One-way quantum computer

The defining principle is that entanglement is prepared first and computation is performed by measurements afterward.¹ A typical resource is a cluster state, a highly entangled state associated with a graph whose vertices represent qubits and whose edges represent controlled-phase entangling operations. Measuring one qubit can teleport a logical state through the graph while applying a gate determined by the measurement basis. The measured qubit is no longer available, which gives the model its “one-way” name.²

The graph need not be a simple lattice: different graph states provide different computational geometries, and suitable families can support universal quantum computation. Entanglement alone is not the whole resource; useful computation also depends on the measurement pattern, classical processing, and the ability to maintain coherence while measurements occur.

Adaptive measurement is the central control mechanism: later measurement bases may depend on earlier random outcomes. Quantum measurements produce classical bits, and those bits determine whether known Pauli corrections—often called by-product operators—must be applied or tracked in a classical “Pauli frame.” By tracking rather than physically applying many corrections, an implementation can reduce control overhead.

Single-qubit measurements in selected bases can implement rotations, teleport logical qubits across the cluster, and realize entangling gates between computational paths. A fixed measurement pattern can therefore represent a quantum algorithm, but its bases are generally not all fixed in advance. The model is computationally equivalent in power to the standard circuit model, although its organization shifts much of the work from gate sequencing to resource-state preparation and measurement scheduling.

One-way computation has been demonstrated with several physical platforms, including photonic qubits, trapped ions, neutral atoms, and superconducting devices. Photonic experiments were especially natural because measurements can be rapid and photons can carry cluster-state entanglement over optical paths; an early experiment implemented elementary one-way protocols with photonic qubits.³ Other platforms can benefit from long-lived matter qubits that store the resource while measurements are made.

The principal engineering difficulties are creating large, high-fidelity cluster states, performing measurements with low error, and preserving entanglement against loss and decoherence. Fault-tolerant versions use specially structured resource states and error-correcting codes, such as topological cluster states, so that imperfect physical measurements can be converted into reliable logical computation.⁴ Resource generation can itself become the dominant cost, particularly when entangling operations are probabilistic.

A less obvious feature is that the resource state can be prepared independently of the particular algorithm: the same large cluster may support many computations through different measurement patterns.¹ This separates quantum memory and entanglement generation from algorithmic control, a useful distinction for modular hardware design.

Not every entangled state is computationally useful. Some graph states support only limited classical simulation, and one-dimensional cluster states are not universal without additional resources, despite being valuable for demonstrating teleportation and sequential processing.² Conversely, certain states with simple preparation procedures can be universal when measurements, feed-forward, and encoded error correction are included. Measurement-based schemes also underpin blind quantum computation, in which a client can delegate a computation while concealing aspects of the input, algorithm, and output from a quantum server.⁵

Cluster state

An entangled graph state used as the consumable resource in one-way quantum computation.

Graph state

A multipartite quantum state specified by a graph and controlled-phase entangling operations on its vertices.

Measurement-based quantum computation

A framework in which computation is driven by measurements on a pre-entangled resource state.

By-product operator

A known, measurement-dependent correction—usually a Pauli operator—that accompanies a teleported logical operation.

Pauli frame

Classical record of pending Pauli corrections that can be propagated without immediately applying them.