One-way quantum computer

Content sourced from Wikipedia, licensed under CC BY-SA 3.0.

The one-way quantum computer, also called the measurement-based quantum computer (MBQC), is a way to perform quantum computing by first creating a highly entangled resource state, usually a cluster state or graph state. This state acts as the resource for the computation. Computation then proceeds by measuring individual qubits in specific bases. It is “one-way” because once a qubit is measured, its part of the resource is consumed.

Each measurement outcome is random, but the overall sequence of measurements is designed so the computation still works. The basis for later measurements often depends on the results of earlier ones, so the measurements cannot all be done at once. After all measurements, a small set of qubits remains as the output. Because the measurements were random, small corrections—called byproducts—are applied to the output to get a deterministic result.

MBQC is universal: any quantum circuit can be translated into an MBQC pattern of entangling operations, measurements, and corrections. The usual flow is: prepare and entangle the resource state, measure the qubits in a chosen order, and then apply corrections to obtain the final output.

The resource state can be understood with graph theory. Each qubit is a vertex, and entangling connections between qubits are the edges. This graph-based view is why MBQC is often described as graph-state or cluster-state computation. The stabilizer formalism from quantum information helps describe and analyze these states.

In practice, photons are a common choice for the qubits in MBQC because they are easy to create, entangle, and measure, though MBQC can also be done with other systems like atoms or quantum dots. Entangling photons deterministically is challenging, so experiments often use probabilistic methods or employ matter systems to assist entanglement. The theory also connects to known ideas about efficiently simulating certain quantum operations classically, while remaining universal when measurements beyond those operations are used.

MBQC links to error correction and fault tolerance through special resource states, such as topological cluster states, which help protect information from errors. Experiments have demonstrated small-scale MBQC, including a two-qubit version of Grover’s search on a tiny cluster state of photons. There are ongoing proposals for scalable photonic MBQC and for using resource states beyond the standard cluster states, such as AKLT states.

In short, the one-way quantum computer performs computations by preparing a fixed, entangled resource and then driving the computation with measurements. It offers a distinct, yet fully universal, approach to quantum computing compared to the traditional gate-based model.