# BLOG

## Recent realizations of logical quantum processors based on reconfigurable atomic arrays

Quantum computers in recent years have been called NISQ (noisy intermediate-scale quantum) devices, and because they have few qubits and are easily affected by noise, they have been used for socially significant purposes. As mentioned in previous explanatory articles, the search continues. However, no commercially valuable NISQ algorithm has yet been discovered, and no convincing theoretical evidence exists to suggest that such an algorithm could ever be found.

Under such circumstances, we are developing QEC (quantum error correction) technology that restores qubit states destroyed by quantum noise, and fault-tolerant quantum computation that implements QEC. is becoming more active. Fault-tolerant quantum computation is expected to demonstrate quantum superiority in commercially valuable problems because it can restore qubit states that are destroyed by noise during computation. However, implementing QEC is not easy as it is still in the development stage both theoretically and technically.

In particular, from the hardware perspective, it is necessary to develop integration technology to increase the number of physical qubits and advanced technology to manipulate these large-scale physical qubits with high precision. Meanwhile, quantum computers that implement QEC consisting of a large number of neutral atoms and fault-tolerant quantum computation have recently been developed “Logical quantum processor based on reconfigurable atom arrays”, Bluvstein et al., Nature (2023). According to it, up to 280 physical qubits are constructed from arrays of relocatable neutral atoms, and entanglement between up to 48 logical qubits is generated and observed using a regionalized architecture. Ta. The contents are explained below.

INTRODUCTION

## Neutral atom quantum computer

Currently, the ion trap type is often adopted as one of the methods of quantum computers. This method treats individual ions (charged atoms) as qubits, but this research uses neutral atoms (atoms with no charge). Generally speaking, it is technically easier to confine a large number of neutral atoms in a narrow region than to confine a large number of ions, and the state of neutral atoms is more stable than that of ions. is present in neutral atoms. For this reason, neutral atom quantum computers are being researched and developed as one of the candidates for fault-tolerant quantum computers. In this study, each rubidium atom, which is a type of neutral atom, was treated as a single physical qubit.

CALCULATOR

## Transport of entangled qubits

Although they are more stable than ions and easier to integrate large numbers of qubits, one of the reasons why they have not been talked about compared to superconducting quantum computers and ion trap quantum computers is that This is because it was difficult to move entangled qubits. In a neutral atom quantum computer, two-quantum gate operation is realized by the long-range van der Waals interaction caused by physically bringing two neutral atoms close together (Rydberg blockade). However, after two entangled neutral atoms are generated by the two-quantum gate operation, it is difficult to separate the two entangled neutral atoms. Therefore, in early neutral atom quantum computers, the placement of neutral atoms was fixed at the initially determined position, and their use was limited to analog quantum computers such as quantum annealers(“Quantum phases of matter on a 256-atom programmable quantum simulator”, Ebadi et al., Nature (2021)). In response to this problem, a technological breakthrough was reported in 2022 that moves a large number of entangled qubits, making it possible to freely perform two-quantum gate operations（“A quantum processor based on coherent transport of entangled atom arrays”, Bluvstein et al., Nature (2022)）.In other words, we could create a quantum computer that we originally wanted to create by bringing two neutral atoms close together to create an entanglement, then pulling one of the entangled neutral atoms apart and bringing it closer to another neutral atom to further entangle them. The basic operations for shaping have been established. Furthermore, in 2023, the two-quantum gate operation fidelity (an indicator of whether gate operations can be executed accurately) will reach 99.5%（“High-fidelity parallel entangling gates on a neutral-atom quantum computer”, Evered et al., Nature (2023)）.These breakthroughs have led to the realization of fault-tolerant quantum computing.

TRANSPORT

Figure 1. Quantum information architecture based on coherent transport of neutral atoms. Atom transport is performed in parallel in two dimensions using optical tweezers. This enables a quantum information architecture that is programmable and capable of non-local connectivity.

(Reprinted from “A quantum processor based on coherent transport of entangled atom arrays”, Bluvstein et al., Nature (2022).)

## Regional architecture and lattice arrangement of atoms

In order to realize fault-tolerant quantum computation using neutral atoms, as shown in Figure 2,

・Save area

・Tangled area

・Reading area

A three-part architecture was adopted. A storage region is a location of qubit storage that is characterized by a long coherence time (time that remains undisturbed by noise). The entanglement region is used as a location where gate operations on single or multiple logical qubits are performed by applying a laser. The readout region is a place where measurements (irradiation of atoms with an imaging beam) can be performed on the physical or logical qubits therein without disturbing other qubits.This architecture is realized using a laser technology called optical tweezers, which allows many rubidium atoms to be arranged in a lattice. Arbitrary arrays are possible, realized by gate operations between qubits that utilize the repulsion phenomenon between rubidium atoms (called Rydberg blockade) and atomic transport using an AOD (acousto-optic deflector). By combining these features, a quantum computer with up to 280 physical qubits was built.

ARCHITECTURE

Figure 2. A regionalized architecture for a large number of neutral atoms consists of a storage zone, an entangling zone, and a readout zone (reproduced from the original paper).

## Entanglement generation of logical qubits

In this study, the encoding of logical qubits based on the surface code, one of the quantum error correction (QEC) methods, was performed. The quantum circuit diagram for an experiment generating entangled states (Bell states) from two logical qubits is shown in Figure 3a. The diagram also illustrates the implementation of gate operations for the two logical qubits. In this case, each of the two logical qubits is encoded using a grid (block) of 49 physical qubits arranged in a square lattice (7 qubits on each side). By moving and aligning these blocks vertically and horizontally, and bringing corresponding physical qubits close to each other, effective gate operations for logical qubits can be globally achieved through the application of laser pulses.

In the event of errors, such as noise occurring in one block, it propagates to the other block. Exploiting this phenomenon can enhance the precision of quantum error correction (QEC), as illustrated in Figure 3b. Figure 3c shows the measurement results of the logical qubits. The high peaks at ++, --, 00, and 11 indeed indicate the successful generation of Bell states for logical qubits. This confirms that the neutral-atom-based quantum computer possesses the capability for entanglement generation and QEC.

ENTANGLEMENT

Figure 3. Experiment entangling two logical qubits (Reproduced from the original paper).

a: Quantum circuit for generating logical Bell states.

b: Schematic diagram illustrating error propagation between blocks and the utilization of it for Quantum Error Correction (QEC).

c: Histogram of measurement results for logical Bell states.

## Control of 280 physical qubits

Figure 4 schematically illustrates an experiment entangling 280 physical qubits as 40 logical qubits. As shown in Figure 4a, the black-bordered region within the entanglement area (blue) consists of 7 physical qubits, forming a single logical qubit in this case. Gate operations can be simultaneously applied to the 70 physical qubits within this entanglement area. The storage area (orange) contains 210 physical qubits, and during gate operations, they are transported to the entanglement area.

As depicted in the quantum circuit diagram in Figure 4b, the manipulation of the state of 40 logical qubits was achieved by processing a total of 280 physical qubits in four steps, with 70 qubits each. Figure 4c presents experimental results showing minimal decay in the state of logical qubits even with an increase in the number of steps. This suggests the potential for constructing larger-scale quantum computers with this architecture.

CONTROL

Figure 4. Experiment entangling 280 physical qubits as 40 logical qubits.

a: Each small circle represents a physical qubit.

b: Quantum circuit for generating the state of 40 logical qubits.

c: Measurement results showing the relationship between the number of steps and the decoherence of the logical qubit states.

This paper also reports the realization of CCZ and CZ as native gates between logical qubits based on a quantum error correction (QEC) scheme known as the three-dimensional color code. While not detailed in this manuscript, these gates belong to a category known as non-Clifford gates, suggesting the potential for this architecture to demonstrate computational capabilities surpassing classical computers. The paper also documents the execution of 228 logical CZ/CNOT and 48 logical CCZ operations for 48 logical qubits. The experiments conducted in this study serve as crucial elements in demonstrating the construction of a large-scale quantum computer using neutral atoms and implementing quantum error correction (QEC). The authors suggest that with increased laser output and improved control methods, scalability up to 10,000 physical qubits could be achieved. Technological innovations that reduce the cost of large-scale error correction systems may accelerate the practical utilization of fault-tolerant quantum computers sooner than previously estimated.

CONCLUSION