Toward fault-tolerant quantum computation without concatenation

Abstract

It has been known that quantum error correction via concatenated codes can be done with exponentially small failure rate if the error rate for physical qubits is below a certain accuracy threshold. Other, unconcatenated codes with their own attractive features-improved accuracy threshold, local operations-have also been studied. By iteratively distilling a certain two-qubit entangled state it is shown how to perform an encoded Toffoli gate, important for universal computation, on CSS codes that are either unconcatenated or, for a range of very large block sizes, singly concatenated.

12 pages, 2 figures, replaced: new stuff on error models, numerical example for concatenation criteria

References in corpus (4)

• Fault-tolerant quantum computation by anyons
• A Theory of Fault-Tolerant Quantum Computation
• Quantum codes on a lattice with boundary
• Threshold Accuracy for Quantum Computation

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• Single-step implementation of high fidelity $n$-bit Toffoli gate
• Quantum gate learning in engineered qubit networks: Toffoli gate with always-on interactions
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• Quantifying the effects of local many-qubit errors and non-local two-qubit errors on the surface code
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• Simple implementation of high fidelity controlled-$i$SWAP gates and quantum circuit exponentiation of non-Hermitian gates
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• Applications of Universal Parity Quantum Computation
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• Magic State Injection with Erasure Qubits
• Quantum codes on high-genus surfaces
• Microwave-activated high-fidelity three-qubit gate scheme for fixed-frequency superconducting qubits
• Implementing a Ternary Decomposition of the Toffoli Gate on Fixed-FrequencyTransmon Qutrits
• A note on threshold theorem of fault-tolerant quantum computation
• Universal fault tolerant quantum computation in 2D without getting tied in knots
• Universal quantum gates for photon-atom hybrid systems assisted by bad cavities