Why Qubit Connectivity Matters

By Yuval Boger
Head of Marketing, QuEra Computing Inc

Qubit connectivity is an important aspect of quantum computing because it determines how qubits can interact with each other. This interaction is necessary to perform quantum operations and run quantum algorithms.

Here are some reasons why qubit connectivity is important:

• Algorithmic Complexity: Many quantum algorithms require many qubits to interact with each other. Connectivity between qubits determines how efficiently these algorithms can be implemented. If the qubits are not directly connected, additional operations may be required to enable their interaction, which can increase the complexity and runtime of the algorithm.
• Error Correction: Quantum error correcting codes, which are critical to building reliable and practical quantum computers, often require special connectivity patterns between qubits. Good connectivity can make error correction more efficient and effective.
• Quantum Entanglement: Qubit Connectivity is essential for creating quantum entanglement. If entanglement is desired between two unconnected qubits, a series of swap operations must be performed, increasing the complexity and possible failure of the algorithm.
• Speed ​​and Efficiency: The fewer operations quantum computing requires, the faster it can be completed and the less chance of error. If the qubits are well connected, fewer operations are needed to perform the computations, increasing the speed and efficiency of quantum computers.

Connectivity varies greatly between different quantum modalities. Here are some examples of high-connectivity quantum architectures:

• Neutral atomic quantum computer: In a neutral atomic computer, a cloud of atoms is trapped and cooled to a temperature close to absolute zero. Then, highly focused laser beams, “optical clamps”, are used to move individual atoms and to perform quantum operations. By adjusting the laser beam array, one can control which atoms interact with each other, allowing a high degree of flexibility in connectivity between qubits. See a video and a more detailed explanation of qubit shuttles here.
• Trapped ion quantum computer: In an ion trapped quantum computer, the ions are retained by an electromagnetic field and the qubits are encoded in the stable electronic state of each ion. All qubits can interact with each other, providing full connectivity.
• Photonic quantum computers, which use light particles (photons) as qubits, could theoretically have high connectivity. This is because photons can easily interact with each other via beam dividers and other optical elements.

Here are some examples of low-connectivity quantum architectures:

• Superconducting quantum computer: In a superconducting quantum computer, the qubits are arranged in a 2D lattice, and each qubit can only interact with its nearest neighbor, which usually consists of two or three qubits. The qubits are fixed and cannot move.
• Quantum annealer: In quantum annealing, the qubits are also arranged in a 2D structure called fixed connectivity. For example, in D-Wave computers, this structure is known as a Chimera graph, where each qubit is connected to six other qubits.

Of course, high-connectivity architectures are not without drawbacks. High connectivity relies on being able to shuttle between qubits, and switching between qubits brings some potential problems. Shuttling a qubit can be a relatively slow process compared to the operating speed of a quantum gate. This can increase total computation time and reduce the number of operations that can be performed before the qubit loses coherence. The process of moving qubits poses a risk of decoherence, namely the loss of quantum states due to interactions with the environment. Shutting qubits also adds an extra layer of complexity to computer design, and it can be challenging to implement, especially in large-scale systems.

In short, qubit connectivity plays a critical role in the performance and functionality of a quantum computer. This impacts the application of quantum algorithms, the creation of quantum entanglement, error correction, and the overall scalability, speed, and efficiency of quantum computing systems. When one considers the choice of a quantum modality for one’s application, qubit connectivity should be one of the factors considered.

About the Author
Yuval Boger is Chief Marketing Officer for QuEra, a leader in quantum computers based on neutral atoms. In his career, he has served as CEO and CMO of market-leading technology companies including quantum computing software, wireless power, and virtual reality. His “Podcast Superposition Guy” hosts CEOs and other thought leaders in quantum computing, quantum sensing, and quantum communications to discuss the business and technical aspects that impact the quantum ecosystem.