Neutral Atom Quantum Computing

WOMANIUM Global Quantum Media Project Initiative

Introduction

Quantum computing has emerged as a revolutionary field with the potential to solve complex problems that are beyond the capabilities of classical computers. Among various approaches, neutral atom quantum computing has gained considerable attention due to its inherent advantages. In this article, we delve into the requirements and concepts involved in neutral atom quantum computing, with a focus on qubits encoded in atoms in optical tweezers, the magneto-optical trap (MOT), gates controlled by light, and interactions using Rydberg states. We will explore these components in detail and highlight recent progress in the field.

Aquila: Neutral Atom Quantum Processor from QuEra Computing : Image Credits: https://www.popsci.com/technology/neutral-atom-quantum-computer/

Qubits Encoded in Atoms in Optical Tweezers

At the core of neutral atom quantum computing lies a vacuum chamber containing an array of trapped atoms, with each atom serving as a qubit. Typically, the qubit is encoded in the spin of the atom. To hold the atoms in place, tightly focused laser beams called optical tweezers are employed. Optical tweezers utilize advanced optical and electronic technologies such as spatial light modulators and acoustic deflectors to create laser beams that trap and manipulate atoms. These laser beams can form arrays of atoms, numbering in the tens or even thousands. The qubits can be measured by imaging the fluorescence emitted by the atoms onto a camera, enabling visualization of fluorescence from individual atoms. Laser beams focused on the atoms allow for the manipulation and control of the qubits through single-qubit and two-qubit gates.

Key hardware components of a quantum processor. The trapping laser light is modified using a spatial light modulator (SLM) to create multiple microtraps at the focal plane of a lens. Additionally, a 2D acousto-optic laser beam deflector (AOD) controls the movement of tweezers, which are responsible for rearranging the atoms in the register. These tweezers are combined with the main trapping beam using a polarizing beam-splitter (PBS). The fluorescence light emitted by the atoms is separated from the trapping laser light using a dichroic mirror and captured by a camera. A photograph in the second part of the figure showcases the central area of a neutral-atom quantum co-processor, highlighting the preparation of the register at its core. Image Credits: https://quantum-journal.org/papers/q-2020-09-21-327/pdf/

Magneto-Optical Trap (MOT)

In addition to optical tweezers, another crucial component in neutral atom quantum computing is the magneto-optical trap (MOT). The MOT is employed for cooling and trapping the neutral atoms within the vacuum chamber. The MOT utilizes a combination of laser cooling and magnetic fields to slow down and trap atoms. Laser beams with specific frequencies and intensities are directed towards the atoms, causing them to absorb and re-emit photons. Through this process, the atoms experience a net loss of momentum, leading to cooling. By applying opposing magnetic fields, a spatially varying magnetic field configuration is created, which enables the trapping of the cooled atoms at the location of the MOT.

(A) A first image identifies optical microtraps loaded with a single atom. Empty traps are turned off, and the loaded traps are moved to fill in the empty sites. A second image verifies the success of the operation. (B) The trap array is produced by an acousto-optic deflector (AOD) that is driven by a multitone radio-frequency (RF) field. The AOD deflects a laser beam, creating an array of tightly focused optical tweezers in a vacuum chamber. A 1:1 telescope is used to image the trap array onto a 0.5-NA microscope objective. This allows for high-resolution imaging of the trap array and the atoms trapped within it.

Interactions Using the Rydberg States

Neutral atoms, by themselves, exhibit weak interactions with each other due to the absence of charge. However, to enable interactions for entanglement and perform two-qubit gates, the atoms are excited to highly excited atomic states known as Rydberg states. These states are reached by exciting the atoms from their electronic ground states using lasers. Rydberg states have unique properties, including the expansion of the electron cloud around the atom, resulting in increased polarizability. This polarizability leads to van der Waals interactions, which grow rapidly with the principal quantum number of the Rydberg state. By selectively exciting the atoms to the Rydberg state, interactions between them can be controlled.

To detect and manipulate Rydberg states in strontium-88, clock and Rydberg states are utilized, initialized from the absolute ground state. Detection of the Rydberg state is achieved by driving it to an auto-ionizing state. Optical tweezers are used for atom-by-atom assembly, creating two configurations: non-interacting (blue) and strongly Rydberg-blockaded pair (red). Fluorescence images show |r〉 (purple) and |g〉 (black) atoms, and the Rydberg, auto-ionization, and clock beams address all atoms simultaneously along the atom array axis. Image Credits: https://www.researchgate.net/figure/Population-and-detection-of-Rydberg-states-in-non-interacting-and-interacting_fig1_341628304

Properties of the Rydberg States

Size: A notable characteristic of these states is that in highly excited states, the electron orbit around the atom expands significantly. Specifically, the size of the orbit increases approximately as the square of the principal quantum number (n).

Polarizability: The equation for polarizability reveals that the electron clouds associated with these states possess a notable attribute of being highly polarizable. The degree of polarizability increases substantially as a function of the sixth power of the quantum number n.

van der Waals Interaction: These interactions between two Rydberg atoms exhibit a noteworthy characteristic in relation to their polarizability. Consequently, despite the presence of relatively weak interactions in low principal quantum number states, it becomes possible to activate immensely strong interactions swiftly to do very fast entanglement and then come back down (to ground state) to turn off the interactions.

van der Waals Interaction

Van der Waals interactions grow even more rapidly, escalating at the eleventh power of the principal quantum number n.

Components in Detail

Optical Tweezers: Optical tweezers serve as a crucial technology for neutral atom quantum computing, enabling the trapping and manipulation of atoms. By focusing laser beams through a microscope objective onto the atoms in the vacuum chamber, a tight tweezer potential is created. Fluorescence emitted by the atoms is imaged onto a camera, allowing for observation and control.

Figure below shows a time trace of the fluorescence signal from a single atom trapped in an optical tweezer. The fluorescence signal is proportional to the number of atoms in the trap, so the peaks in the signal correspond to times when there is a single atom in the trap. The valleys in the signal correspond to times when there are no atoms in the trap, or when there are multiple atoms in the trap.

Single Atom Detection. Image Credits: https://www.nature.com/articles/35082512

The reason why the atoms leave the trap most of the time is because of a process called light-assisted collisions. Light-assisted collisions occur when two atoms approach each other and are excited to a higher energy state by the light field of the optical tweezer. The excited atoms then repel each other and are ejected from the trap.

The fact that light-assisted collisions can eject multiple atoms from the trap is actually a fortunate thing, because it allows us to deterministically prepare a single atom in the tweezer. This is done by loading the trap with atoms and then stopping the loading once a single atom has been detected. This way, we can be sure that there is only one atom in the trap at any given time.

The time that the atoms stay in the optical tweezer is not that long. It is typically only a few milliseconds, and it is limited by the rate at which additional atoms are loaded into the trap.

Rearrangement: Neutral atom quantum computers often face challenges in loading large arrays of qubits due to the stochastic loading process. However, an important concept known as rearrangement allows for the deterministic preparation of arrays. By taking a picture of the loaded sites and moving the atoms accordingly, defect-free arrays can be created.

(A) Fluorescence images before (top) and after (bottom) rearrangement of individual atoms captured by EMCCD camera. Defects are detected and traps are rearranged using the protocol indicated by arrows for selected atoms. (B) Examples of successfully rearranged arrays (first two pictures) and one instance with a visible defect after rearrangement (last picture). The final arrangement of atoms is highly flexible, enabling clusters with 2 (top) or 10 (bottom) atoms. Nonperiodic arrangements and adjustable lattice spacings are achievable. (D) High-resolution CCD image of the trap array with an array of 100 tweezers and an RF tone spacing of 0.49 MHz, corresponding to a real-space distance of 2.6 μm between focused beams. Image Credits: https://www.science.org/doi/10.1126/science.aah3752

There exist advanced algorithms suitable for 2D scenarios, enabling the manipulation of individual atoms to relocate them accurately. Remarkably, researchers have even achieved this feat in three dimensions. As a result, the concept of rearrangement significantly facilitates the deterministic arrangement of arrays.

Single-atom fluorescence in 3D arrays. Image Credits: https://www.nature.com/articles/s41586-018-0450-2

Rydberg Blockade: The interaction mechanism used to generate entanglement in neutral atom quantum computers is the Rydberg blockade. When one atom is in the Rydberg state, it blocks the excitation of a nearby atom to the same state due to the large energy cost imposed by van der Waals interactions. This blockade radius, typically ranging from 5 to 15 microns, allows for the creation of entangled states in a controlled manner.

A Rydberg blockade-controlled phase gate is demonstrated on input states a) |01⟩ and b) |11⟩. Quantum information is encoded in the basis states |0⟩ and |1⟩, with state |1⟩ coupled to a Rydberg level |r⟩ using an excitation Rabi frequency Ω. The controlled phase gate is implemented using a three-pulse sequence: 1) a π pulse on the control atom |1⟩ → |r⟩, 2) a 2π pulse on the target atom |1⟩ → |r⟩ → |1⟩, and 3) a π pulse on the control atom |r⟩ → |1⟩. In panel a), the control atom starts in state |0⟩ and is not Rydberg excited, resulting in no blockade. In panel b), the control atom is in state |1⟩, which is Rydberg excited, leading to the blockade of the target atom excitation. Image Credits: https://arxiv.org/pdf/0909.4777.pdf

In the context of Rydberg interactions, the coupling between atoms is achieved using a laser, allowing for the generation of Rabi oscillations on a specific transition. However, when placing an atom near another that is already in a Rydberg state, the van der Waals interaction between them alters or increases the energy required to excite the second atom into the Rydberg state. If this energy shift, denoted as U, exceeds the laser’s Rabi frequency, omega, the excitation process becomes blocked or “blockaded.” Consequently, it becomes impossible to simultaneously excite both atoms within a certain radius known as the blockade radius. Remarkably, the effectiveness of the Rydberg blockade interaction mechanism is not dependent on the precise value of U, as long as it is significantly larger than the laser’s Rabi frequency. Thus, we can summarize that the Rydberg blockade prevents the simultaneous excitation of two atoms to the Rydberg state within a characteristic blockade radius.

When the distance between the two atoms, represented by ‘r’, is less than the blockade radius, it becomes impossible to simultaneously excite both atoms.

Recent Progress

Significant advancements have been made in neutral atom quantum computing. Two-qubit gate fidelities exceeding 0.995 and entanglement fidelity reaching approximately 0.998 have been achieved. Mid-circuit measurements for error correction and the development of field programmable circuits have opened new possibilities for scalable quantum computing. Collaborative efforts, such as the one between Lucan and Saffman, have demonstrated programmable quantum circuits capable of running sequences of gate operations.

A 12-atom 1D cluster-state graph is generated using |+⟩ initialized qubits and CZ gates. Atom images show configuration after first and second gate layers. Quantum circuit represents preparation and measurement of 1D cluster state with dynamical decoupling. Raw stabilizers (Si = Z_(i−1)X_iZ_(i+1)) shown. Seven-qubit Steane code depicted as graph state. Circuit prepares logical |+⟩L state in four parallel gate layers. Measured stabilizers and logical operators displayed with error detection based on post-selection. Stabilizers and logical operators measured with two settings, error bars represent 68% confidence intervals. Image Credits: https://www.nature.com/articles/s41586-022-04592-6/figures/2

Conclusion

Neutral atom quantum computing offers a promising avenue for achieving powerful quantum computation. By encoding qubits in atoms held in optical tweezers, utilizing the magneto-optical trap (MOT) for cooling and trapping, and employing interactions through Rydberg states, researchers have made significant progress towards building functional quantum computers. The ability to manipulate and control individual atoms with high precision opens up new possibilities for solving complex problems. As research continues to explore different atomic species, including alkaline-earth atoms, and push the boundaries of qubit manipulation, the era of practical quantum computing draws nearer.

References

Photo by Sigmund on Unsplash

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