[Paper Review] Quantum computing via measurements only

Robert Raussendorf, Hans J. Briegel|ArXiv.org|Oct 7, 2000

Quantum Computing Algorithms and Architecture12 references61 citations

TL;DR

This paper proposes a universal quantum computing model based solely on one-qubit measurements on a cluster state—a highly entangled many-body resource state. By measuring individual qubits in specific bases, any quantum circuit can be implemented, with measurement outcomes corrected via adaptive basis choices, demonstrating that entanglement in the cluster state serves as the sole resource for universal quantum computation.

ABSTRACT

A quantum computer promises efficient processing of certain computational tasks that are intractable with classical computer technology. While basic principles of a quantum computer have been demonstrated in the laboratory, scalability of these systems to a large number of qubits, essential for practical applications such as the Shor algorithm, represents a formidable challenge. Most of the current experiments are designed to implement sequences of highly controlled interactions between selected particles (qubits), thereby following models of a quantum computer as a (sequential) network of quantum logic gates. Here we propose a different model of a scalable quantum computer. In our model, the entire resource for the quantum computation is provided initially in form of a specific entangled state (a so-called cluster state) of a large number of qubits. Information is then written onto the cluster, processed, and read out form the cluster by one-particle measurements only. The entangled state of the cluster thus serves as a universal substrate for any quantum computation. Cluster states can be created efficiently in any system with a quantum Ising-type interaction (at very low temperatures) between two-state particles in a lattice configuration.

Motivation & Objective

• To develop a scalable quantum computing model independent of sequential gate operations.
• To demonstrate that a single, pre-entangled cluster state can serve as a universal resource for quantum computation.
• To show that all quantum algorithms can be implemented via adaptive single-qubit measurements on this resource.
• To establish a framework where quantum computation is driven entirely by measurement, not unitary evolution.
• To address scalability and fault tolerance by enabling circuit splitting and reuse of cluster states.

Proposed method

• The scheme uses a cluster state—prepared via a single Ising-type interaction step on a lattice of qubits—as the universal quantum resource.
• Quantum computation is implemented by performing adaptive single-qubit measurements in specified bases on the cluster state.
• Measurement outcomes determine subsequent measurement bases, enabling conditional dynamics and universal gate implementation.
• The cluster state satisfies eigenvalue equations involving Pauli operators, ensuring that measurement-induced projections yield correct entangled output states.
• Measurement results induce local corrections (e.g., σₓ and σ_z rotations), which are compensated by adjusting later measurement bases.
• The method allows implementation on irregular cluster geometries by bending and stretching circuit components without altering topology.

Experimental results

Research questions

• RQ1 Can universal quantum computation be achieved using only one-qubit measurements on a pre-entangled resource state?
• RQ2 How can quantum circuits be encoded and executed on a cluster state through measurement alone?
• RQ3 What is the role of measurement outcomes in determining the effective quantum dynamics and gate implementation?
• RQ4 Can the scheme be made scalable and fault-tolerant through cluster state reuse and circuit partitioning?
• RQ5 How does the topology of the cluster lattice affect the implementation of quantum circuits?

Key findings

• A cluster state satisfies a set of eigenvalue equations involving Pauli operators, which ensures that measurements project qubits into desired entangled states.
• Any quantum circuit can be implemented on a sufficiently large cluster state using only single-qubit measurements with adaptive basis choices.
• Measurement outcomes induce local corrections (e.g., σₓ and σ_z rotations), which can be accounted for by adjusting the measurement basis of subsequent qubits.
• The scheme is mathematically equivalent whether input is encoded before or after entanglement, proving that cluster states are a genuine universal resource.
• Circuit implementation is flexible: components can be deformed in shape as long as the topological structure is preserved.
• Cluster states can be reused by splitting large computations into parts and re-entangling the cluster, enabling fault tolerance via standard error correction on each segment.