State Transfer instead of Teleportation in Measurement-based Quantum Computation

Quantum measurement is universal for quantum computation (Nielsen [2], Leung [3,4]). The model of quantum computation introduced by Nielsen and further developed by Leung relies on a generalized form of teleportation. In order to simulate any n-qubit unitary transformation with this model, 4 auxiliary qubits are required. Moreover Leung exhibited a universal family of observables composed of 4 two-qubit measurements. We introduce a model of quantum computation via measurements only, relying on state transfer : state transfer only retains the part of teleportation which is necessary for computating. In order to simulate any n-qubit unitary transformation with this new model, only one auxiliary qubit is required. Moreover we exhibit a universal family of observables composed of 3 one-qubit measurements and only one two-qubit measurement. This model improves those of Nielsen and Leung in terms of both the number of auxiliary qubits and the number of two-qubit measurements required for quantum universality. In both cases, the minimal amounts of necessary resources are now reached: one auxiliary qubit (because measurement is destructive) and one two-qubit measurement (for creating entanglement). 1 Quantum computation via measurements only based on teleportation The proof of the universality of measurement-based quantum computation proceeds by simulating all quantum circuits. This proof is based on a 3-level decomposition of the problem: steps of simulation of U, where a unitary transformation U is simulated up to a Pauli operator (i.e. a step of simulation of U on |φ〉 produces σU |φ〉, where σ is a Pauli operator); full simulation of U, which combines a step of simulation of U with steps of simulation of Pauli operators; and simulation of a quantum circuit, which combines full simulations of unitary transformations.