day it would require 13 million physical qubits.Comment: 22 pages, 4 figure

Versatile ytterbium ion trap experiment for operation of scalable ion-trap chips with motional heating and transition-frequency measurements

We present the design and operation of an ytterbium ion trap experiment with a setup offering versatile optical access and 90 electrical interconnects that can host advanced surface and multilayer ion trap chips mounted on chip carriers. We operate a macroscopic ion trap compatible with this chip carrier design and characterize its performance, demonstrating secular frequencies >1 MHz, and trap and cool nearly all of the stable isotopes, including 171Yb+ ions, as well as ion crystals. For this particular trap we measure the motional heating rate 〈ṅ〉 and observe an 〈ṅ〉∝1/ω2 behavior for different secular frequencies ω. We also determine a spectral noise density SE(1 MHz)=3.6(9)×10-11 V2 m-2 Hz-1 at an ion electrode spacing of 310(10) μm. We describe the experimental setup for trapping and cooling Yb+ ions and provide frequency measurements of the 2S1/2↔2P1/2 and 2D3/2↔3D[3/2]1/2 transitions for the stable 170Yb+, 171Yb+, 172Yb+, 174Yb+, and 176Yb+ isotopes which are more precise than previously published work

Optimal control with a multidimensional quantum invariant

Optimal quantum control of continuous variable systems poses a formidable computational challenge because of the high-dimensional character of the system dynamics. The framework of quantum invariants can significantly reduce the complexity of such problems, but it requires the knowledge of an invariant compatible with the Hamiltonian of the system in question. We explore the potential of a Gaussian invariant that is suitable for quadratic Hamiltonians with any given number of motional degrees of freedom for quantum optimal control problems that are inspired by current challenges in ground-state-to-ground-state shuttling of trapped-ions.Comment: 9 pages, 4 figure

Blueprint for a microwave trapped ion quantum computer

The availability of a universal quantum computer may have a fundamental impact on a vast number of research fields and on society as a whole. An increasingly large scientific and industrial community is working toward the realization of such a device. An arbitrarily large quantum computer may best be constructed using a modular approach. We present a blueprint for a trapped ion–based scalable quantum computer module, making it possible to create a scalable quantum computer architecture based on long-wavelength radiation quantum gates. The modules control all operations as stand-alone units, are constructed using silicon microfabrication techniques, and are within reach of current technology. To perform the required quantum computations, the modules make use of long-wavelength radiation–based quantum gate technology. To scale this microwave quantum computer architecture to a large size, we present a fully scalable design that makes use of ion transport between different modules, thereby allowing arbitrarily many modules to be connected to construct a large-scale device. A high error–threshold surface error correction code can be implemented in the proposed architecture to execute fault-tolerant operations. With appropriate adjustments, the proposed modules are also suitable for alternative trapped ion quantum computer architectures, such as schemes using photonic interconnects

Microfabricated Ion Traps

Ion traps offer the opportunity to study fundamental quantum systems with high level of accuracy highly decoupled from the environment. Individual atomic ions can be controlled and manipulated with electric fields, cooled to the ground state of motion with laser cooling and coherently manipulated using optical and microwave radiation. Microfabricated ion traps hold the advantage of allowing for smaller trap dimensions and better scalability towards large ion trap arrays also making them a vital ingredient for next generation quantum technologies. Here we provide an introduction into the principles and operation of microfabricated ion traps. We show an overview of material and electrical considerations which are vital for the design of such trap structures. We provide guidance in how to choose the appropriate fabrication design, consider different methods for the fabrication of microfabricated ion traps and discuss previously realized structures. We also discuss the phenomenon of anomalous heating of ions within ion traps, which becomes an important factor in the miniaturization of ion traps

Quantum computer based on shuttling trapped ions

A microchip-based quantum computer has been built incorporating an architecture in which calculations are carried out by shuttling atomic ions. The device exhibits excellent performance and potential for scaling up