Error mitigation for universal gates on encoded qubits

Abstract

The Eastin-Knill theorem states that no quantum error correcting code can have a universal set of transversal gates. For CSS codes that can implement Clifford gates transversally it suffices to provide one additional non-Clifford gate, such as the T-gate, to achieve universality. Common methods to implement fault-tolerant T-gates like magic state distillation generate a significant hardware overhead that will likely prevent their practical usage in the near-term future. Recently methods have been developed to mitigate the effect of noise in shallow quantum circuits that are not protected by error correction. Error mitigation methods require no additional hardware resources but suffer from a bad asymptotic scaling and apply only to a restricted class of quantum algorithms. In this work, we combine both approaches and show how to implement encoded Clifford+T circuits where Clifford gates are protected from noise by error correction while errors introduced by noisy encoded T-gates are mitigated using the quasi-probability method. As a result, Clifford+T circuits with a number of T-gates inversely proportional to the physical noise rate can be implemented on small error-corrected devices without magic state distillation. We argue that such circuits can be out of reach for state-of-the-art classical simulation algorithms.

v2: 11 pages, 7 figures; published version

References in corpus (4)

• Restrictions on Transversal Encoded Quantum Gate Sets
• A magic state's fidelity can be superior to the operations that created it
• Error mitigation and quantum-assisted simulation in the error corrected regime
• Simple scheme for encoding and decoding a qubit in unknown state for various topological codes

Cited by in corpus (20)

• Quantum Error Mitigation
• Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors
• Fundamental limits of quantum error mitigation
• Circuit knitting with classical communication
• Matching and maximum likelihood decoding of a multi-round subsystem quantum error correction experiment
• Generalized quantum subspace expansion
• Purification-based quantum error mitigation of pair-correlated electron simulations
• Hunting for quantum-classical crossover in condensed matter problems
• Error mitigation and quantum-assisted simulation in the error corrected regime
• Error statistics and scalability of quantum error mitigation formulas
• Efficiently improving the performance of noisy quantum computers
• Variational quantum algorithm for unconstrained black box binary optimization: Application to feature selection
• Error Suppression for Arbitrary-Size Black Box Quantum Operations
• Mitigating Quantum Errors via Truncated Neumann Series
• Quantum Error Mitigation via Quantum-Noise-Effect Circuit Groups
• A Practical Framework for Quantum Error Mitigation
• Characterizing and mitigating coherent errors in a trapped ion quantum processor using hidden inverses
• Quantum error mitigation for rotation symmetric bosonic codes with symmetry expansion
• Automated quantum error mitigation based on probabilistic error reduction
• Dual Map Framework for Noise Characterization of Quantum Computers