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 or microwave regime.
We propose the use of a trapped electron to implement quantum logic operations. The fundamental controlled-NOT gate is shown to be feasible. The two quantum bits are stored in the internal and external (motional) degrees of freedom.
We describe a simplified scheme for quantum logic with a collection of laser-cooled trapped atomic ions. Building on the scheme of Cirac and Zoller, we show how the fundamental controlled-NOT gate between a collective mode of ion motion and the internal states of a single ion can be reduced to a single laser pulse, and the need for a third auxiliary internal electronic state can be eliminated.
We simulate four quantum error correcting codes under error models inspired by realistic noise sources in near-term ion trap quantum computers: $T_2$ dephasing, gate overrotation, and crosstalk. We use this data to find preferred codes for given error parameters along with logical error biases and a pseudothreshold which compares the physical and logical gate failure rates for a CNOT gate. Using these results we conclude that Bacon-Shor-13 is the most promising near term candidate as long as the impact of crosstalk can be mitigated through other means.
We propose a scheme for quantum logic with neutral atoms stored in an array of holographic dipole traps where the positions of the atoms can be rearranged by using holographic optical tweezers. In particular, this allows for the transport of two atoms to the same well where an external control field is used to perform gate operations via the molecular interaction between the atoms. We show that optimal control techniques allow for the fast implementation of the gates with high fidelity.
Essentially all known quantum gates rely on a weak-coupling approximation resulting in linear dynamics. With the explicit example of trapped ions, we show how high-fidelity quantum gates can be achieved outside such an approximation, and we derive readily implementable driving fields to realize gates with extremely high fidelities for ions well outside the Lamb-Dicke regime with motional temperatures achievable by only Doppler cooling.
Applying a magnetic field gradient to a trapped ion allows long-wavelength microwave radiation to produce a mechanical force on the ion's motion when internal transitions are driven. We demonstrate such a coupling using a single trapped \Yb{171}~ion, and use it to produce entanglement between the spin and motional state, an essential step towards using such a field gradient to implement multi-qubit operations.
We demonstrate a two-qubit logic gate driven by near-field microwaves in a room-temperature microfabricated ion trap. We measure a gate fidelity of 99.7(1)\%, which is above the minimum threshold required for fault-tolerant quantum computing. The gate is applied directly to $^{43}$Ca$^+$ "atomic clock" qubits (coherence time $T_2^*\approx 50\,\mathrm{s}$) using the microwave magnetic field gradient produced by a trap electrode. We introduce a dynamically-decoupled gate method, which stabilizes the qubits against fluctuating a.c.\ Zeeman shifts and avoids the need to null the microwave field.
We present a detailed analysis and design of a neutral atom quantum logic device based on atoms in optical traps interacting via dipole-dipole coupling of Rydberg states. The dominant physical mechanisms leading to decoherence and loss of fidelity are enumerated. Our results support the feasibility of performing single and two-qubit gates at MHz rates with decoherence probability and fidelity errors at the level of $10^{-3}$ for each operation. Current limitations and possible approaches to further improvement of the device are discussed.
A scheme to implement quantum logic gates by manipulating trapped ions through interaction with monochromatic external laser field and quantized cavity field, beyond the Lamb-Dicke regime, is presented. Characteristic times, for implementing ionic state transitions using non-resont laser pulse or quantized cavity field, shows a sharp decline for large Lamb-Dicke parameter value of $η_{L}=η_{c}=0.2$, and is seen to decrease further with increase in number of initial state vibrational quanta $m$.
We propose the implementation of selective interactions of atom-motion subspaces in trapped ions. These interactions yield resonant exchange of population inside a selected subspace, leaving the others in a highly dispersive regime. Selectivity allows us to generate motional Fock (and other nonclassical) states with high purity out of a wide class of initial states, and becomes an unconventional cooling mechanism when the ground state is chosen. Individual population of number states can be distinctively measured, as well as the motional Wigner function. Furthermore, a protocol for implementin…
We present a scheme utilizing position-dependent ac Stark shifts for doing quantum logic with trapped ions. By a proper choice of direction, position and size, as well as power and frequency of a far-off-resonant Gaussian laser beam, specific ac Stark shifts can be assigned to the individual ions, making them distinguishable in frequency-space. In contrast to previous all-optical based quantum gates with trapped ions, the present scheme enables individual addressing of single ions and selective addressing of any pair of ions for two-ion quantum gates, without using tightly focused laser beams.…
We study the deterministic entanglement of a pair of neutral atoms trapped in an optical lattice by coupling to excited-state molecular hyperfine potentials. Information can be encoded in the ground-state hyperfine levels and processed by bringing atoms together pair-wise to perform quantum logical operations through induced electric dipole-dipole interactions. The possibility of executing both diagonal and exchange type entangling gates is demonstrated for two three-level atoms and a figure of merit is derived for the fidelity of entanglement. The fidelity for executing a CPHASE gate is calcu…
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 microfabricated surface-electrode traps, it should be possible to achieve gate speeds that are comparable to those of optically induced gates for realistic distances between the ion crystal and the electrode surface. Magnetic-field-mediated gates have the potential to significantly reduce the overhead in laser beam control and motional state initialization compared to c…
Trapped atomic ions have proven to be one of the most promising candidates for the realization of quantum computation due to their long trapping times, excellent coherence properties, and exquisite control of the internal atomic states. Integrating ions (quantum memory) with photons (distance link) offers a unique path to large-scale quantum computation and long-distance quantum communication. In this article, we present a detailed review of the experimental implementation of a heralded photon-mediated quantum gate between remote ions, and the employment of this gate to perform a teleportation…
Taking recent experiments as examples, we discuss the conditions for sub-wavelength probing of optical field structures by single trapped atoms. We calculate the achievable resolution, highlighting its connection to the fringe visibility in an interference experiment. We show that seemingly different physical pictures, such as spatial averaging, phase modulation, and which-way information, describe the situation equally and lead to identical results. The connection to Bohr's moving slit experiment is pointed out.
We demonstrate laser-driven two-qubit and single-qubit logic gates with fidelities 99.9(1)% and 99.9934(3)% respectively, significantly above the approximately 99% minimum threshold level required for fault-tolerant quantum computation, using qubits stored in hyperfine ground states of calcium-43 ions held in a room-temperature trap. We study the speed/fidelity trade-off for the two-qubit gate, for gate times between 3.8$μ$s and 520$μ$s, and develop a theoretical error model which is consistent with the data and which allows us to identify the principal technical sources of infidelity.
We introduce and demonstrate experimentally: (1) a framework called "gate set tomography" (GST) for self-consistently characterizing an entire set of quantum logic gates on a black-box quantum device; (2) an explicit closed-form protocol for linear-inversion gate set tomography (LGST), whose reliability is independent of pathologies such as local maxima of the likelihood; and (3) a simple protocol for objectively scoring the accuracy of a tomographic estimate without reference to target gates, based on how well it predicts a set of testing experiments. We use gate set tomography to characteriz…
We demonstrate quantum control techniques for a single trapped ion in a cryogenic, surface-electrode trap. A narrow optical transition of Sr+ along with the ground and first excited motional states of the harmonic trapping potential form a two-qubit system. The optical qubit transition is susceptible to magnetic field fluctuations, which we stabilize with a simple and compact method using superconducting rings. Decoherence of the motional qubit is suppressed by the cryogenic environment. AC Stark shift correction is accomplished by controlling the laser phase in the pulse sequencer, eliminatin…
Active quantum error correction has been identified as a crucial ingredient of future quantum computers, motivating the recent experimental efforts to encode logical quantum bits using small topological codes. In addition to the demonstration of the beneficial role of the encoding, a break-even point in the progress towards large-scale quantum computers will be the implementation of a universal set of gates. This mid-term challenge will soon be faced by various quantum technologies, which urges the need of realistic assessments of their prospects. In this work, we pursue this goal by assessing…
We show how to construct a multi-qubit control gate on a quantum register of an arbitrary size N. This gate performs a single-qubit operation on a specific qubit conditioned by the state of other N-1 qubits. We provide an algorithm how to build up an array of networks consisting of single-qubit rotations and multi-qubit control-NOT gates for the synthesis of an arbitrary entangled quantum state of N qubits. We illustrate the algorithm on a system of cold trapped ions. This example illuminates the efficiency of the direct implementation of the multi-qubit CNOT gate compared to its decomposition…
We demonstrate polarisation-preserving frequency conversion of single-photon-level light at 854 nm, resonant with a trapped-ion transition and qubit, to the 1550-nm telecom C band. A total photon in / fiber-coupled photon out efficiency of $\sim$ 30 % is achieved, for a free-running photon noise rate of $\sim$ 60 Hz. This performance would enable telecom conversion of 854-nm polarisation qubits, produced in existing trapped-ion systems, with a signal-to-noise ratio greater than 1. In combination with near-future trapped-ion systems, our converter would enable the observation of entanglement be…
We present a multilayer surface-electrode ion trap with embedded 3D microwave circuitry for implementing entangling quantum logic gates. We discuss the electromagnetic full-wave simulation procedure that has led to the trap design and the characterization of the resulting microwave field-pattern using a single ion as a local field probe. The results agree with simulations within the uncertainty; compared to previous traps, this design reduces detrimental AC Zeeman shifts by three orders of magnitude. The design presented here can be viewed as an entangling gate component in a library for surfa…
The micromotion of ion crystals confined in Paul traps is usually considered an inconvenient nuisance, and is thus typically minimised in high-precision experiments such as high-fidelity quantum gates for quantum information processing. In this work, we introduce a particular scheme where this behavior can be reversed, making micromotion beneficial for quantum information processing. We show that using laser-driven micromotion sidebands, it is possible to engineer state-dependent dipole forces with a reduced effect of off-resonant couplings to the carrier transition. This allows one, in a cert…
Trapped ions are a promising tool for building a large-scale quantum computer. However, the number of required radiation fields for the realisation of quantum gates in any proposed ion-based architecture scales with the number of ions within the quantum computer, posing a major obstacle when imagining a device with millions of ions. Here we present a fundamentally different concept for trapped-ion quantum computing where this detrimental scaling entirely vanishes, replacing millions of radiation fields with only a handful of fields. The method is based on individually controlled voltages appli…
We study from the point of view of quantum logic the properties of the collective oscillations of a linear chain of ions trapped in a linear Paul trap and composed of two ion species. We discuss extensively sympathetic cooling of the chain and the effect of anharmonicity on laser-cooling and quantum-information processing.
One limit to the fidelity of quantum logic operations on trapped ions arises from heating of the ions' collective modes of motion. Sympathetic cooling of the ions during the logic operations may eliminate this source of errors. We discuss benefits and drawbacks of this proposal, and describe possible experimental implementations. We also present an overview of trapped-ion dynamics in this scheme.
Fault-tolerant quantum error correction (QEC) is crucial for unlocking the true power of quantum computers. QEC codes use multiple physical qubits to encode a logical qubit, which is protected against errors at the physical qubit level. Here we use a trapped ion system to experimentally prepare $m$-qubit GHZ states and sample the measurement results to construct $m\times m$ logical states of the $[[m^2,1,m]]$ Shor code, up to $m=7$. The synthetic logical fidelity shows how deeper encoding can compensate for additional gate errors in state preparation for larger logical states. However, the opt…
We propose blue-detuned optical traps that are suitable for trapping of both ground state and Rydberg excited atoms. Addition of a background compensation field or suitable choice of the trap geometry provides a magic trapping condition for ground and Rydberg atoms at the trap center. Deviations from the magic condition at finite temperature are calculated. Designs that achieve less than 200 kHz differential trap shift between Cs ground and 125s Rydberg states for 10 μK Cs atoms are presented. Consideration of the trapping potential and photoionization rates
Many efforts are currently underway to build a device capable of large scale quantum information processing (QIP). Whereas QIP has been demonstrated for a few qubits in several systems, many technical difficulties must be overcome in order to construct a large-scale device. In one proposal for large-scale QIP, trapped ions are manipulated by precisely controlled light pulses and moved through and stored in multizone trap arrays. The technical overhead necessary to precisely control both the ion geometrical configurations and the laser interactions is demanding. Here we propose methods that sig…
Universal ion trap computation on Decoherence Free Subspaces (DFS) using only two qubit operations is presented. The DFS is constructed for the collective dephasing model. Encoded single and two-qubit logical operations are implemented via the Sorensen-Molmer interaction. Alternation of the effective Hamiltonians for two particular phase configurations of control fields approximates an anisotropic exchange interaction. This is universal over suitable encodings of one logical qubit into three physical qubits which are also DFS under collective decoherence.
A simple alternative scheme for implementing quantum gates with a single trapped cold two-level ion beyond the Lamb-Dicke (LD) limit is proposed. Basing on the quantum dynamics for the laser-ion interaction described by a generalized Jaynes-Cummings model, one can introduce two kinds of elementary quantum operations i.e., the simple rotation on the bare atomic state, generated by applying a resonant pulse, and the joint operation on the internal and external degrees of the ion, performed by using an off-resonant pulse. Several typical quantum gates, including Hadamard gate, controlled-Z and co…
Interactions among qubits are essential for performing two-qubit quantum logic operations. However, nature gives us only nearest neighbor interactions in simple and controllable settings. Here we propose a strategy to induce interactions among two atomic entities that are not necessarily neighbors of each other through their common coupling with a cavity field. This facilitates fast multiqubit quantum logic operations through a set of two-qubit operations. The ideas presented here are applicable to various quantum computing proposals for atom based qubits such as, trapped ions, atoms trapped i…
Although the initial proposal for ion trap quantum computation made use of an auxiliary internal level to perform logic between ions, this resource is not necessary in principle. Instead, one may perform such operations directly using sideband laser pulses, operating with an arbitrary (sufficiently small) Lamb-Dicke parameter. We explore the potential of this technique, showing how to perform logical operations between the internal state of an ion and the collective motional state and giving explicit constructions for a controlled-not gate between ions.
We propose a new system for implementing quantum logic gates: neutral atoms trapped in a very far-off-resonance optical lattice. Pairs of atoms are made to occupy the same well by varying the polarization of the trapping lasers, and then a near-resonant electric dipole is induced by an auxiliary laser. A controlled-NOT can be implemented by conditioning the target atomic resonance on a resolvable level shift induced by the control atom. Atoms interact only during logical operations, thereby suppressing decoherence.
A microfabricated phase Fresnel lens was used to image ytterbium ions trapped in a radio frequency Paul trap. The ions were laser cooled close to the Doppler limit on the 369.5 nm transition, reducing the ion motion so that each ion formed a near point source. By detecting the ion fluorescence on the same transition, near diffraction limited imaging with spot sizes of below 440 nm (FWHM) was achieved. This is the first demonstration of imaging trapped ions with a resolution on the order of the transition wavelength.
We introduce a novel scheme that combines phonon-mediated quantum logic gates in trapped ions with the benefits of continuous dynamical decoupling. We demonstrate theoretically that a strong driving of the qubit decouples it from external magnetic-field noise, enhancing the fidelity of two-qubit quantum gates. Moreover, the scheme does not require ground-state cooling, and is inherently robust to undesired ac-Stark shifts. The underlying mechanism can be extended to a variety of other systems where a strong driving protects the quantum coherence of the qubits without compromising the two-qubit…
A single laser-cooled and trapped 9Be+ ion is used to investigate methods of coherent quantum-state synthesis and quantum logic. We create and characterize nonclassical states of motion including "Schroedinger-cat" states. A fundamental quantum logic gate is realized which uses two states of the quantized ion motion and two ion internal states as qubits. We explore some of the applications for, and problems in realizing, quantum computation based on multiple trapped ions.
Quantum information can be processed using large ensembles of ultracold and trapped neutral atoms, building naturally on the techniques developed for high-precision spectroscopy and metrology. This article reviews some of the most important protocols for universal quantum logic with trapped neutrals, as well as the history and state-of-the-art of experimental work to implement these in the laboratory. Some general observations are made concerning the different strategies for qubit encoding, transport and interaction, including tradeoffs between decoherence rates and the likelihood of twoqubit …
The interaction between the electric dipole moment of a trapped molecular ion and the configuration of the confined Coulomb crystal couples the orientation of the molecule to its motion. We consider the practical feasibility of harnessing this interaction to initialize, process, and read out quantum information encoded in molecular ion qubits without optically illuminating the molecules. We present two schemes wherein a molecular ion can be entangled with a co-trapped atomic ion qubit, providing, among other things, a means for molecular state preparation and measurement. We also show that vir…
iSwitch: QEC on Demand via In-Situ Encoding of Bare Qubits for Ion Trap Architectures
University of California, San Diego（加州大学圣地亚哥分校）；Quantinuum；Cisco Quantum Lab（思科量子实验室）；University of California, Berkeley（加州大学伯克利分校）；University of California, Los Angeles（加州大学洛杉矶分校）；Oak Ridge National Laboratory（橡树岭国家实验室）
We demonstrate key multi-qubit quantum logic primitives in a dual-species trapped-ion system based on $^{40}$Ca+ and $^{88}$Sr+ ions, using two optical qubits with quantum-logic-control frequencies in the red to near-infrared range. With all ionization, cooling, and control wavelengths in a wavelength band similar for the two species and centered in the visible, and with a favorable mass ratio for sympathetic cooling, this pair is a promising candidate for scalable quantum information processing. Same-species and dual-species two-qubit gates, based on the Moelmer-Soerensen interaction and perf…
After pumped from $5s_{1/2}$ ground state to $6p_{1/2}$ state, the population inversion between $6s_{1/2}$ and $5p_{1/2,3/2}$ will be established for Rubidium four-level active optical clock. In this paper, we calculate AC Stark shift due to lattice trapping laser which dominates the frequency shift of clock transition in lattice trapped Rubidium four-level active optical clock. Several magic wavelengths are found that can form desired optical lattice trapping potential. By choosing a proper intensity and linewidth of trapping laser, the fractional frequency uncertainty of clock transition due…
The fidelity of laser-driven quantum logic operations on trapped ion qubits tend to be lower than microwave-driven logic operations due to the difficulty of stabilizing the driving fields at the ion location. Through stabilization of the driving optical fields and use of composite pulse sequences, we demonstrate high fidelity single-qubit gates for the hyperfine qubit of a $^{171}\text{Yb}^+$ ion trapped in a microfabricated surface electrode ion trap. Gate error is characterized using a randomized benchmarking protocol, and an average error per randomized Clifford group gate of $3.6(3)\times1…
Optical trapping of molecules with long coherence times is crucial for many protocols in quantum information and metrology. However, the factors that limit the lifetimes of the trapped molecules remain elusive and require improved understanding of the underlying molecular structure. Here we show that measurements of vibronic line strengths in weakly and deeply bound $^{88}$Sr$_2$ molecules, combined with \textit{ab initio} calculations, allow for unambiguous identification of vibrational quantum numbers. This, in turn, enables the construction of refined excited potential energy curves that in…
Entanglement between a stationary quantum system and a flying qubit is an essential ingredient of a quantum-repeater network. It has been demonstrated for trapped ions, trapped atoms, color centers in diamond, or quantum dots. These systems have transition wavelengths in the blue, red or near-infrared spectral regions, whereas long-range fiber-communication requires wavelengths in the low-loss, low-dispersion telecom regime. A proven tool to interconnect flying qubits at visible/NIR wavelengths to the telecom bands is quantum frequency conversion. Here we use an efficient polarization-preservi…
Based on the multi-level model, we have calculated light shifts for Zeeman states of hyperfine levels of cesium (Cs) 6S1/2 ground state and 6P3/2 excited state.The magic-wavelength linearly-polarized optical dipole trap (ODT) for Cs 6S1/2 F=4, mF=+4 - 6P3/2 F'=5, mF=+5 transition is experimentally constructed and characterized by using the laser-induced fluorescence spectra of trapped single Cs atoms. The magic wavelength is 937.7 nm which produces almost the same light shift for 6S1/2 F=4, mF=+4 ground state and 6P3/2 F'=5, mF=+5 excited state with linearly-polarized ODT laser beam. Compared …
