Applicability of Rydberg atoms to quantum computers is examined from experimental point of view. In many theoretical proposals appeared recently, excitation of atoms into highly excited Rydberg states was considered as a way to achieve quantum entanglement in cold atomic ensembles via dipole-dipole interaction that could be strong for Rydberg atoms. Appropriate conditions to realize a conditional quantum phase gate have been analyzed. We also present the results of modeling experiments on microwave spectroscopy of single- and multi-atom excitations at the one-photon 37S-37P and two-photon 37S-38S transitions in an ensemble of a few sodium Rydberg atoms. The microwave spectra were investigated for various final states of the ensemble initially prepared in its ground state. The quantum NOT operation with single atoms was found to be affected by the Doppler effect and fluctuations of the microwave field. The spectrum of full excitation of several Rydberg atoms was much narrower than that of a single atom. This effect might be useful for the high-resolution spectroscopy. The results may be also applied to the studies on collective laser excitation of ground-state atoms aiming to realize quantum gates.
We discuss a method for scaling a neutral atom Rydberg gate quantum processor to a large number of qubits. Limits are derived showing that the number of qubits that can be directly connected by entangling gates with errors at the $10^{-3}$ level using long range Rydberg interactions between sites in an optical lattice, without mechanical motion or swap chains, is about 500 in two dimensions and 7500 in three dimensions. A scaling factor of 60 at a smaller number of sites can be obtained using collective register encoding in the hyperfine ground states of the rare earth atom Holmium. We present…
Trapped Rydberg ions are a promising novel approach to quantum computing and simulations. They are envisaged to combine the exquisite control of trapped ion qubits with the fast two-qubit Rydberg gates already demonstrated in neutral atom experiments. Coherent Rydberg excitation is a key requirement for these gates. Here, we carry out the first coherent Rydberg excitation of an ion and perform a single-qubit Rydberg gate, thus demonstrating basic elements of a trapped Rydberg ion quantum computer.
Quantum scrambling measured by out-of-time-ordered correlator (OTOC) has an important role in understanding the physics of black holes and evaluating quantum chaos. It is known that Rydberg atom has been a general interest due to its extremely favourable properties for building a quantum simulator. Fast and efficient quantum simulators can be developed by studying quantum scrambling in related systems. Here we present a general quantum circuit to theoretically implement an interferometric protocol which is a technique proposed to measure OTOC functions. We apply this circuit to measure OTOC an…
Cold atoms in highly excited Rydberg states are promising candidates to implement quantum logic gates of a quantum computer via long-range dipole-dipole interaction. Two-qubit gates require a controlled interaction of only two close Rydberg atoms. We report on the first spectroscopic observation of the resonant dipole-dipole interaction between two cold rubidium Rydberg atoms confined in a small laser excitation volume. The interaction strength was controlled by fine-tuning of the Rydberg levels into a Forster resonance using the Stark effect. The observed resonance line shapes are in good agr…
Accurate data on electric-dipole transition matrix elements (EDTMs) for bound-bound Rydberg-atom transitions become increasingly important in science and technology. Here we compute radial EDTMs of rubidium using the length, velocity and acceleration gauges for electric-dipole-allowed transitions between states with principal and angular-momentum quantum numbers ranging from 15 to 100. Wave-functions are computed based upon model potentials from Marinescu et al., Phys. Rev. A {\bf{49}}, 982 (1994). Length-gauge EDTMs, often used for low-$\ell$ transitions, are found to deviate from the fundame…
We present a blueprint for building a fault-tolerant universal quantum computer with Rydberg atoms. Our scheme, which is based on the surface code, uses individually-addressable optically-trapped atoms as qubits and exploits electromagnetically induced transparency to perform the multi-qubit gates required for error correction and computation. We discuss the advantages and challenges of using Rydberg atoms to build such a quantum computer, and we perform error correction simulations to obtain an error threshold for our scheme. Our findings suggest that Rydberg atoms are a promising candidate f…
Accurate quantum gates are basic elements for building quantum computers. There has been great interest in designing quantum logic gates by using blockade effect of Rydberg atoms recently. The fidelity and operation speed of these gates, however, are fundamentally limited by an intrinsic blockade error. Here we propose a type of quantum gates, which are based on Rydberg blockade effect, yet free from any blockade error. In contrast to the "blocking" method in previous schemes, we use Rydberg energy shift to realize a rational generalized Rabi frequency so that a $π$ phase for one input state o…
Quantum gates and entanglement based on dipole-dipole interactions of neutral Rydberg atoms are relevant to both fundamental physics and quantum information science. The precision and robustness of the Rydberg-mediated entanglement protocols are the key factors limiting their applicability in experiments and near-future industry. There are various methods for generating entangling gates by exploring the Rydberg interactions of neutral atoms, each equipped with its own strengths and weaknesses. The basics and tricks in these protocols are reviewed, with specific attention paid to the achievable…
Alkaline-earth-like~(AEL) atoms with two valence electrons and a nonzero nuclear spin can be excited to Rydberg state for quantum computing. Typical AEL ground states possess no hyperfine splitting, but unfortunately a GHz-scale splitting seems necessary for Rydberg excitation. Though strong magnetic fields can induce a GHz-scale splitting, weak fields are desirable to avoid noise in experiments. Here, we provide two solutions to this outstanding challenge with realistic data of well-studied AEL isotopes. In the first theory, the two nuclear spin qubit states $|0\rangle$ and $|1\rangle$ are ex…
Generating quantum entanglement in large systems on time scales much shorter than the coherence time is key to powerful quantum simulation and computation. Trapped ions are among the most accurately controlled and best isolated quantum systems with low-error entanglement gates operated via the vibrational motion of a few-ion crystal within tens of microseconds. To exceed the level of complexity tractable by classical computers the main challenge is to realise fast entanglement operations in large ion crystals. The strong dipole-dipole interactions in polar molecule and Rydberg atom systems all…
Atoms in highly excited (Rydberg) states have a number of unique properties which make them attractive for applications in quantum information. These are large dipole moments, lifetimes and polarizabilities, as well as strong long-range interactions between Rydberg atoms. Experimental methods of laser cooling and precision spectroscopy enable the trapping and manipulation of single Rydberg atoms and applying them for practical implementation of quantum gates over qubits of a quantum computer based on single neutral atoms in optical traps. In this paper, we give a review of the experimental and…
We introduce a generative pretained transformer (GPT) designed to learn the measurement outcomes of a neutral atom array quantum computer. Based on a vanilla transformer, our encoder-decoder architecture takes as input the interacting Hamiltonian, and outputs an autoregressive sequence of qubit measurement probabilities. Its performance is studied in the vicinity of a quantum phase transition in Rydberg atoms in a square lattice array. We explore the ability of the architecture to generalize, by producing groundstate measurements for Hamiltonian parameters not seen in the training set. We focu…
We theoretically investigate the possibility of creating phonon-mediated spin-spin interactions between neutral atoms trapped in optical tweezers. By laser coupling the atoms to Rydberg states, collective modes of motion appear. We show that these can be used to mediate effective spin-spin interactions or quantum logic gates between the atoms in analogy to schemes employed in trapped ions. In particular, we employ Rydberg dressing in a novel scheme to induce the needed interaction, and we show that it is possible to replicate the working of the Mølmer-Sørensen entanglement scheme. The Mølmer-S…
We question the microcanonical hypothesis, often made to account for the thermalization of complex closed quantum systems, on the specific example of a chain of two-level atoms optically driven by a resonant laser beam and strongly interacting via Rydberg-Rydberg dipole-dipole interactions. Along its (necessarily unitary) evolution, this system is indeed expected to thermalize, i.e. observables, such as the number of excitations, stop oscillating and reach equilibrium-like expectation values. The latter are often calculated through assuming the system can be effectively described by a thermal-…
Platforms of Rydberg atoms have been proposed as promising candidates to solve some combinatorial optimization problems. Here, we compute quantitative requirements on the system sizes and noise levels that these platforms must fulfill to reach quantum advantage in approximately solving the Unit-Disk Maximum Independent Set problem. Using noisy simulations of Rydberg platforms of up to 26 atoms interacting through realistic van der Waals interactions, we compute the average approximation ratio that can be attained with a simple quantum annealing-based heuristic within a fixed temporal computati…
In this chapter, we present an overview of experiments with trapped Rydberg ions and outline the advantages and challenges of developing applications of this new platform for quantum computing, sensing and simulation. Trapped Rydberg ions feature several important properties, unique in their combination: they are tightly bound in a harmonic potential of a Paul trap, in which their internal and external degrees of freedom can be controlled in a precise fashion. High fidelity state preparation of both internal and motional states of the ions has been demonstrated, and the internal states have be…
Due to its potential for implementing a scalable quantum computer, multiqubit Toffoli gate lies in the heart of quantum information processing. In this article, we demonstrate a multiqubit blockade gate with atoms arranged in a three-dimension spheroidal array. The gate performance is greatly improved by the method of optimizing control-qubit distributions on the spherical surface via evolutionary algorithm, which leads to an enhanced asymmetric Rydberg blockade. This spheroidal configuration, not only arises a well preservation for the dipole blockade energy between arbitrary control-target p…
Protocols of coherent motion control for an interaction-driven Rydberg gate
Institute for Molecular Science, National Institutes of Natural Sciences（国立自然科学研究所分子科学研究所）；ETH Zürich（苏黎世联邦理工学院）；RIKEN Center for Quantum Computing (RQC)（理化学研究所量子计算中心）
The strong interaction between individual Rydberg atoms provides a powerful tool exploited in an ever-growing range of applications in quantum information science, quantum simulation, and ultracold chemistry. One hallmark of the Rydberg interaction is that both its strength and angular dependence can be fine-tuned with great flexibility by choosing appropriate Rydberg states and applying external electric and magnetic fields. More and more experiments are probing this interaction at short atomic distances or with such high precision that perturbative calculations as well as restrictions to the…
Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Ludwig-Maximilians-Universität（路德维希-马克西米利安大学）；Technische Universität München（慕尼黑工业大学）
We describe and analyze an architecture for quantum optimization to solve maximum independent set (MIS) problems using neutral atom arrays trapped in optical tweezers. Optimizing independent sets is one of the paradigmatic, NP-hard problems in computer science. Our approach is based on coherent manipulation of atom arrays via the excitation into Rydberg atomic states. Specifically, we show that solutions of MIS problems can be efficiently encoded in the ground state of interacting atoms in 2D arrays by utilizing the Rydberg blockade mechanism. By studying the performance of leading classical a…
We show that the quantum dimer state on the Kagome lattice, which was recently realized with high fidelity in a Rydberg quantum simulator [Semeghini et al., Science 374, 6572 (2021)], offers a sufficient resource for universal measurement-based quantum computations. In particular, we provide an efficient encoding of logical qubits in this state, and give explicit measurement sequences that implement a universal set of gates on these qubits. Since the building blocks of the proposed measurements have already been experimentally implemented, our work highlights one possible path towards promotin…
Previously, we had proposed the technique of light shift imbalance induced blockade which leads to a condition where a collection of non-interacting atoms under laser excitation remains combined to a superposition of the ground and the first excited states, thus realizing a collective state quantum bit which in turn can be used to realize a quantum computer. In this paper, we show first that the light shift imbalance by itself is actually not enough to produce such a blockade, and explain the reason why the limitation of our previous analysis had reached this constraint. We then show that by i…
Recently, Rydberg atoms appeared as a viable alternative to the quantum gates built on atomic or molecular ions. The lifetimes of the circular Rydberg states can be in the millisecond range. That prevents inherent metastability of the Rydberg atoms to influence computation at the typical decoherence times, which are now being achieved in the range of 1 ms. The paper proposes to use a pinning potential of an image charge on a cryogenic substrate (liquid He, in particular) to confine large densities of Rydberg atoms to dielectric surfaces. The substrate can also act as a natural cooler medium. A…
Arrays of optically trapped atoms excited to Rydberg states have recently emerged as a competitive physical platform for quantum simulation and computing, where high-fidelity state preparation and readout, quantum logic gates and controlled quantum dynamics of more than 100 qubits have all been demonstrated. These systems are now approaching the point where reliable quantum computations with hundreds of qubits and realistically thousands of multiqubit gates with low error rates should be within reach for the first time. In this article we give an overview of the Rydberg quantum toolbox, emphas…
Symmetric $C_Z$ gate for ultracold neutral atoms based on counterdiabatic driving at Rydberg excitation
Rzhanov Institute of Semiconductor Physics SB RAS（拉扎诺夫半导体物理研究所西伯利亚分院）；Novosibirsk State University（新西伯利亚国立大学）；Novosibirsk State Technical University（新西伯利亚国立技术大学）；Institute of Laser Physics SB RAS（激光物理研究所西伯利亚分院）；Division of Precision Measurement Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences（中国科学院精密测量科学与技术创新研究院武汉物理与数学研究所精密测量物理研究室）
Neutral atom arrays have recently emerged as a promising platform for quantum information processing. One important remaining roadblock for the large-scale application of these systems is the ability to perform error-corrected quantum operations. To entangle the qubits in these systems, atoms are typically excited to Rydberg states, which could decay or give rise to various correlated errors that cannot be addressed directly through traditional methods of fault-tolerant quantum computation. In this work, we provide the first complete characterization of these sources of error in a neutral-atom…
We study the implementation of a high fidelity controlled-phase gate in a Rydberg quantum computer. The protocol is based on a symmetric gate with respect to the two qubits as experimentally realized by Levine et al [Phys. Rev. Lett. 123, 170503 (2019)], but allows for arbitrary pulse shapes with time-dependent detuning. Optimizing the pulse shapes, we introduce laser pulses which shorten the time spent in the Rydberg state by 10% and reduce the leading contribution to the gate infidelity, i.e., the decay from the Rydberg state. Remarkably, this reduction can be achieved for smooth pulses in d…
Dispersion forces have a sizeable effect on the energy levels of highly excited Rydberg atoms when brought close to material surfaces. Rydberg atoms experience energy shifts in the GHz range at micrometer distances, suggestive of considerable state admixture. We show that despite the non-applicability of perturbation theory for Rydberg atoms near a surface, the energy shift due to the dispersion interaction can be obtained from an exact diagonalization of the interaction Hamiltonian by finding the zeros of the Pick function. Moreover, we show that contrary to intuition from single-mode approac…
With Rydberg dipole interactions, a mesoscopic atomic ensemble may behave like a two-level single atom, resulting in the so-called picture of superatom. It is in potential a strong candidate as a qubit in quantum information science, especially for efficient coupling with single photons via collective enhancement that is essential for building quantum internet to connect remote quantum computers. Previously, preliminary studies have been carried out in demonstrating basic concept of Rydberg superatom, a single-photon source, and entanglement with a single photon, etc. While a crucial element o…
Implementation of non-local arbitrary two-qubit controlled gates via geometric quantum computation with Rydberg anti-blockade
Zhejiang Normal University（浙江师范大学）；Zhejiang Institute of Photoelectronics（浙江光电子研究所）；Key Laboratory of Optical Information Detection and Display Technology of Zhejiang, Zhejiang Normal University（浙江省光学信息探测与显示技术重点实验室）
There is a significant ongoing effort in realizing quantum annealing with different physical platforms. The challenge is to achieve a fully programmable quantum device featuring coherent adiabatic quantum dynamics. Here we show that combining the well-developed quantum simulation toolbox for Rydberg atoms with the recently proposed Lechner-Hauke-Zoller~(LHZ) architecture allows one to build a prototype for a coherent adiabatic quantum computer with all-to-all Ising interactions and, therefore, a novel platform for quantum annealing. In LHZ a infinite-range spin-glass is mapped onto the low ene…
Concentration-Free Quantum Kernel Learning in the Rydberg Blockade
Département de physique, Université de Sherbrooke（谢布罗克大学物理系）；Département de génie électrique et de génie informatique, Université de Sherbrooke（谢布罗克大学电气与计算机工程系）
Quantum algorithms promise quadratic or exponential speedups for applications in cryptography, chemistry and material sciences. The topologies of today's quantum computers offer limited connectivity, leading to significant overheads for implementing such quantum algorithms. One-dimensional topology displacements that remedy these limits have been recently demonstrated for architectures based on Rydberg atoms, and they are possible in principle in photonic and ion trap architectures. We present the first optimal quantum circuit-to-architecture mapping algorithm that exploits such one-dimensiona…
