Fusion-Based Quantum Computation: A Promising Future for Photonic Architectures

Fusion-Based Quantum Computation (FBQC) and Measurement-Based Quantum Computation (MBQC) are alternative models to the traditional Circuit-Based Quantum Computation (CBQC). FBQC is ideal for photonic architectures, replacing the coherent evolution of a quantum register with measurement and teleportation.

MBQC uses a large multi-qubit entangled state with single-qubit measurements to detect and fix errors. Both models face challenges such as photon loss, but solutions include error correction procedures and fusion gates. The future of FBQC is promising, with new models offering intrinsic fault-tolerance features and aiding error detection. However, further research is needed to exploit their potential fully.

What is the Concept of Fusion-Based Quantum Computation?

Quantum computation is a complex field that involves using quantum bits, or qubits, to perform calculations. The traditional model of quantum computation, known as Circuit-Based Quantum Computation (CBQC), involves initializing a register, applying a sequence of quantum gates that define a particular algorithm, and quantum measurements that produce the outcomes of the computation. However, other models of quantum computation have proven to be more natural for implementation on certain physical platforms. One such model is Fusion-Based Quantum Computation (FBQC).

FBQC is particularly well-suited for photonic architectures because it substitutes the coherent evolution of a quantum register with measurement and teleportation. This model is equivalent to CBQC and can perform any quantum algorithm. The process of FBQC involves two steps. First, a large multi-quit entangled state is created. The size of this state depends on the complexity of the corresponding CBQC circuit. Then, the entire state undergoes a sequence of adaptive single-qubit measurements.

How Does Measurement-Based Quantum Computation Work?

Measurement-Based Quantum Computation (MBQC) is another quantum computation model similar to FBQC. In MBQC, a large multi-qubit entangled state is created, and then the entire state undergoes a sequence of adaptive single-qubit measurements. A special type of entangled states, known as cluster states, serves as a resource for MBQC-based quantum computing.

The MBQC model is compatible with modern error correction codes, and the outcomes of the single-qubit measurements can also be used to detect and fix errors occurring during the algorithm execution. Preparing the initial resource state is the most demanding stage of the MBQC. The number of qubits in this state depends on the algorithm depth and it is usually impractical to create the whole state at once.

What are the Challenges and Solutions in Quantum Computation?

One of the challenges in quantum computation is photon loss. This is particularly a problem in linear-optical systems, which also suffer from the limited probability of success in entangling operations. To overcome these issues, the conveyor-like algorithm execution strategy must be aided with an error correction procedure.

The structure of the resource state defines the fault-tolerance properties to the qubit loss and erroneous entangling operations. The initial cluster state of an MBQC-based processor can be assembled using multiple copies of identical few-qubit entangled states known as resource states. The assembly may be carried out by applying fusion gates to entangle separate resource states.

How Does Fusion-Based Quantum Computation Work?

In FBQC, resource states are generated, and then reconfigurable fusion gates are applied to them. These two steps may be repeated continuously until the algorithm’s outcome is measured. The fusion network, which represents the mutual configuration of resource states and fusions, determines a specific FBQC model.

A graph with two distinct sets of edges conveniently represents a fusion network. The first set contains graphs corresponding to the resource states, and the second indicates the locations of the fusion gates between the resource qubits. Some fusion networks possess intrinsic fault-tolerance features, which allow the use of fusion gate outcomes for error detection and application of an error-correction protocol.

What are the Future Prospects of Fusion-Based Quantum Computation?

The future of FBQC looks promising with the development of new fusion-based quantum computation models. These models are based on different resource states and have intrinsic fault-tolerance features. The fusion networks based on these resource states can be used to detect and apply an error correction protocol.

Developing these models and networks is a significant step towards practically implementing quantum computation. However, further research is needed to fully understand these models’ potential and overcome the challenges associated with quantum computation.