Scalable quantum computers, sprouting from Rydberg atoms

The principles of quantum computing, logic gate operations, quantum coding and quantum algorithms have been successfully demonstrated in physical body systems with a few quantum bits, confirming that there are no principle difficulties in the realization of quantum computing. However, there are two major obstacles to actually developing a quantum computer, one of which is the problem of physical scalability and the other is the problem of fault-tolerant computing.

Canada D-Wave's quantum annealing machine, has now embraced 5000 quantum bits, but the quantum annealing machine does not make all the quantum bits entangled, each quantum bit is only entangled with the neighboring quantum bits and interact, can not establish a set of parallel computation, but rather a whole, a single quantum state.

In fact, the key to achieving exponential acceleration in a quantum computer is to realize the entanglement of multiple quantum bits. However, since the interactions between neutral atoms are very weak, it is difficult to obtain the ideal multi-atom entangled state in an ordinary neutral atom system. Therefore, attention has been focused on Rydberg atoms with long-range interactions.

As early as in 2000, it was proposed to realize quantum logic gates using Rydberg atoms, and in recent years the rapid progress made in the field of ultracold atoms has brought new opportunities for the study of Rydberg atoms. Rydberg atoms with highly excited states have promising applications in quantum information technology, quantum simulation, and quantum metrology.

In June 2020, a team of researchers from the California Institute of Technology found that Rydberg strontium atom arrays are promising for quantum computer fabrication. Single- and double-quantum bit operations using Rydberg strontium atom arrays can achieve fidelity higher than 99%, close to that of superconducting quantum bits or ion traps.

The Miraculous Reedburg Atom

Rydberg atoms are highly excited state atoms whose outer electrons are excited to a large principal quantum number n. Because of some characteristics not possessed by other neutral atoms, such as larger orbital radius, longer radiation lifetime and stronger electric dipole moment, Rydberg atoms have important applications in the field of quantum information.

In 1885, Swiss physicist Johann Balmer discovered that the width of the spectral lines of the hydrogen atom could be expressed in a simple form. Subsequently, in 1890, the Swedish physicist Johannes Rydberg modified Balmer's empirical formula in the form of a wave number (the reciprocal of wavelength) and gave a formula for the binding energy of the hydrogen atom:

where Ry is the Rydberg constant, and the Rydberg constant for the hydrogen atom is 13.6 eV. With the establishment of Bohr's model of the atom, it was further determined in 1913 that n in the formula was the principal quantum number of the atom. Bohr found that the Rydberg constant was related to additional fundamental physical constants and gave specific expressions for the Rydberg constant:

where Z is the atomic nuclear charge, e is the electron charge, me is the electron mass, ε0 is the vacuum dielectric constant, and ћ is Planck's constant. On this basis combined with the Rydberg formula one can calculate the energy of the Rydberg state with a very large principal quantum number n.

Johannes Rydberg

A Rydberg state is a state in which the electrons outside the nucleus are farther away from the nucleus (which can be much larger than the size of the nucleus), and therefore the Rydberg state has a high ionization energy, is susceptible to interactions with microwave fields, radiofrequency electric fields, and classical laser fields, and has a long lifetime. Atoms with Rydberg states are called Rydberg atoms. Rydberg atoms have dipole-dipole interactions, i.e., long-range van der Waals forces.

Of the many properties of Rydberg atoms, the most widely studied are the strong long-range interactions. For atoms trapped in a light lattice or ultracold atoms, the interactions between them are small and essentially negligible, e.g., less than 1 Hz between two atoms separated by 1 μm.

The interaction between Rydberg atoms, on the other hand, exhibits a van der Waals interaction when the atomic spacing is small, which is proportional to n6, and a resonance dipole-dipole interaction when the atomic spacing is large, which is proportional to n3. The interactions between the Rydberg atoms are strong due to the large principal quantum number of the Rydberg atoms, n. The interaction between the Rydberg atoms and the Coulomb interaction with the captured ions is very small.

Unlike the Coulombic interactions between trapped ions, the interaction strengths between Rydberg atoms vary over a wide range and can be controlled by the coupled optical field, which makes them significantly superior to trapped ions and ordinary neutral atoms in realizing various quantum gate operations.

The Rydberg atom is a promising physical system for realizing quantum computers because of its long-lived Rydberg states and extremely strong Rydberg interatomic interactions. The long-lived Rydberg state is particularly well suited for storing quantum information, and it greatly reduces the effect of the atom's spontaneous radiation on quantum information. Strong Rydberg interatomic interactions can directly couple two atoms, which is highly conducive to the realization of double-bit gates or interatomic entanglement.

The use of Rydberg atom interactions allows the transfer of entangled states between multiple atoms through excited state transfer in addition to more optimized multi-atom entanglement.

In addition, strong interactions between Rydberg atoms induce an effect of suppressed excitation called dipole blocking, i.e., within a certain range, if an atom is excited to a Rydberg state, the excitation of other atoms in the neighborhood is suppressed.

A system of Rydberg atoms confined within the radius of the Rydberg blockage allows only one Rydberg atom to be excited to the Rydberg state, resulting in the formation of a mesoscopic scale (the scale between the macroscopic and microscopic) Rydberg superatom. It is easier to prepare Rydberg superatoms than Rydberg monatoms, and the collective low-energy states of Rydberg superatoms are particularly well suited to encode quantum bits, which are more robust to leakage of atoms than those encoded by single atoms.

The blocking effect was first observed in the 87Rb (rubidium) atomic gas in 2004 by British physicist David Tong et al. Subsequently it was shown that Förster resonance can enhance this dipole blocking effect.

Since then, the research work no longer only stops at experimentally observing the blocking effect, but people have also proposed many schemes to widely apply the blocking effect to the field of quantum information. For example, the blocking effect of the Rydberg atom system can be utilized to realize quantum gate operation, prepare entangled states, prepare single-photon sources and realize quantum simulators.

During the past decades, people have been working on various properties of Rydberg atoms. However, in earlier years, due to the immaturity of the technology, one could only obtain atoms in the Rydberg state from hot vapor and atomic beams.

In recent years, with the development of laser cooling technology, it has finally been possible to gain a real insight into one of the most important properties of Rydberg atoms without the interference of the thermal energy of the atoms: the strong interactions between the atoms. In the supercooled state, the long-range interactions between atoms gradually come to the fore, and the dynamics of the whole system is almost entirely determined by the long-range interactions.

With the development of quantum information technology, Rydberg atoms are more and more often used as research objects, especially in the preparation of quantum entanglement, Rydberg atoms have an incomparable advantage over ordinary atoms. Utilizing its long-range interactions, the entanglement preparation of larger many-body systems can be realized on a larger scale.

Applications of the Reedburg Atom

Implementing quantum logic gate operations is the basis for quantum computers. the first quantum gate implementation using Rydberg atoms was proposed in 2000 by D. Jaksch et al. at the University of Innsbruck. This was followed by Harvard University's Mikhail Lukin et al. who utilized entanglement between atoms to extend the system to larger, ultracold quantum gases.

Various schemes for realizing phase gates, CNOT gates and CZ gates using the Rydberg atom system have been proposed since then. Some of these schemes combine Rydberg atoms with atomic coherence effects, e.g., gate operations realized in combination with excited Raman adiabatic processes and gate operations realized in combination with electromagnetically induced transparency.

Using Rydberg atoms, not only can we realize dual-atom quantum gates with high fidelity, but also multi-bit phase gates. And these schemes for realizing quantum logic gates do not only remain in theoretical studies; in 2014, German physicist M. M. Muller et al. also experimentally verified the realization of CZ gates.

In the field of quantum communication, quantum entanglement is one of the indispensable resources. There are many schemes to realize quantum entanglement, which can realize entanglement between photons and entanglement between ion systems, etc., and can also realize entanglement through the Rydberg atomic system.

In 2010, Tatjana Wilk et al. of the Max Planck Society, Germany, experimentally achieved the preparation of entangled states of two87 Rb atoms using the dipole blocking effect of Rydberg atoms.In 2012, French physicist Serge Haroche et al. passed Rydberg atoms through a microcavity thereby obtaining entanglement between light and atoms.In 2014, the Bhaktavatsala Rao et al. used the interaction between two different Rydberg states to artificially introduce dissipation into the system to devise schemes to achieve entanglement. The refinement of these entanglement schemes has laid the foundation for realizing quantum communication over long distances.

As Rydberg atoms have important applications in the field of quantum information, some research results have been achieved in China in recent years. For example, in October 2016, the Wuhan Institute of Physics and Mathematics of the Chinese Academy of Sciences (WIPM) launched the project "Research on photonic and atomic quantum state sources based on Rydberg blockage".

The project is based on the manipulation of cold atomic Rydberg states, and intends to realize entangled atoms and associated photons, which will be used as a new type of quantum state source applied to quantum precision measurement technology, and provide effective support for the breakthrough of the traditional limit of measurement technology. Moreover, it is not only valuable in the field of precision measurement, but also has a wide range of application prospects in the fields of quantum computation, quantum simulation, and quantum communication.

At the mid-term summary in July 2018, the project has made a series of outstanding progress, including the realization of fast excited Raman superadiabatic heat transfer under conditions close to the quantum limit, the first international realization of the entanglement of two atoms with heteronuclear nuclei based on the Rydberg blockage, and the theoretical prediction of the existence of non-hyperbolic matter-wave solitons.

Guo Guangcan academician led by the Chinese Academy of Sciences Key Laboratory of Quantum Information "based on the Rydberg atom quantum information experimental research" project also followed. 2020 April, the laboratory professors Shi Baoshen, Ding Dongsheng and the United Kingdom Durham University, the laboratory in cooperation with the Rydberg atom based on the experimental realization of multi-body self-organization simulation, the main research results have been published in the international physics journal Physics Review X on April 29th.

The strong interactions between atoms in the Rydberg atom system allowed the researchers to observe non-equilibrium phase transitions in the system at room temperature. Baosen Shi, Dongsheng Ding et al. have proposed a new detection method to observe nonequilibrium phase transitions through the electromagnetically induced transparency effect of Rydberg atoms. The frequency resolution is improved by two orders of magnitude compared with the conventional method.

Conceptual diagram based on the Rydberg atomic many-body phase transition

In terms of quantum simulation, in August 2019, a research group at the Department of Physics, Tsinghua University, proposed a new quantum simulation scheme in the Rydberg atom many-body system. By laser-embellishing the ground-state Rydberg atoms, they can obtain the equivalent spin exchange between the ground-state atoms and the Rydberg atoms without the need to introduce resonant dipole-dipole interactions, and then quantum regulate the spin transport process in the Rydberg atom many-body system.

In recent years, the School of Physics of Zhengzhou University and the Gravity Center of Huazhong University of Science and Technology have also been conducting research on Rydberg atoms.

In March 2020, a non-destructive Rydberg atom umbrella gate scheme was proposed by the Quantum Information and Quantum Computing Group of the School of Physics, Zhengzhou University. By introducing auxiliary interactions and appropriately choosing the system parameters, the feasibility of the non-destructive Rydberg umbrella gate was theoretically verified.

The Gravity Center of Huazhong University of Science and Technology (HUST) focuses on the preparation of cold atomic microsystems by the more mature laser cooling technique, which utilizes the collective enhancement effect of the atomic system and the excitation blocking effect of the Rydberg atoms to efficiently prepare the Rydberg singly excited states and convert them into the desired light quantum states by Raman light.

In the Department of Quantum Physics and Quantum Information, led by Academician Pan Jianwei, ultracold strontium atom Rydberg quantum gas is also one of the research directions, headed by Prof. Matthias Weidemüller of the University of Heidelberg, Germany, which focuses on the study of Rydberg state excitations, Rydberg precision spectroscopy, Rydberg embellishments, the self-ionization effect, Rydberg state interactions, and other novel quantum phenomena and effects.

Scalable Quantum Computing

Building scalable quantum computers using Rydberg atoms is currently in the theoretical stage.

Gerard Higgins and Markus Hennrich of the University of Stockholm, Sweden, and the University of Innsbruck, Austria, are working on the Rydberg Ion Trap quantum computer.In 2017, the group used lasers to excite a strontium ion to a Rydberg excited state, and then used it to demonstrate the Rydberg gate of a single quantum bit, which is the envisioned Rydberg Ion Trap one of the basic elements of a quantum computer.

The researchers confined a strontium ion in a trap, then used a laser to excite a low-quantum-bit state up to the first excited state, and then excited that state to a higher-energy state, a Rydberg excited state. The study shows that the Rydberg excited states are realized in a coherent manner, which is necessary for building multi-qubit Rydberg gates.

One of the biggest challenges facing quantum computers today is how to proportionally increase the number of entangled quantum bits in each logic gate, which is essential for performing practical quantum computations. In part, part of the reason it is so difficult to increase the number is that the multibit quantum gates commonly used in ion-trap systems create problems of spectral crowding as the number of quantum bits increases.

However, the Rydberg ion-trap system effectively avoids the interference of spectral crowding, which means that if Rydberg ion-trap quantum bits are used to build a quantum computer, it may provide a new path to solving the bottleneck problem that quantum computers encounter as the number of quanta increases.

In addition, Rydberg ion trap quantum computers have other advantages, including better control over quantum bits and faster gate operations.

On June 22, 2020, Higgins' research group published the latest research progress in the journal Nature suggesting that imprisoned Rydberg ions could be the next step in scaling up quantum computers to a size that can be practically used. Because of their strong interactions, Rydberg ions can exchange quantum information in less than a microsecond.

Ion trap with strontium ions in the center (blue section)

Chi Zhang, a researcher at Stockholm University's Department of Physics, explains, "We use this interaction to perform quantum computing operations (entanglement gates) at speeds that are about 100 times faster than those typical in ion trap systems."

Not coincidentally, in early June a team of researchers from the California Institute of Technology found that the Rydberg strontium atom array is promising for quantum computer fabrication. The results have been published in a paper in the journal Nature Physics.

In this study, the researchers looked at a system of neutral atoms based on Rydberg atoms. To use such atoms in a quantum computer, they would have to be entangled and there would need to be many of them, usually arranged in an array.

The research team developed a method for demonstrating the entanglement of Rydberg atoms in an array, which allows for the efficient detection of Rydberg states with greatly improved detection fidelity. The study shows that single-quantum-bit and double-quantum-bit operations using arrays of strontium Rydberg atoms can be achieved with a fidelity higher than 99%, close to that of superconducting quantum bits or ion traps.

It also suggests that the study of quantum computers based on neutral atoms is a viable research option direction for the fabrication of true quantum computers.

Reference Links:

[1]https://cpb.iphy.ac.cn/EN/10.1088/1674-1056/abd76f

[2]https://mp.weixin.qq.com/s/NDwrVMH8P5EmPMl-nBdbTw