G. J. Milburn
We show how a conditional displacement of the vibrational mode of trapped ions can be used to simulate nonlinear collective and interacting spin systems including nonlinear tops and Ising models (a universal two qubit gate), independent of the vibrational state of the ion. Thus cooling to the vibrational ground state is unnecessary provided the heating rate is not too large.
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This thesis provides an overview of an approach to quantum simulations using magnesium-25 ions stored in a linear Paul trap as the carriers of quantum information. Their quantum state is manipulated and read out using ultraviolet laser beams. Several important steps towards realising the first experiments have been undertaken, the most striking of which is cooling the ions to their motional ground state. We describe a first experiment simulating cosmological particle creation in the Early Universe and discuss the expected results.
We propose to experimentally explore the Haldane phase in spin-one XXZ antiferromagnetic chains using trapped ions. We show how to adiabatically prepare the ground states of the Haldane phase, demonstrate their robustness against sources of experimental noise, and propose ways to detect the Haldane ground states based on their excitation gap and exponentially decaying correlations, nonvanishing nonlocal string order, and doubly-degenerate entanglement spectrum.
Simulating the flight gate assignment problem on a trapped ion quantum computer
本文在IonQ Aria囚禁离子量子计算机上使用VQE和CVaR求解航班登机口分配问题，通过小规模完整运行和大规模推理实验证明当前及近期量子硬件能以高概率获得良好解。
We study the open system dynamics of a harmonic oscillator coupled with an artificially engineered reservoir. We single out the reservoir and system variables governing the passage between Lindblad type and non-Lindblad type dynamics of the reduced system's oscillator. We demonstrate the existence of conditions under which virtual exchanges of energy between system and reservoir take place. We propose to use a single trapped ion coupled to engineered reservoirs in order to simulate quantum Brownian motion.
Simulating quantum phenomena in extreme spacetimes in the laboratory represents a powerful approach to explore fundamental physics in the interplay of quantum field theory and general relativity. Here we propose to simulate the movement of a Dirac particle propagating with a superluminal velocity caused by the emergent Alcubierre warp drive spacetime using trapped ions. We demonstrate that the platform allows observing the tilted lightcone that manifests as a superluminal velocity, which is in agreement with the prediction of general relativity. Furthermore, the Zitterbewegung effect arising f…
Simulating the spin-boson model with a controllable reservoir in an ion trap
本研究利用一串被困离子模拟自旋-玻色子模型，通过调整离子数量、位置、激光失谐及频率分量来设计结构化储层的谱密度，观察其对信息坍缩与复苏的影响，证明离子阱是模拟复杂开放量子动力学的强大平台。
We propose an experimental scheme to simulate and observe the Klein tunneling of relativistic Maxwell particles with trapped ions. We explore the scattering dynamics of the pseudospin-one Maxwell particles and demonstrate that the scattered state should be a superposition of a reflection state, a localization state, and a transmission state. The probabilities of these states can be analytically obtained by the approach of Landau-Zener transition. We further show that the Maxwell Hamiltonian and the associated scattering dynamics can be mimicked with two trapped ions. The Maxwell spinors are en…
We propose a scheme involving cold atoms trapped in optical lattices to observe different phenomena traditionally linked to quantum-optical systems. The basic idea consists of connecting the trapped atomic state to a non-trapped state through a Raman scheme. The coupling between these two types of atoms (trapped and free) turns out to be similar to that describing light-matter interaction within the rotating-wave approximation, the role of matter and photons being played by the trapped and free atoms, respectively. We explain in particular how to observe phenomena arising from the collective s…
Conical intersections are common in molecular physics and photochemistry, and are often invoked to explain observed reaction products. A conical intersection can occur when an excited electronic potential energy surface intersects with the ground electronic potential energy surface in the coordinate space of the nuclear positions. Theory predicts that the conical intersection will result in a geometric phase for a wavepacket on the ground potential energy surface. Although conical intersections have been observed experimentally, the geometric phase has not been observed in a molecular system. …
Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be…
We explore the feasibility of implementing a small surface code with 9 data qubits and 8 ancilla qubits, commonly referred to as surface-17, using a linear chain of 171Yb+ ions. Two-qubit gates can be performed between any two ions in the chain with gate time increasing linearly with ion distance. Measurement of the ion state by fluorescence requires that the ancilla qubits be physically separated from the data qubits to avoid errors on the data due to scattered photons. We minimize the time required to measure one round of stabilizers by optimizing the mapping of the two-dimensional surface c…
For many quantum information implementations with trapped ions, effective shuttling operations are important. Here we discuss the efficient separation and recombination of ions in surface ion trap geometries. The maximum speed of separation and recombination of trapped ions for adiabatic shuttling operations depends on the secular frequencies the trapped ion experiences in the process. Higher secular frequencies during the transportation processes can be achieved by optimising trap geometries. We show how two different arrangements of segmented static potential electrodes in surface ion traps …
Chiaverini et al. [Quant. Inf. Comput. 5, 419 (2005)] recently suggested a linear Paul trap geometry for ion trap quantum computation that places all of the electrodes in a plane. Such planar ion traps are compatible with modern semiconductor fabrication techniques and can be scaled to make compact, many zone traps. In this paper we present an experimental realization of planar ion traps using electrodes on a printed circuit board to trap linear chains of tens of 0.44 micron diameter charged particles in a vacuum of 15 Pa (0.1 torr). With these traps we address concerns about the low trap dept…
We have investigated ion dynamics associated with a dual linear ion trap where ions can be stored in and moved between two distinct locations. Such a trap is a building block for a system to engineer arbitrary quantum states of ion ensembles. Specifically, this trap is the unit cell in a strategy for scalable quantum computing using a series of interconnected ion traps. We have transferred an ion between trap locations 1.2 mm apart in 50 $μ$s with near unit efficiency ($> 10^{6}$ consecutive transfers) and negligible motional heating, while maintaining internal-state coherence. In addition, we…
We consider two different kinds of fluctuations in an ion trap potential: external fluctuating electrical fields, which cause statistical movement (``wobbling'') of the ion relative to the center of the trap, and fluctuations of the spring constant, which are due to fluctuations of the ac-component of the potential applied in the Paul trap for ions. We write down master equations for both cases and, averaging out the noise, obtain expressions for the heating of the ion. We compare our results to previous results for far-off resonance optical traps and heating in ion traps. The effect of fluctu…
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 princi…
We present a scheme to prepare a quantum state in a ion trap with probability approaching to one by means of ion trap quantum computing and Grover's quantum search algorithm acting on trapped ions.
Dense array of ions in microfabricated traps represent one possible way to scale up ion trap quantum computing. The ability to address individual ions is an important component of such a scheme. We demonstrate individual addressing of trapped ions in a microfabricated surface-electrode trap using a magnetic field gradient generated on-chip. A frequency splitting of 310(2) kHz for two ions separated by 5 um is achieved. Selective single qubit operations are performed on one of two trapped ions with an average of 2.2+/-1.0% crosstalk. Coherence time as measured by the spin-echo technique is unaf…
Trapped ion technology has seen advances in performance, robustness, and versatility over the last decade. With increasing numbers of trapped ion groups world-wide, a myriad of trap architectures are currently in use. Applications of trapped ions include: quantum simulation, computing and networking, time standards and fundamental studies in quantum dynamics. Design of such traps is driven by these various research aims, but some universally desirable properties have lead to the development of ion trap foundries. The excellent control achievable with trapped ions and the ability to do photonic…
There has been much interest in developing methods for transferring quantum information. We discuss a way to transfer quantum information between two trapped ions through a wire. The motion of a trapped ion induces oscillating charges in the trap electrodes. By sending this current to the electrodes of a nearby second trap, the motions of ions in the two traps are coupled. We investigate the electrostatics of a set-up where two separately trapped ions are coupled through an electrically floating wire. We also discuss experimental issues, including possible sources of decoherence.
We propose a new experimental testbed that uses ions in the collective ground state of a static trap for studying the analog of quantum-field effects in cosmological spacetimes, including the Gibbons-Hawking effect for a single detector in de Sitter spacetime, as well as the possibility of modeling inflationary structure formation and the entanglement signature of de Sitter spacetime. To date, proposals for using trapped ions in analog gravity experiments have simulated the effect of gravity on the field modes by directly manipulating the ions' motion. In contrast, by associating laboratory ti…
We demonstrate a method for loading surface electrode ion traps by electron impact ionization. The method relies on the property of surface electrode geometries that the trap depth can be increased at the cost of more micromotion. By introducing a buffer gas, we can counteract the rf heating assocated with the micromotion and benefit from the larger trap depth. After an initial loading of the trap, standard compensation techniques can be used to cancel the stray fields resulting from charged dielectric and allow for the loading of the trap at ultra-high vacuum.
Atomic ions trapped in ultra-high vacuum form an especially well-understood and useful physical system for quantum information processing. They provide excellent shielding of quantum information from environmental noise, while strong, well-controlled laser interactions readily provide quantum logic gates. A number of basic quantum information protocols have been demonstrated with trapped ions. Much current work aims at the construction of large-scale ion-trap quantum computers using complex microfabricated trap arrays. Several groups are also actively pursuing quantum interfacing of trapped io…
We propose a method for scaling trapped ions for large-scale quantum computation and communication based on a probabilistic ion-photon mapping. Deterministic quantum gates between remotely located trapped ions can be achieved through detection of spontaneously-emitted photons, accompanied by the local Coulomb interaction between neighboring ions. We discuss gate speeds and tolerance to experimental noise for different probabilistic entanglement schemes.
We demonstrate a two-dimensional 11-zone ion trap array, where individual laser-cooled atomic ions are stored, separated, shuttled, and swapped. The trap geometry consists of two linear rf ion trap sections that are joined at a 90 degree angle to form a T-shaped structure. We shuttle a single ion around the corners of the T-junction and swap the positions of two crystallized ions using voltage sequences designed to accommodate the nontrivial electrical potential near the junction. Full two-dimensional control of multiple ions demonstrated in this system may be crucial for the realization of sc…
Trapped atomic ions have become one of the most promising architectures for a quantum computer, and current effort is now devoted to the transport of trapped ions through complex segmented ion trap structures in order to scale up to much larger numbers of trapped ion qubits. This paper covers several important issues relevant to ion transport in any type of complex multidimensional rf (Paul) ion trap array. We develop a general theoretical framework for the application of time-dependent electric fields to shuttle laser-cooled ions along any desired trajectory, and describe a method for determi…
A quantum information processor is proposed that combines experimental techniques and technology successfully demonstrated either in nuclear magnetic resonance experiments or with trapped ions. An additional inhomogenenous magnetic field applied to an ion trap i) shifts individual ionic resonances (qubits), making them distinguishable by frequency, and, ii) mediates the coupling between internal and external degrees of freedom of trapped ions. This scheme permits one to individually address and coherently manipulate ions confined in an electrodynamic trap using radiation in the radiofrequency …
We widen the range of applications for quantum computing by introducing digital quantum simulation methods for coherent light-matter interactions: We simulate an experiment where the emitted light from a single ion was interfering with its mirror image [Eschner et. al., Nature 431, 495 (2001)]. Using the quantum simulation software q1tsim we accurately reproduce the interference pattern which had been observed experimentally and also show the effect of the mirror position on the spontaneous emission rate of the ion. In order to minimize the number of required qubits we implement a qubit-reinit…
We present the design and operation of an ytterbium ion trap experiment with a setup offering versatile optical access and 90 electrical inter-connects that can host advanced surface and multi-layer ion trap chips mounted on chip carriers. We operate a macroscopic ion trap compatible with this chip carrier design and characterise 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 tap we measure the motional heating rate, <n-dot>, and observe a <n-dot> proportional to…
We characterise the performance of a surface-electrode ion "chip" trap fabricated using established semiconductor integrated circuit and micro-electro-mechanical-system (MEMS) microfabrication processes which are in principle scalable to much larger ion trap arrays, as proposed for implementing ion trap quantum information processing. We measure rf ion micromotion parallel and perpendicular to the plane of the trap electrodes, and find that on-package capacitors reduce this to <~ 10 nm in amplitude. We also measure ion trapping lifetime, charging effects due to laser light incident on the trap…
Ion Trapping with a Laser-written 3D Miniaturized Monolithic Linear Paul Trap for Microcavity Integration
本文提出一种激光写入的金镀熔融石英单片线性Paul阱，实现高数值孔径接入与电极精确隔离，并成功演示离子囚禁，为微腔集成奠定基础。
We fabricate superconducting ion traps with niobium and niobium nitride and trap single 88Sr ions at cryogenic temperatures. The superconducting transition is verified and characterized by measuring the resistance and critical current using a 4-wire measurement on the trap structure, and observing change in the rf reflection. The lowest observed heating rate is 2.1(3) quanta/sec at 800 kHz at 6 K and shows no significant change across the superconducting transition, suggesting that anomalous heating is primarily caused by noise sources on the surface. This demonstration of superconducting ion …
This submission is an introduction to microfabricated ion traps. We cover the basics of Paul traps, various geometries for realizing the traps, a number of design considerations, and, finally, a review of existing microfabricated traps.
This paper presents a method to describe dynamics of an ion confined in a realistic finite range trap. We model this realistic potential with a solvable one and we obtain dynamical variables (raising and lowering operators) of this potential. We consider coherent interaction of this confined ion in a finite range trap and we show that its center-of-mass motion steady state is a special kind of nonlinear coherent states. Physical properties of this state and their dependence on the finite range of potential are studied.
Recent experiments [K. R. Brown, et al., Nature 471, 196 (2011); and M. Harlander, et al., Nature 471, 200 (2011)] have demonstrated the coherent manipulations on the external vibrations of two ions, confined individually in the separated ion traps. Using these recently developed techniques, we propose here an approach to realize the coherent operations, e.g., the universal quantum gates, between the separated ion-trap qubits encoded by two internal atomic states of the trapped ions. Our proposal operates beyond the usual Lamb-Dicke limits, and could be applied to the scalable ion traps couple…
We propose a scheme to perform basic gates of quantum computing and prepare entangled states in a system with cold trapped ions located in a single mode optical cavity. General quantum computing can be made with both motional state of the trapped ion and cavity state being qubits. We can also generate different kinds of entangled states in such a system without state reduction, and can transfer quantum states from the ion in one trap to the ion in another trap. Experimental requirement for achieving our scheme is discussed.
We show how NOON states may be generated in ion traps. We use the individual interaction of light with each of two vibrational modes of the ion to entangle them. This allows us to generate NOON states with N=8.
Simulating sparse SYK model with a randomized algorithm on a trapped-ion quantum computer
研究利用随机算法TETRIS在囚离子量子计算机上模拟稀疏SYK模型，通过高保真量子操作和全连接结构计算洛施密特振幅，评估未来大规模模拟的量子资源需求。
We theoretically and experimentally examine the effects of anharmonic terms in the trapping potential for linear chains of trapped ions. We concentrate on two different effects that become significant at different levels of anharmonicity. The first is a modification of the oscillation frequencies and amplitudes of the ions' normal modes of vibration for multi-ion crystals, resulting from each ion experiencing a different curvature in the potential. In the second effect, which occurs with increased anharmonicity or higher excitation amplitude, amplitude-dependent shifts of the normal-mode frequ…
We describe a efficient way to photoionize strontium atoms in a linear radio-frequency trap. We use a 2-photon second order process to excite the autoionization resonance (4d2 + 5p2) 1D2. A doubled pulsed Ti:Saphire laser system is used at 431nm to provide 100fsec pulses at 82Mhz. The fabrication of the laser systems for addressing the Sr+ transitions necessary for laser cooling and excitation of quantum jumps, vacuum system and ion trap structure are also described in detail. With the current setup a easy and repeatable trapping of linear ion chains is achieved at UHV pressures.
Dense arrays of trapped ions provide one way of scaling up ion trap quantum information processing. However, miniaturization of ion traps is currently limited by sharply increasing motional state decoherence at sub-100 um ion-electrode distances. We characterize heating rates in cryogenically cooled surface-electrode traps, with characteristic sizes in 75 um to 150 um range. Upon cooling to 6 K, the measured rates are suppressed by 7 orders of magnitude, two orders of magnitude below previously published data of similarly sized traps operated at room temperature. The observed noise depends str…
Internal states of different ions in an electrodynamic trap are coupled when a static magnetic field is applied -- analogous to spin-spin coupling in molecules used for NMR. This spin-spin interaction can be used, for example, to implement quantum logic operations in ion traps using NMR methods. The collection of trapped ions can be viewed as a $N$-qubit molecule with adjustable coupling constants.
We describe the optimal realization of entangling quantum gates for trapped ions mediated by a dissipative bus mode. With suitably shaped control pulses one can substantially decrease ion-phonon entanglement while maintaining the mediated interaction.
The theory of interactions between lasers and cold trapped ions as it pertains to the design of Cirac-Zoller quantum computers is discussed. The mean positions of the trapped ions, the eigenvalues and eigenmodes of the ions' oscillations, the magnitude of the Rabi frequencies for both allowed and forbidden internal transitions of the ions and the validity criterion for the required Hamiltonian are calculated. Energy level data for a variety of ion species is also presented.
A new scheme for the individual addressing of ions in a trap is described that does not rely on light beams tightly focused onto only one ion. The scheme utilizes ion micromotion that may be induced in a linear trap by dc offset potentials. Thus coupling an individual ion to the globally applied light fields corresponds to a mere switching of voltages on a suitable set of compensation electrodes. The proposed scheme is especially suitable for miniaturized rf (Paul) traps with typical dimensions of about 20-40 microns.
Trapped-ion quantum information processors store information in atomic ions maintained in position in free space via electric fields. Quantum logic is enacted via manipulation of the ions' internal and shared motional quantum states using optical and microwave signals. While trapped ions show great promise for quantum-enhanced computation, sensing, and communication, materials research is needed to design traps that allow for improved performance by means of integration of system components, including optics and electronics for ion-qubit control, while minimizing the near-ubiquitous electric-f…
In designing an ion trap, geometry and rf source should be optimized such that the trap depth is maximized while the ion remain stable. In a quadrupole linear trap, stable parameters $a$ and $q$ are utilized frequently in describing the stability. However, in a surface trap, the trap have to be mapped to the linear quadrupole trap so that $a$ and $q$ can be evaluated. This work explains how to handle them for surface trap designing and how the geometry and rf source affect it. We conclude that the $q$ parameter should be 0.2~0.22 so that the trap is stable.
We describe a possible architecture to implement a universal bosonic simulator (UBS) using trapped ions. Single ions are confined in individual traps, and their motional states represent the bosonic modes. Single-mode linear operators, nonlinear phase-shifts, and linear beam splitters can be realized by precisely controlling the trapping potentials. All the processes in a bosonic simulation, except the initialization and the readout, can be conducted beyond the Lamb-Dicke regime. Aspects of our proposal can also be applied to split adiabatically a pair of ions in a single trap.
Two-ion crystals constitute a platform for investigations of quantum nature that can be extended to any ion species or charged particle provided one of the ions in the crystal can be directly laser-cooled and manipulated with laser radiation. This paper presents the formation of two-ion crystals for quantum metrology in a 7-tesla open-ring Penning trap. $^{40}$Ca$^+$ ions are produced either internally by photoionization or externally in a (Paul-trap) source, transported through the strong magnetic field gradient of the superconducting solenoid, and captured in-flight with a mean kinetic energ…
Trapped ion hardware has made significant progress recently and is now one of the leading platforms for quantum computing. To construct two-qubit gates in trapped ions, experimental manipulation approaches for ion chains are becoming increasingly prevalent. Given the restricted control technology, how implementing high-fidelity quantum gate operations is crucial. Many works in current pulse design optimization focus on ion-phonon and effective ion-ion coupling while ignoring the higher-order expansion impacts of these two terms brought on by experiment defects. This paper proposed a novel robu…
We present a number of alternative designs for Penning ion traps suitable for quantum information processing (QIP) applications with atomic ions. The first trap design is a simple array of long straight wires which allows easy optical access. A prototype of this trap has been built to trap Ca+ and a simple electronic detection scheme has been employed to demonstrate the operation of the trap. Another trap design consists of a conducting plate with a hole in it situated above a continuous conducting plane. The final trap design is based on an array of pad electrodes. Although this trap design l…
Based on resonant sideband excitation, we present a scheme for the generation of six-qubit cluster state in ion-trap system. One can realize experimentally this scheme with presently available techniques.
The decoherence in trapped ion induced by coupling the ion to the engineered reservoir is studied in this paper. The engineered reservoir is simulated by random variations in the trap frequency, and the trapped ion is treated as a two-level system driven by a far off-resonant plane wave laser field. The dependence of the decoherence rate on the amplitude of the superposition state is given.
We have experimentally observed the dynamics of a single polariton and two polaritons in a two-ion chain. By driving two trapped ions at a motional blue-sideband transition, we realize the anti-Jaynes-Cummings-Hubbard model. When a single polariton exists in a trapped-ion chain, the polariton hops between the ion sites. On the other hand, when there are single polaritons at each ion site, the hopping of the polaritons is suppressed because of the polariton-polariton interaction induced by the nonlinearity of the anti-Jaynes-Cummings interaction, thereby realizing the blockade of polariton hopp…
An approach is proposed to implement the universal quantum gates between the ions confined individually in the separated traps. Instead of the typical adiabatic operations, performed for manipulating the ion-ion coupling, here the switchable couplings between ions are implemented non-adiabatically by using the fast laser pulses. Consequently, the desirable quantum gates between the ions could be implemented by using only a series of laser pulses. The proposal may be conveniently generalized to the quantum computation with the scalable ion-traps.
Quasiclassical dynamics of trapped ions is characterized by applying the time dependent variational principle (TDVP) on coherent state orbits, in case of quadrupole and octupole combined (Paul and Penning) and radiofrequency (RF) traps. A dequantization algorithm is proposed, by which the classical Hamilton (energy) function associated to the system results as the expectation value of the quantum Hamiltonian on squeezed coherent states. We develop such method and particularize the quantum Hamiltonian for a combined and for a RF trap, with axial symmetry and a RF anharmonic electric potential. …
Raman interaction of a trapped ultracold ion with two traveling wave lasers has been used extensively in the ion trap experiments. We solve this interaction in the absence of the rotating wave approximation by a continued fraction, without considering the restriction of the Lamb-Dicke limit and the weak excitation regime. Some interesting characteristics of the ion-trap system, particularly for the ion outside the weak excitation regime are found. Finally, a comparison of our results with the solution under the rotating wave approximation is made.
Quantum computing gates are proposed to apply on trapped ions in decoherence-free states. As phase changes due to time evolution of components with different eigenenergies of quantum superposition are completely frozen, quantum computing based on this model would be perfect. Possible application of our scheme in future ion-trap quantum computer is discussed.
By means of the Ising terms generated by Coulomb interaction between ions and the magnetic field gradient, we carry out teleportation with insurance with trapped ions. We show the feasibility and the favorable feature of our scheme by comparing with the recently achieved teleportation experiments with trapped ions.
In this paper we present numerical modeling results for endcap and linear ion traps, used for experiments at the National Physical Laboratory in the UK and Innsbruck University respectively. The secular frequencies for Strontium-88 and Calcium-40 ions were calculated from ion trajectories, simulated using boundary-element and finite-difference numerical methods. The results were compared against experimental measurements. Both numerical methods showed high accuracy with boundary-element method being more accurate. Such simulations can be useful tools for designing new traps and trap arrays. Th…
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