Measurement-based quantum computing and cluster states

Short answer: Measurement-based quantum computing, also called the one-way model, does its computation using only single-qubit measurements on a particular entangled state called a cluster state. The measurements imprint a circuit on the state and destroy its entanglement as they go, so the measurement sequence is the program. It was proposed by Raussendorf and Briegel in 2001 and is a theoretical model, described here at explainer level.

How does the one-way model function?

The scheme consists entirely of one-qubit measurements applied to a specific class of entangled states known as cluster states. These measurements are used to imprint a quantum logic circuit onto the state. The 2001 paper says the measurements imprint a circuit on the state while destroying its entanglement, so the cluster state acts as a "one-way" quantum computer, where the sequence of measurements forms the program. The authors say this underlying computational model differs from the network model of quantum computation.

What distinguishes the computational model?

The underlying computational model is fundamentally different from standard circuit models because the basic dynamical operations are non-unitary quantum measurements. Despite being non-unitary, these measurements can simulate arbitrary quantum dynamics, including unitary dynamics. A 2005 review says such models challenge the conventional understanding of quantum information processing. The model relates quantum algorithms to mathematical graphs, providing a structural framework for analyzing the computation. A 2003 paper says it proves the scheme's universality.

What are the resource requirements and limitations?

The 2003 paper also investigates the scaling of required resources. The cluster state serves as the central physical resource, and the computation relies on a sequence of projective measurements on this state. However, not all states are suitable substrates for quantum computation. Measurements on any quantum state that is linearly prepared in one dimension can be efficiently simulated on a classical computer. Therefore, such states are not candidates for use as a substrate for quantum computation. Additionally, the cluster state cannot occur as the exact ground state of any naturally occurring physical system. The review states this as a proof about exact ground states.

What practical circuits have been analyzed?

The 2003 paper gives examples of circuits of practical interest within this framework. Examples include the circuit for the quantum Fourier transformation and the quantum adder. The analysis also extends to computation with clusters of finite size, addressing the constraints of limited resource availability. The paper relates quantum algorithms to mathematical graphs. It describes theory, and this article makes no claim about hardware.

FAQ

What is measurement-based quantum computing?

A scheme in which a computation consists entirely of one-qubit measurements on a cluster state. The measurements imprint a quantum logic circuit on the state and destroy its entanglement.

Why is it called one-way?

Because the entanglement is consumed as the computation runs, so the cluster state cannot be reused. The measurements form the program.

How does it differ from the circuit model?

The 2003 detailed paper says its underlying computational model differs from the network model. A 2005 review adds that its basic dynamical operations are non-unitary measurements that can still simulate arbitrary quantum dynamics.

Is it universal?

The 2003 paper says it proves the scheme's universality.

What are the limits?

The 2005 review proves that measurements on any state linearly prepared in one dimension can be efficiently simulated on a classical computer, so such states are not candidates, and that the cluster state cannot occur as the exact ground state of any naturally occurring physical system.