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arXiv:1308.5209 · Physical Review A

Demonstrating elements of measurement-based quantum error correction

Stefanie Barz, Rui Vasconcelos, Chiara Greganti, Michael J. Zwerger, Wolfgang Dür, Hans J. Briegel, Philip John Walther

Published Oct 2, 2014• 15 citations
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Abstract

In measurement-based quantum computing an algorithm is performed by measurements on highly entangled resource states. To date, several implementations were demonstrated, most of them assuming perfect noise-free environments. Here we consider measurement-based information processing in the presence of noise and demonstrate quantum error detection. We implement the protocol using a four-qubit photonic cluster state where we first encode a general qubit nonlocally such that phase errors can be detected. We then read out the error syndrome and analyze the output states after decoding. Our demonstration shows a building block for measurement-based quantum computing which is crucial for realistic scenarios.

DOI
10.1103/physreva.90.042302

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Measurement-Based Quantum Computing (MBQC) is an alternative to the quantum circuit model, whereby the computation proceeds via measurements on an entangled resource state. Noise processes are a major experimental challenge to the construction of a quantum computer. Here, we investigate how noise processes affecting physical states affect the performed computation by considering MBQC on a one-dimensional cluster state. This allows us to break down the computation in a sequence of building blocks and map physical errors to logical errors. Next, we extend the Matrix Product State construction to mixed states (which is known as Matrix Product Operators) and once again map the effect of physical noise to logical noise acting within the correlation space. This approach allows us to consider more general errors than the conventional Pauli errors, and could be used in order to simulate noisy quantum computation.
Quantum computers will eventually reach a size at which quantum error correction becomes imperative. Quantum information can be protected from qubit imperfections and flawed control operations by encoding a single logical qubit in multiple physical qubits. This redundancy allows the extraction of error syndromes and the subsequent detection or correction of errors without destroying the logical state itself through direct measurement. Here we show the encoding and syndrome measurement of a fault-tolerant logical qubit via an error detection protocol on four physical qubits, represented by trapped atomic ions. This demonstrates for the first time the robustness of a fault-tolerant qubit to imperfections in the very operations used to encode it. The advantage persists in the face of large added error rates and experimental calibration errors.
Integrated photonics provides a versatile platform for encoding and processing quantum information.However, the encoded quantum states are sensitive to noise, which limits their capability to perform complicated quantum computations.Here, we use a five-qubit linear cluster state on a silicon photonic chip to implement a quantum error-correction code and demonstrate its capability of identifying and correcting a single-qubit error.The encoded quantum information is reconstructed from a single-qubit error and an average state fidelity of 0.863 ± 0.032 is achieved for different input states.We further extend the scheme to demonstrate a fault-tolerant measurement-based quantum computation (MBQC) on stabilizer formalism that allows us to redo the qubit operation against the failure of the teleportation process.Our work provides a proof-of-concept working prototype of error correction and MBQC in an integrated photonic chip.
We present a hybrid scheme for quantum computation that combines the modular structure of elementary building blocks used in the circuit model with the advantages of a measurement-based approach to quantum computation. We show how to construct optimal resource states of minimal size to implement elementary building blocks for encoded quantum computation in a measurement-based way, including states for error correction and encoded gates. The performance of the scheme is determined by the quality of the resource states, where within the considered error model a threshold of the order of 10% local noise per particle for fault-tolerant quantum computation and quantum communication.
The ability to perform quantum error correction (QEC) and robust gate operations on encoded qubits opens the door to demonstrations of quantum algorithms. Contemporary QEC schemes typically require mid-circuit measurements with feed-forward control, which are challenging for qubit control, often slow, and susceptible to relatively high error rates. In this work, we propose and experimentally demonstrate a universal toolbox of fault-tolerant logical operations on error-detecting codes without mid-circuit measurements on a trapped-ion quantum processor. We present modular logical state teleportation between two four-qubit error-detecting codes without measurements during algorithm execution. Moreover, we realize a fault-tolerant universal gate set on an eight-qubit error-detecting code hosting three logical qubits, based on state injection, which can be executed by coherent gate operations only. We apply this toolbox to experimentally realize Grover's quantum search algorithm fault-tolerantly on three logical qubits encoded in eight physical qubits, with the implementation displaying clear identification of the desired solution states. Our work demonstrates the practical feasibility and provides first steps into the largely unexplored direction of measurement-free quantum computation.