A. Recati, T. Calarco, P. Zanardi, J. I. Cirac, P. Zoller
We propose an all-geometric implementation of quantum computation using neutral atoms in cavity QED. We show how to perform generic single- and two-qubit gates, the latter by encoding a two-atom state onto a single, many-level atom. We compare different strategies to overcome limitations due to cavity imperfections.
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Holonomic swap and controlled-swap gates of neutral atoms via selective Rydberg pumping
提出基于选择性里德伯泵浦和含时软控制的中性原子完整交换门快速实现方案，并扩展至三量子比特受控交换门，以抑制失谐与退相干。
Our goal is to provide a new approach to the construction of geometry-induced entanglement between a pair of $Λ$ type atoms in a system consists of $N$ identical atoms by means of nonadiabatic quantum holonomies. By employing the quantum Zeno effect, we introduce a tripod type interaction Hamiltonian between two selected atoms trapped in an optical cavity, which allows arbitrary geometric entangling power. This would be a substantial step toward resolving the feasibility of realizing universal nonadiabatic holonomic entangling two-qubit gates.
We propose a protocol to realize atomic nonadiabatic holonomic quantum computation (NHQC) with two computational atoms and an auxiliary atom. Dynamics of the system is analyzed in the regime of Rydberg blockade, and robust laser pulses are designed via reverse engineering, so that quantum gates can be easily realized with high fidelities. In addition, we also study the evolution suffering from dissipation with a master equation. The result indicates that decays of atoms can be heralded by measuring the state of the auxiliary atom, and nearly perfect unitary evolution can be obtained if the aux…
In this paper, we propose a scheme for implementing the nonadiabatic holonomic quantum computation (NHQC+) of two Rydberg atoms by using invariant-based reverse engineering (IBRE). The scheme is based on Förster resonance induced by strong dipole-dipole interaction between two Rydberg atoms, which provides a selective coupling mechanism to simply the dynamics of system. Moreover, for improving the fidelity of the scheme, the optimal control method is introduced to enhance the gate robustness against systematic errors. Numerical simulations show the scheme is robust against the random noise in …
Geometric quantum gates via dark paths in Rydberg atoms
该研究利用里德伯原子暗路径与失谐驱动补偿相互作用，构建对系统误差和外部噪声均鲁棒、且可扩展的通用非绝热和乐 N 量子比特门。
Quantum holonomic gates hold built-in resilience to local noises and provide a promising approach for implementing fault-tolerant quantum computation. We propose to realize high-fidelity holonomic $(N+1)$-qubit controlled gates using Rydberg atoms confined in optical arrays or superconducting circuits. We identify the scheme, deduce the effective multi-body Hamiltonian, and determine the working condition of the multiqubit gate. Uniquely, the multiqubit gate is immune to systematic errors, i.e., laser parameter fluctuations and motional dephasing, as the $N$ control atoms largely remain in the…
Holonomic quantum computation is the idea to use non-Abelian geometric phases to implement universal quantum gates that are robust to fluctuations in control parameters. Here, we propose a compact design for a holonomic quantum computer based on coupled three-level systems. The scheme does not require adiabatic evolution and can be implemented in arrays of atoms or ions trapped in tailored standing wave potentials.
Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors as well as high-speed realization. Several schemes of its implementation have been put forward based on various physical systems, each of which has some particular merits. In this paper, we put forward an alternative scheme of nonadiabatic holonomic quantum computation, in which a universal set of quantum gates is realized based on Rydberg superatoms. A Rydberg superatom is a mesoscopic atomic ensemble that allows for only a single Rydberg excitation shared by many atoms wi…
Holonomic quantum computation: a scalable adiabatic architecture
本文提出一种基于全几何亚稳门的可扩展量子计算框架，通过微分几何分析揭示了这些门的几何本质和抗噪声特性，并结合最近的里德堡量子计算进展验证其可行性。
We consider an atom-field coupled system, in which two pairs of four-level atoms are respectively driven by laser fields and trapped in two distant cavities that are connected by an optical fiber. First, we show that an effective squeezing reservoir can be engineered under appropriate conditions. Then, we show that a two-qubit geometric CPHASE gate between the atoms in the two cavities can be implemented through adiabatically manipulating the engineered reservoir along a closed loop. This scheme that combines engineering environment with decoherence-free space and geometric phase quantum compu…
Nonadiabatic holonomic quantum computation (NHQC) has attracted significant attention due to its fast evolution and the geometric nature induced resilience to local noises. However, its long operation time and complex physical implementation make it hard to surpass the dynamical scheme, and thus hindering its wide application. Here, we present to implement NHQC with the shortest path under some conditions, through the inverse Hamiltonian engineering technique, which posseses higher fidelity and stronger robustness than previous NHQC schemes. Meanwhile, the gate performance in our scheme can be…
Nonadiabatic holonomic quantum computation provides the means to perform fast and robust quantum gates by utilizing the resilience of non-Abelian geometric phases to fluctuations of the path in state space. While the original scheme [New J. Phys. {\bf 14}, 103035 (2012)] needs two loops in the Grassmann manifold (i.e., the space of computational subspaces of the full state space) to generate an arbitrary holonomic one-qubit gate, we propose single-loop one-qubit gates that constitute an efficient universal set of holonomic gates when combined with an entangling holonomic two-qubit gate. Our on…
Quantum computing has been attracting tremendous efforts in recent years. One prominent application is to perform quantum simulations of electron correlations in large molecules and solid-state materials, where orbital degrees of freedom are crucial to quantitatively model electronic properties. Electron orbitals unlike quantum spins obey crystal symmetries, making the atomic orbital in optical lattices a natural candidate to emulate electron orbitals. Here, we construct atom-orbital qubits by manipulating $s$- and $d$-orbitals of atomic Bose-Einstein condensation in an optical lattice. Noise-…
The protection of the coherence of open quantum systems against the influence of their environment is a very topical issue. A scheme is proposed here which protects a general quantum system from the action of a set of arbitrary uncontrolled unitary evolutions. This method draws its inspiration from ideas of standard error-correction (ancilla adding, coding and decoding) and the Quantum Zeno Effect. A pedagogical demonstration of our method on a simple atomic system, namely a Rubidium isotope, is proposed.
$d$-pod realization of nonadiabatic holonomic quantum computation
本文提出将非绝热全息量子计算推广到$d$-pod构型，利用光或微波脉冲实现通用单、双qudit门，并以qutrit为例展示每个门至多两个回路、三个脉冲的紧凑实现。
Geometric Phases in Two-Level Mixing: From Neutral Mesons to Holonomic Qubits and Topological Majorana Modes
本文通过几何相位统一了中性介子振荡、量子比特操作与Kitaev链拓扑，揭示了类CP参数、Bargmann不变量及动量空间绕数的内在联系。
We propose a protocol for bosonic binomial-code nonadiabatic holonomic quantum computation in a system composed of an artificial atom ultrastrongly coupled to a cavity resonator. In our protocol, the binomial codes, formed by superpositions of Fock states, can greatly save physical resources to correct errors in quantum computation. We apply to the system strong driving fields designed by shortcuts-to-adiabatic methods. This reduces the gate time to tens of nanoseconds. Decoherence of the system accumulated over time can be effectively reduced by such a fast evolution. Noise induced by control…
We investigate an all-out optical setup allowing for generation of non-Abelian geometric phases on its large degenerate eigenspaces. The proposal has the form of an M -pod system and can be implemented in terms of integrated photonic waveguide structures. We show that by injecting a larger number of photons into the optical setup, the degeneracy of eigenspaces scales rapidly. After studying the spectral properties of our system for the general case, we show how arbitrary U(4) transformations can be generated on the dark subspace of an optical tripod filled with two photons. Moreover, a degener…
We present an experimentally feasible scheme to implement holonomic quantum computation in the ultrastrong-coupling regime of light-matter interaction. The large anharmonicity and the Z2 symmetry of the quantum Rabi model allow us to build an effective three-level Λ-structured artificial atom for quantum computation. The proposed physical implementation includes two gradiometric flux qubits and two microwave resonators where single-qubit gates are realized by a two-tone driving on one physical qubit, and a two-qubit gate is achieved with a time-dependent coupling between the field quadratures …
We present a theoretical scheme that allows to perform a universal set of holonomic gates on a two qubit register, formed by a $^{13}$C nuclear spin coupled to the electron spin of a nitrogen-vacancy center in diamond. Strong hyperfine interaction between the electron spin and the spins of the first three shells of $^{13}$C atoms allows to operate the state of the register on the submicrosecond timescale using microwave pulses only. We describe the system and the operating regime analytically and numerically, as well as simulate the initialization protocols.
The geometric aspects of quantum mechanics are underlined most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a closed path in Hilbert space. The geometric phase is determined only by the shape of this path and is -- in its simplest form -- a real number. However, if the system contains degenerate energy levels, matrix-valued geometric phases, termed non-abelian holonomies, can emerge. They play an important role for the creation of synthetic gauge fields in cold atomic gases and the description of non-abelian anyon statistics. Moreov…
Investigation of Floquet engineered non-Abelian geometric phase for holonomic quantum computing
本研究在超冷铷原子中通过Floquet工程实现非阿贝尔几何相位，验证了单量子比特绝热量子门操作，同时指出该技术仍存在与简并系统类似的局限。
Arrays of neutral-atom qubits in optical tweezers are a promising platform for quantum computation. Despite experimental progress, a major roadblock for realizing neutral atom quantum computation is the qubit initialization. Here we propose that supersymmetry -- a theoretical framework developed in particle physics -- can be used for ultra-high fidelity initialization of neutral-atom qubits. We show that a single atom can be deterministically prepared in the vibrational ground state of an optical tweezer by adiabatically extracting all excited atoms to a supersymmetric auxiliary tweezer. The s…
We demonstrate guiding of cold neutral atoms along a current carrying wire. Atoms either move in Kepler-like orbits around the wire or are guided in a potential tube on the side of the wire which is created by applying an additional homogeneous bias field. These atom guides are very versatile and promising for applications in atom optics.
Photovoltaic effect of neutral atoms using inhomogeneous light in double-trap opened system is studied theoretically. Using asymmetric external driving field to replacing original asymmetric chemical potential of atoms, we create polarization of atom population in the double-trap system. The polarization of atom number distribution induces net current of atoms and works as collected carriers in the cell. The cell can work even under partially coherent light. The whole configuration is described by quantum master equation considering weak tunneling between the system and its reservoirs at finit…
We propose a protocol for creating a fully entangled GHZ-type state of neutral atoms in spatially separated optical atomic clocks. In our scheme, local operations make use of the strong dipole-dipole interaction between Rydberg excitations, which give rise to fast and reliable quantum operations involving all atoms in the ensemble. The necessary entanglement between distant ensembles is mediated by single-photon quantum channels and collectively enhanced light-matter couplings. These techniques can be used to create the recently proposed quantum clock network based on neutral atom optical cloc…
Research on quantum compilation of neutral atom quantum computing platform
针对中性原子量子计算平台编译方法不成熟的问题，本文综述基于矩阵分解的方法，并提出可将任意酉操作分解为平台适配量子门、且电路可直接运行的编译算法。
Motivated by recent developments of hydrodynamical quantum mechanical analogs [J. W. M. Bush, Annu. Rev. Fluid Mech. 47, 269-292 (2015)] we provide a relativistic model for a classical particle coupled to a scalar wave-field through a holonomic constraint. In presence of an external Coulomb field we define a regime where the particle is guided by the wave in a way similar to the old de Broglie phase-wave proposal. Moreover, this dualistic mechanical analog of the quantum theory is reminiscent of the double-solution approach suggested by de Broglie in 1927 and is able to reproduce the Bohr-Somm…
Neutral Atoms in Optical Tweezers as Messenger Qubits for Scaling up a Trapped Ion Quantum Computer
提出用光镊穿梭中性原子作为确定性信使，在模块化囚禁离子量子寄存器间执行原子-离子纠缠门，实现比光子互连快两个数量级的远程纠缠。
In this work we study the de Haas van Alfhen (dHvA) effect for neutral atoms with a nonvanishing magnetic moment interacting with an electric field. Considering the particles confined in a two dimensional (2D) atomic cloud and using the Landau-Aharonov-Casher (LAC) theory, we obtain the effective magnetic field as well as the energy eigenfunctions and eigenvalues of the system. Assuming the neutral atoms as being $ ^{87}\mathrm{Rb} $ ultracold Rydberg atoms we calculate the degeneracy of the energy levels. Under a strong effective magnetic field regime we present the quantum oscillations in th…
We develop a method to entangle neutral atoms using cold controlled collisions. We analyze this method in two particular set-ups: optical lattices and magnetic micro-traps. Both offer the possibility of performing certain multi-particle operations in parallel. Using this fact, we show how to implement efficient quantum error correction and schemes for fault-tolerant computing.
We derive the non-retarded energy shift of a neutral atom for two different geometries. For an atom close to a cylindrical wire we find an integral representation for the energy shift, give asymptotic expressions, and interpolate numerically. For an atom close to a semi-infinite halfplane we determine the exact Green's function of the Laplace equation and use it derive the exact energy shift for an arbitrary position of the atom. These results can be used to estimate the energy shift of an atom close to etched microstructures that protrude from substrates.
Many proposals for quantum information processing require precise control over the motion of neutral atoms, as in the manipulation of coherent matter waves or the confinement and localization of individual atoms. Patterns of micron-sized wires, fabricated lithographically on a flat substrate, can conveniently produce large magnetic-field gradients and curvatures to trap cold atoms and to facilitate the production of Bose-Einstein condensates. This paper describes tools and techniques for the construction of such devices.
By placing changeable nanofabricated structures (wires, dots, etc.) on an atom mirror one can design guiding and trapping potentials for atoms. These potentials are similar to the electrostatic potentials which trap and guide electrons in semiconductor quantum devices like quantum wires and quantum dots. This technique will allow the fabrication of nanoscale atom optical devices.
Realization of controlled Remote implementation of operation
研究CRIO技术以实现高安全性的远程操作，基于光子-腔-原子系统构建CZ门与非绝热完整几何受控门，并利用反阻塞效应和动力学方案提升门在退相干下的鲁棒性。
We present a scheme for a reconstruction of states of quantum systems from incomplete tomographic-like data. The proposed scheme is based on the Jaynes principle of Maximum Entropy. We apply our algorithm for a reconstruction of motional quantum states of neutral atoms. As an example we analyze the experimental data obtained by the group of C. Salomon at the ENS in Paris and we reconstruct Wigner functions of motional quantum states of Cs atoms trapped in an optical lattice.
Hardware-Aware Compilation and Execution of Bivariate Bicycle Codes on Neutral-Atom Systems
针对中性原子系统执行双变量自行车码需硬件感知映射的问题，提出Park-n-Ride系统，通过协同设计码抽象与硬件执行，实现qLDPC原语在该阵列上的高效执行。
We introduce lossless state detection of trapped neutral atoms based on cavity-enhanced fluorescence. In an experiment with a single 87-Rb atom, a hyperfine-state-detection fidelity of 99.4% is achieved in 85 microseconds. The quantum bit is interrogated many hundreds of times without loss of the atom while a result is obtained in every readout attempt. The fidelity proves robust against atomic frequency shifts induced by the trapping potential. Our scheme does not require strong coupling between the atom and cavity and can be generalized to other systems with an optically accessible quantum b…
We theoretically study bipartite entanglement purification with neutral atoms via cavity-assistant interaction and linear optical elements. We focus on entanglement distillation and the recurrence protocol, whose performances under idealized and realistic conditions are discussed. The implementation of these purification protocols has been tested with numerical simulations. We analyze the performance and stability of all required operations and emphasize that all techniques are feasible with current experimental technology.
We propose several schemes for implementing a fast two-qubit quantum gate for neutral atoms with the gate operation time much faster than the time scales associated with the external motion of the atoms in the trapping potential. In our example, the large interaction energy required to perform fast gate operations is provided by the dipole-dipole interaction of atoms excited to low-lying Rydberg states in constant electric fields. A detailed analysis of imperfections of the gate operation is given.
One can implement fast two-qubit entangling gates by exploiting the Rydberg blockade. Although various theoretical schemes have been proposed, experimenters have not yet been able to demonstrate two-atom gates of high fidelity due to experimental constraints. We propose a novel scheme, which only uses a single Rydberg pulse illuminating both atoms, for the construction of neutral-atom controlled-phase gates. In contrast to the existing schemes, our approach is simpler to implement and requires neither individual addressing of atoms nor adiabatic procedures. With parameters estimated based on a…
We investigate the scattering of neutral polarizable atoms from an electrically charged wire placed in a homogeneous magnetic field. The atoms carry an induced electric dipole. The reflecting wire is discussed. We calculate the scattering amplitude and cross section the practically more important case that atoms are totally absorbed at the surface of the wire. If the magnetic field is present, there is a dominating Aharonov-Bohm peak in the forward direction followed by decreasing oscillations for larger angles. An experimental realization of this modulated Aharonov-Bohm scattering should be p…
We present the first demonstration of a CNOT gate using neutral atoms. Our implementation of the CNOT uses Rydberg blockade interactions between neutral atoms held in optical traps separated by >8 μ\rm m. We measure CNOT fidelities of F=0.73 and 0.72 using two different gate protocols, and show by measurement of parity oscillations that the gate can be used to generate two-atom states with fidelity at the threshold for entanglement. We anticipate that the long range nature of the Rydberg interaction will be attractive for future extensions of this work to multi-qubit systems.
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 …
In the Thomas-Fermi model for the atom or ion, the electric potential $ϕ$ and electron density $n$ are both expressed in terms of a screening number $χ$ and the radius $x$. The second order differential equation for the screening function $χ(x)$ cannot be solved in closed form. Two approximate formulas for the screening function of the neutral atom are proposed: the first formula is analytically simple, the second formula has the roles of dependent and independent variable interchanged. Both formulas reproduce the true screening function very accurately.
Using optical dipole forces we have realized controlled transport of a single or any desired small number of neutral atoms over a distance of a centimeter with sub-micrometer precision. A standing wave dipole trap is loaded with a prescribed number of cesium atoms from a magneto-optical trap. Mutual detuning of the counter-propagating laser beams moves the interference pattern, allowing us to accelerate and stop the atoms at preselected points along the standing wave. The transportation efficiency is close to 100%. This optical "single-atom conveyor belt" represents a versatile tool for future…
Energy levels of neutral atoms have been re-examined by applying an alternative perturbative scheme in solving the Schrodinger equation for the Yukawa potential model with a modified screening parameter. The predicted shell binding energies are found to be quite accurate over the entire range of the atomic number $Z$ up to 84 and compare very well with those obtained within the framework of hyper-virial-Pade scheme and the method of shifted large-N expansion. It is observed that the new perturbative method may also be applied to the other areas of atomic physics.
We propose a scheme to achieve quantum computation with neutral atoms whose interactions are catalyzed by single photons. Conditional quantum gates, including an $N$-atom Toffoli gate and nonlocal gates on remote atoms, are obtained through cavity-assisted photon scattering in a manner that is robust to random variation in the atom-photon coupling rate and which does not require localization in the Lamb-Dicke regime. The dominant noise in our scheme is automatically detected for each gate operation, leading to signalled errors which do not preclude efficient quantum computation even if the err…
A neutral-atom system serves as a promising platform for realizing gate-based quantum computing because of its capability to trap and control several atomic qubits in different geometries and the ability to perform strong, long-range interactions between qubits; however, the two-qubit entangling gate fidelity lags behind competing platforms such as superconducting systems and trapped ions. The aim of our work is to design a fast, robust, high-fidelity controlled-Z (CZ) gate, based on the Rydberg-blockade mechanism, for neutral atoms. We propose a gate procedure that relies on simultaneous and …
We propose a scalable neutral atom quantum computer with an on-demand interaction. Artificial lattice of near field optical traps is employed to trap atom qubits. Interactions between atoms can be turned off if the atoms are separated by a high enough potential barrier so that the size of the atomic wave function is much less than the interatomic distance. One-qubit gate operation is implemented by a gate control laser beam which is attached to an individual atom. Two-qubit gate operation between a particular pair of atoms is introduced by leaving these atoms in an optical lattice and making t…
We propose a new quantum-computing scheme using ultracold neutral ytterbium atoms in an optical lattice. The nuclear Zeeman sublevels define a qubit. This choice avoids the natural phase evolution due to the magnetic dipole interaction between qubits. The Zeeman sublevels with large magnetic moments in the long-lived metastable state are also exploited to address individual atoms and to construct a controlled-multiqubit gate. Estimated parameters required for this scheme show that this proposal is scalable and experimentally feasible.
We propose a cooling scheme to prepare stationary entanglement of neutral atoms in the Rydberg blockade regime by combination of periodically collective laser pumping and dissipation. In each cycle, the controlled unitary dynamics process can selectively pump atoms away from the non-target state while maintaining the target state unchanged. The subsequent dissipative process redistributes the populations of ground states through the engineered spontaneous emission. After a number of cycles, the system will be eventually stabilized into the desired steady state independent of the initial state.…
A dynamics regime of Rydberg atoms, unselective ground-state blockade (UGSB), is proposed in the context of Rydberg antiblockade (RAB), where the evolution of two atoms is suppressed when they populate in an identical ground state. UGSB is used to implement a SWAP gate in one step without individual addressing of atoms. Aiming at circumventing common issues in RAB-based gates including atomic decay, Doppler dephasing, and fluctuations in the interatomic coupling strength, we modify the RAB condition to achieve a dynamical SWAP gate whose robustness is much greater than that of the nonadiabatic…
We optically detect the positions of single neutral cesium atoms stored in a standing wave dipole trap with a sub-wavelength resolution of 143 nm rms. The distance between two simultaneously trapped atoms is measured with an even higher precision of 36 nm rms. We resolve the discreteness of the interatomic distances due to the 532 nm spatial period of the standing wave potential and infer the exact number of trapping potential wells separating the atoms. Finally, combining an initial position detection with a controlled transport, we place single atoms at a predetermined position along the tra…
We show how realistic cavity-assisted interaction between neutral atoms and coherent optical pulses, and measurement techniques, combined with optical transportation of atoms, allow for a universal set of quantum gates acting on decoherence-free subspace (DFS) in deterministic way. The logical qubits are immunized to the dominant source of decoherece--dephasing; while, the influences of additional errors are shown by numerical simulations. We analyze the performance and stability of all required operations and emphasize that all techniques we use are feasible with current experimental technolo…
We present an omnidirectional matter wave guide on an atom chip. The rotational symmetry of the guide is maintained by a combination of two current carrying wires and a bias field pointing perpendicular to the chip surface. We demonstrate guiding of thermal atoms around more than two complete turns along a spiral shaped 25mm long curved path (curve radii down to 200$μ$m) at various atom--surface distances (35-450$μ$m). An extension of the scheme for the guiding of Bose-Einstein condensates is outlined.
Mode multiplexing for scalable cavity-enhanced operations in neutral-atom arrays
提出利用单光学腔的多模式实现中性原子阵列中快速、并行的腔增强操作，支持多达50种模式复用，可加速中电路综合征提取并提高远程纠缠分布速率。
Fast measurement of neutral atoms with a multi-atom gate
本文提出利用快速多原子Rydberg门实现中性原子快速测量，通过减少测量积分时间并提高保真度，实现光子收集效率提升和灵敏度降低。
We present a proposal for quantum information processing with neutral atoms trapped in optical lattices as qubits. Initialization and coherent control of single qubits can be achieved with standard laser cooling and spectroscopic techniques. We consider entangling two-qubit logic gates based on optically induced dipole-dipole interactions, calculating a figure-of-merit for various protocols. Massive parallelism intrinsic to the lattice geometry makes this an intriguing system for scalable, fault-tolerant quantum computation.
We theoretically study specific schemes for performing a fundamental two-qubit quantum gate via controlled atomic collisions by switching microscopic potentials. In particular we calculate the fidelity of a gate operation for a configuration where a potential barrier between two atoms is instantaneously removed and restored after a certain time. Possible implementations could be based on microtraps created by magnetic and electric fields, or potentials induced by laser light.
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