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arXiv:1310.0228

Measurement-based Quantum Computation Under Different Types of Noises

Ding Zhong, Jian Wang, Ning Dai, Liang-Zhu Mu, Heng Fan

Published Oct 1, 2013• 0 citations
arXivHTMLPDF

Abstract

Measurement based quantum computation (MBQC) is an effective paradigm for universal quantum computation. In this scheme, the universal set of quantum gates are realized by only local measurements on the prior prepared cluster states. The inevitable decoherence is harmful to the realization of those quantum gates. Here, we investigate the performance of the quantum gates exposed to different type of noises. We find that some errors may not influence the success of the quantum gates, in contrast, some others may destroy their realization. We show that there is a controlling pattern that can protect quantum gates from certain types of noises and thus can improve the success probability of the gates implementation.

DOI
10.48550/arxiv.1310.0228

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Measurement based quantum computation (MBQC) is an effective paradigm for universal quantum computation. In this scheme, the universal set of quantum gates are realized by only local measurements on the prior prepared cluster states. The inevitable decoherence is harmful to the realization of those quantum gates. Here, we investigate the performance of the quantum gates exposed to different type of noises. We find that some errors may not influence the success of the quantum gates, in contrast, some others may destroy their realization. We show that there is a controlling pattern that can protect quantum gates from certain types of noises and thus can improve the success probability of the gates implementation.
The Measurement Based Quantum Computation (MBQC) model achieves universal quantum computation by employing projective single qubit measurements with classical feedforward on a highly entangled multipartite cluster state. Rapid advances in improving scalability of quantum computing systems have enabled the generation of large cluster states for implementing MBQC on various platforms. This review focuses on three such efforts, each utilizing a different quantum computing technology viz., superconducting qubits, trapped ion qubits and squeezed photon states. MBQC is being increasingly employed on optical platforms which can generate large entangled resource states but lack the ability to perform deterministic entangling gates.
We investigate the fidelity of measurement-based quantum computation (MBQC) when it is coupled with a boson environment, by measuring the cluster-state fidelity and gate fidelity. Two schemes of cluster-state preparation are studied. In the controlled-Z (CZ) creation scheme, cluster states are prepared by entangling all qubits in $|+\ensuremath{\rangle}$ state with CZ gates at all neighboring sites. The fidelity shows an oscillation pattern over time. The influence of the environmental temperature is evaluated, and suggestions are given to enhance the performance of MBQCs realized in this way. In the Hamiltonian creation scheme, cluster states are made by cooling a system with cluster Hamiltonians, of which the ground states are cluster states. A fidelity sudden-drop phenomenon is discovered. When the coupling is below a threshold, MBQC systems are highly robust against the noise. Our main environmental model is one with a single collective bosonic mode.
Measurement-based quantum computation (MBQC) is a universal platform to realize unitary gates, only using measurements that act on a preprepared entangled resource state. By deforming the measurement bases, as well as the geometry of the resource state, we show that MBQC circuits always transmit and act on the input state but generally realize nonunitary logical gates. In contrast to the stabilizer formalism that is often used for unitary gates, we find that ZX-calculus is an ideal computation method for these nonunitary gates. As opposed to unitary gates, nonunitary gates cannot be applied with certainty, due to the randomness of quantum measurements. We maximize the success probability of realizing nonunitary gates and discuss applications including imaginary time evolution, which we demonstrate on a noisy intermediate-scale quantum device.
A possible alternative to the standard model of measurement-based quantum computation (MBQC) is offered by the sequential model of MBQC---a particular class of quantum computation via ancillae. Although these two models are equivalent under ideal conditions, their relative resilience to noise in practical conditions is not yet known. We analyze this relationship for various noise models in the ancilla preparation and in the entangling-gate implementation. The comparison of the two models is performed utilizing both the gate infidelity and the diamond distance as figures of merit. Our results show that in the majority of instances the sequential model outperforms the standard one in regard to a universal set of operations for quantum computation. Further investigation is made into the performance of sequential MBQC in experimental scenarios, thus setting benchmarks for possible cavity-QED implementations.
Quantum computers, leveraging the principles of quantum mechanics, hold the potential to surpass classical computers in numerous applications, with implications across various domains. Besides the well-known gate model, Measurement-based Quantum Computation (MBQC) is another promising computational approach to achieve universal quantum computation. In MBQC, large ensembles of qubits are prepared in a highly entangled cluster state, forming the basis for executing quantum computations through sequential measurements. Cluster states are realized using both continuous variables (CV) and discrete variables (DV) techniques. In the CV-based methods, Frequency Domain Multiplexing (FDM), Time Domain Multiplexing (TDM), Spatial Domain Multiplexing (SDM), and hybrid schemes are employed. This paper thoroughly discusses and compares these approaches, elucidating their strengths and limitations. Additionally, the generation of photonic cluster states in DV is explored and some recent results are reported. Some recent state-of-the-art advancements in photonic and superconducting qubits entanglement, which can potentially serve as cluster states, are also presented. Finally, we highlight the approach that exhibits the most promising characteristics for achieving efficient cluster state realization in the context of MBQC.
Universal quantum computation is anticipated to provide solutions to classically intractable problems. Measurement-based quantum computation (MBQC) is one of the leading candidates to achieve universal quantum computation. In MBQC, the development of the underlying quantum algorithms is governed by single-qubit measurements on a highly entangled cluster state of qubits. Recent advances in MBQC mainly explore the physical aspects of MBQC (i.e. Physical development of cluster states) and as most of the simulators that exist today are for the gate-based model of quantum computation, and to date, there is no MBQC-dedicated simulator for MBQC-based algorithmic development. This paper exploits a well-maintained, and popular gate-based simulation framework developed by IBM called Qiskit to design MBQC-based quantum algorithms. We implement various gates, including Hadamard, and CNOT gates, to demonstrate the universality of MBQC in Qiskit. We also demonstrate MBCQ-based algorithm development in Qiskit by implementing MBQC-based teleportation protocol and Grover’s algorithm. The objective of this exercise is to demonstrate that the existing gate-based simulators can be used for developing MBQC-based quantum designs, which would help the research community in exploring the advantages that MBQC can offer compared to other quantum computation models.