Fault-tolerant magic state preparation with flag qubits

Abstract

Magic state distillation is one of the leading candidates for implementing universal fault-tolerant logical gates. However, the distillation circuits themselves are not fault-tolerant, so there is additional cost to first implement encoded Clifford gates with negligible error. In this paper we present a scheme to fault-tolerantly and directly prepare magic states using flag qubits. One of these schemes uses a single extra ancilla, even with noisy Clifford gates. We compare the physical qubit and gate cost of this scheme to the magic state distillation protocol of Meier, Eastin, and Knill, which is efficient and uses a small stabilizer circuit. In some regimes, we show that the overhead can be improved by several orders of magnitude.

26 pages, 17 figures, 5 tables. Comments welcome! v2 (published version): quantumarticle documentclass and expanded discussions on the fault-tolerant schemes

References in corpus (12)

• Surface codes: Towards practical large-scale quantum computation
• Restrictions on Transversal Encoded Quantum Gate Sets
• A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
• Experimental demonstration of fault-tolerant state preparation with superconducting qubits
• Fault-tolerant conversion between the Steane and Reed-Muller quantum codes
• Efficient magic state factories with a catalyzed |CCZ> to 2|T> transformation
• A magic state's fidelity can be superior to the operations that created it
• Codes and Protocols for Distilling $T$, controlled-$S$, and Toffoli Gates
• Simulating the performance of a distance-3 surface code in a linear ion trap
• Distillation with sublogarithmic overhead
• Code Deformation and Lattice Surgery Are Gauge Fixing
• Fault-tolerant protection of near-term trapped-ion topological qubits under realistic noise sources

Cited by in corpus (59)

• Demonstration of fault-tolerant universal quantum gate operations
• Building a fault-tolerant quantum computer using concatenated cat codes
• Magic State Distillation: Not as Costly as You Think
• Topological and subsystem codes on low-degree graphs with flag qubits
• Quantifying the magic of quantum channels
• Encoding a magic state with beyond break-even fidelity
• Efficient classical simulation of noisy random quantum circuits in one dimension
• Efficiently computable bounds for magic state distillation
• Triangular color codes on trivalent graphs with flag qubits
• Universal quantum computing with twist-free and temporally encoded lattice surgery
• Flag fault-tolerant error correction for any stabilizer code
• Low overhead fault-tolerant quantum error correction with the surface-GKP code
• The cost of universality: A comparative study of the overhead of state distillation and code switching with color codes
• Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics
• Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits
• Fault-tolerant preparation of approximate GKP states
• Time-Efficient Constant-Space-Overhead Fault-Tolerant Quantum Computation
• Experimental Demonstration of Logical Magic State Distillation
• Path-Independent Quantum Gates with Noisy Ancilla
• Measurement-free fault-tolerant quantum error correction in near-term devices
• Flag fault-tolerant error correction, measurement, and quantum computation for cyclic CSS codes
• Lower bound for the T count via unitary stabilizer nullity
• Variational circuit compiler for quantum error correction
• A circuit-level protocol and analysis for twist-based lattice surgery
• Strategies for practical advantage of fault-tolerant circuit design in noisy trapped-ion quantum computers
• Fault-Tolerant Code Switching Protocols for Near-Term Quantum Processors
• Universal Fault-Tolerant Quantum Computing with Stabiliser Codes
• High-Fidelity Magic-State Preparation with a Biased-Noise Architecture
• Quantifying dynamical magic with completely stabilizer preserving operations as free
• Constraints on magic state protocols from the statistical mechanics of Wigner negativity
• Extended flag gadgets for low-overhead circuit verification
• Efficient Magic State Distillation by Zero-Level Distillation
• Achieving fault tolerance on capped color codes with few ancillas
• Automated Synthesis of Fault-Tolerant State Preparation Circuits for Quantum Error Correction Codes
• Fault-tolerant quantum error correction using error weight parities
• Measurement-free fault-tolerant logical zero-state encoding of the distance-three nine-qubit surface code in a one-dimensional qubit array
• Decoding Merged Color-Surface Codes and Finding Fault-Tolerant Clifford Circuits Using Solvers for Satisfiability Modulo Theories
• Mitigating errors in logical qubits
• On maximum-likelihood decoding with circuit-level errors
• Parallel syndrome extraction with shared flag qubits for Calderbank-Shor-Steane codes of distance three
• Low-overhead magic state distillation with color codes
• Fault-tolerant quantum speedup from constant depth quantum circuits
• Stabilizer ground states for simulating quantum many-body physics: theory, algorithms, and applications
• Decomposition of Clifford Gates
• Concatenate codes, save qubits
• Dynamical subset sampling of quantum error correcting protocols
• Efficient fault-tolerant code switching via one-way transversal CNOT gates
• Low-Depth Flag-Style Syndrome Extraction for Small Quantum Error-Correction Codes
• Quantum Circuit Discovery for Fault-Tolerant Logical State Preparation with Reinforcement Learning
• Concatenated Steane code with single-flag syndrome checks
• Measurement sequences for magic state distillation
• Demonstration of two-dimensional connectivity for a scalable error-corrected ion-trap quantum processor architecture
• End-to-end switchless architecture for fault-tolerant photonic quantum computing
• From Magic State Distillation to Dynamical Systems
• Logical Noise Bias in Magic State Injection
• Scalable Low-overhead Superconducting Non-local Coupler with Exponentially Enhanced Connectivity
• Efficient simulation of logical magic state preparation protocols
• Real-time hybrid quantum-classical computations for trapped-ions with Python control-flow
• Universal fault tolerant quantum computation in 2D without getting tied in knots