Fault-tolerant quantum computation with few qubits

Abstract

Reliable qubits are difficult to engineer, but standard fault-tolerance schemes use seven or more physical qubits to encode each logical qubit, with still more qubits required for error correction. The large overhead makes it hard to experiment with fault-tolerance schemes with multiple encoded qubits. The 15-qubit Hamming code protects seven encoded qubits to distance three. We give fault-tolerant procedures for applying arbitrary Clifford operations on these encoded qubits, using only two extra qubits, 17 total. In particular, individual encoded qubits within the code block can be targeted. Fault-tolerant universal computation is possible with four extra qubits, 19 total. The procedures could enable testing more sophisticated protected circuits in small-scale quantum devices. Our main technique is to use gadgets to protect gates against correlated faults. We also take advantage of special code symmetries, and use pieceable fault tolerance.

10 pages, 5 figures

References in corpus (2)

• Quantum error correction with only two extra qubits
• Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study

Cited by in corpus (83)

• Topological and subsystem codes on low-degree graphs with flag qubits
• Digitization of Scalar Fields for Quantum Computing
• A quantum network stack and protocols for reliable entanglement-based networks
• Flag fault-tolerant error correction with arbitrary distance codes
• Approximate unitary $t$-designs by short random quantum circuits using nearest-neighbor and long-range gates
• Neutral Atom Quantum Computing Hardware: Performance and End-User Perspective
• Error-transparent operations on a logical qubit protected by quantum error correction
• Efficient classical simulation of noisy random quantum circuits in one dimension
• Triangular color codes on trivalent graphs with flag qubits
• Flag fault-tolerant error correction for any stabilizer code
• Universal quantum computing with twist-free and temporally encoded lattice surgery
• Low overhead fault-tolerant quantum error correction with the surface-GKP code
• Fault-tolerant magic state preparation with flag qubits
• Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits
• Neural network decoder for topological color codes with circuit level noise
• Fault-tolerant preparation of approximate GKP states
• Crosstalk Suppression for Fault-tolerant Quantum Error Correction with Trapped Ions
• Programmable Heisenberg interactions between Floquet qubits
• Experimental Demonstration of Logical Magic State Distillation
• Hardware-Encoding Grid States in a Non-Reciprocal Superconducting Circuit
• Path-Independent Quantum Gates with Noisy Ancilla
• Genuine quantum networks: superposed tasks and addressing
• Demonstrating Bayesian Quantum Phase Estimation with Quantum Error Detection
• Flag fault-tolerant error correction, measurement, and quantum computation for cyclic CSS codes
• Error detection on quantum computers improves accuracy of chemical calculations
• Partitioning qubits in hypergraph product codes to implement logical gates
• Tailored XZZX codes for biased noise
• Distributed quantum error correction for chip-level catastrophic errors
• Fault-tolerant qubit from a constant number of components
• Protecting Expressive Circuits with a Quantum Error Detection Code
• A circuit-level protocol and analysis for twist-based lattice surgery
• Entangling four logical qubits beyond break-even in a nonlocal code
• Modeling noise and error correction for Majorana-based quantum computing
• Universal bound on the cardinality of local hidden variables in networks
• Is error detection helpful on IBM 5Q chips ?
• Improving the efficiency of joint remote state preparation in noisy environment with weak measurement
• Constraints on magic state protocols from the statistical mechanics of Wigner negativity
• Extended flag gadgets for low-overhead circuit verification
• Making existing software quantum safe: a case study on IBM Db2
• Logical Clifford Synthesis for Stabilizer Codes
• The role of entropy in topological quantum error correction
• Achieving fault tolerance on capped color codes with few ancillas
• Fault-Tolerant Computing with Single Qudit Encoding
• Un-Weyl-ing the Clifford Hierarchy
• Fundamental thresholds of realistic quantum error correction circuits from classical spin models
• Transversal Diagonal Logical Operators for Stabiliser Codes
• Fault-tolerant quantum error correction using error weight parities
• Using Quantum Computers to Speed Up Dynamic Testing of Software
• Implementations of more general solid-state (SWAP)${}^{1/m}$ and controlled-(swap)${}^{1/m}$ gates
• Decoding Merged Color-Surface Codes and Finding Fault-Tolerant Clifford Circuits Using Solvers for Satisfiability Modulo Theories
• Implementing fault-tolerant non-Clifford gates using the [[8,3,2]] color code
• Parallel syndrome extraction with shared flag qubits for Calderbank-Shor-Steane codes of distance three
• Mitigating Errors on Superconducting Quantum Processors through Fuzzy Clustering
• Kerdock Codes Determine Unitary 2-Designs
• Code switching revisited: Low-overhead magic state preparation using color codes
• Surface Code Design for Asymmetric Error Channels
• Experimental Simulation of Hybrid Quantum Systems and Entanglement on a Quantum Computer
• Concatenate codes, save qubits
• Fault-tolerant syndrome extraction and cat state preparation with fewer qubits
• Characterization, synthesis, and optimization of quantum circuits over multiple-control $\text{Z}$-rotation gates: A systematic study
• Low-Depth Flag-Style Syndrome Extraction for Small Quantum Error-Correction Codes
• Efficient fault-tolerant code switching via one-way transversal CNOT gates
• Machine learning of quantum channels on NISQ devices
• Adaptive Syndrome Extraction
• Effectiveness of the syndrome extraction circuit with flag qubits on IBM quantum hardware
• Efficiently computing logical noise in quantum error correcting codes
• Concatenated Steane code with single-flag syndrome checks
• Efficient fault-tolerant implementations of non-Clifford gates with reconfigurable atom arrays
• From Classical to quantum stochastic process
• Reducing Quantum Error Correction Overhead with Versatile Flag-Sharing Syndrome Extraction Circuits
• Classical Coding Approaches to Quantum Applications
• Universal graph representation of stabilizer codes
• Fidelity of the Kitaev honeycomb model under a quench
• Targeted Clifford logical gates for hypergraph product codes
• General entropic constraints on CSS codes within magic distillation protocols
• Efficient simulation of logical magic state preparation protocols
• Quantum Computation and Communication in Bosonic Systems
• Tailoring Fault-Tolerance to Quantum Algorithms
• Structural encoding with classical codes for computational-basis bit-flip correction in the early fault-tolerant regime
• Error detection without post-selection in adaptive quantum circuits
• Weakly Fault-Tolerant Computation in a Quantum Error-Detecting Code
• Between Shor and Steane: A unifying construction for measuring error syndromes
• Testing of flag-based fault-tolerance on IBM quantum devices