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Fault-tolerant quantum computation
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Recently, it was realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Interest in quantum computation has since been growing. One of the main difficulties of realizing quantum computation is that decoherence tends to destroy the information in a superposition of states in a quantum computer, thus making long computations impossible. A futher difficulty is that inaccuracies in quantum state transformations throughout the computation accumulate, rendering the output of long computations unreliable. It was previously known that a quantum circuit with t gates could tolerate O(1/t) amounts of inaccuracy and decoherence per gate. We show, for any quantum computation with t gates, how to build a polynomial size quantum circuit that can tolerate O(1/(log t)^c) amounts of inaccuracy and decoherence per gate, for some constant c. We do this by showing how to compute using quantum error correcting codes. These codes were previously known to provide resistance to errors while storing and transmitting quantum data.
Forward citations
Cited by 16 Pith papers
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A distillation-teleportation protocol for fault-tolerant QRAM
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Flood of multipartite Rains entanglement
New multipartite Rains-type entanglement measures are defined, with one-shot and asymptotic pure-state distillation bounds proven in terms of them.
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Restrictions on non-Clifford fault tolerance and ruling out beyond-SQL quantum metrology
Constant signal-aligned noise makes asymptotic beyond-SQL quantum sensing impossible for any protocol, including encoded, biased, adaptive, and nonstabilizer schemes.
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A superconducting surface-code processor with lattice-surgery logical operations
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Performance and achievable rates of the Gottesman-Kitaev-Preskill code for pure-loss and amplification channels
Infinite-energy GKP codes can reach the quantum capacity of pure loss and pure amplification at integer values of the channel-strength ratio, as shown through near-optimal transpose-channel decoding.
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The Utility of Sparse Error Detection in Quantum Simulations
Sparse error detection in small Iceberg codes reduces systematic errors in simulated Schwinger-model observables under depolarizing noise, with diminishing returns after a few detection layers.
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Arbitrary-Distance Quantum Error Correction with Gauss's Law for $\mathbb Z_2$ Lattice Gauge Theory
Gauss's law constraints in Z2 lattice gauge theory can be made into quantum error-correcting codes of arbitrary distance, with provably optimal encoding rate within the constructed family.
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Efficient simulation of logical magic state preparation protocols
A classical simulation method that propagates circuit-level Pauli noise to a Clifford error makes logical magic-state preparation protocols simulable in time polynomial in qubits and the target state's stabilizer rank.
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An apologia for islands
Entanglement islands and Page curves can arise in massless gravity without an external bath, and compactly supported gauge-invariant operators exist in islands around generic symmetry-breaking black hole backgrounds.
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Spacetime Markov length: a diagnostic for fault tolerance via mixed-state phases
The paper introduces the spacetime Markov length: the decay length of conditional mutual information of syndrome history, and provides evidence that its divergence marks the fault-tolerance threshold.
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A Universal Circuit Set Using the $S_3$ Quantum Double
A complete circuit-level blueprint for universal quantum computation using the D(S3) quantum double, with anyon interferometry and a concatenated local error-correcting code.
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Projection measurement of the comb basis through free-electron-photon interactions
A PINEM-based homodyne scheme projects free electrons onto their comb basis non-destructively, with applications to quantum error mitigation and EPR steering detection.
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Kagome edge states under lattice termination, spin-orbit coupling, and magnetic order
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A Resource Comparison of Logical T-State Preparation
Compares resource costs of logical T-state preparation via distillation, cultivation, and code switching using native metrics from existing literature plus a Shor factoring case study.
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Design Automation in Quantum Error Correction
A comprehensive review of automated tools and methods for designing quantum error-corrected circuits, with case studies on T-gate optimization, surface-code layout, ML decoders, and verification.
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