Error Rates and Resource Overheads of Repetition Cat Qubits

Abstract

We estimate and analyze the error rates and the resource overheads of the repetition cat qubit approach to universal and fault-tolerant quantum computation. The cat qubits stabilized by two-photon dissipation exhibit an extremely biased noise where the bit-flip error rate is exponentially suppressed with the mean number of photons. In a recent work, we suggested that the remaining phase-flip error channel could be suppressed using a 1D repetition code. Indeed, using only bias-preserving gates on the cat-qubits, it is possible to build a universal set of fault-tolerant logical gates at the level of the repetition cat qubit. In this paper, we perform Monte-Carlo simulations of all the circuits implementing the protected logical gates, using a circuit-level error model. Furthermore, we analyze two different approaches to implement a fault-tolerant Toffoli gate on repetition cat qubits. These numerical simulations indicate that very low logical error rates could be achieved with a reasonable resource overhead, and with parameters that are within the reach of near-term circuit QED experiments.

arXiv comment16 pages, 13 figures

References in corpus (48)

• Quantum Teleportation is a Universal Computational Primitive
• Improved Simulation of Stabilizer Circuits
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Multiple Particle Interference and Quantum Error Correction
• Quantum Computing with Very Noisy Devices
• Fault-tolerant quantum computation with high threshold in two dimensions
• Quantum computation with optical coherent states
• Dynamically protected cat-qubits: a new paradigm for universal quantum computation
• Roads towards fault-tolerant universal quantum computation
• Confining the state of light to a quantum manifold by engineered two-photon loss
• Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
• Macroscopically distinct quantum superposition states as a bosonic code for amplitude damping
• Restrictions on Transversal Encoded Quantum Gate Sets
• A quantum memory with near-millisecond coherence in circuit QED
• Building a fault-tolerant quantum computer using concatenated cat codes
• Exponential suppression of bit-flips in a qubit encoded in an oscillator
• Universal fault-tolerant quantum computation with only transversal gates and error correction
• Quantum error correction with only two extra qubits
• Magic State Distillation: Not as Costly as You Think
• Ultrahigh Error Threshold for Surface Codes with Biased Noise
• Subsystem fault tolerance with the Bacon-Shor code
• Fault-tolerant quantum computation against biased noise
• Towards practical classical processing for the surface code
• Bias-preserving gates with stabilized cat qubits
• Repetition Cat Qubits for Fault-Tolerant Quantum Computation
• Fault-tolerant conversion between the Steane and Reed-Muller quantum codes
• Quantum computation with realistic magic state factories
• Coherent oscillations inside a quantum manifold stabilized by dissipation
• Stabilized Cat in Driven Nonlinear Cavity: A Fault-Tolerant Error Syndrome Detector
• Quantum information processing with bosonic qubits in circuit QED
• Efficient magic state factories with a catalyzed |CCZ> to 2|T> transformation
• Flag fault-tolerant error correction with arbitrary distance codes
• Universal transversal gates with color codes - a simplified approach
• Fault-tolerant quantum computation
• Fault-tolerant thresholds for the surface code in excess of 5% under biased noise
• Fault-tolerant error correction with the gauge color code
• Surface code implementation of block code state distillation
• Using concatenated quantum codes for universal fault-tolerant quantum gates
• Space, time, parallelism and noise requirements for reliable quantum computing
• Codes and Protocols for Distilling $T$, controlled-$S$, and Toffoli Gates
• A fault-tolerant non-Clifford gate for the surface code in two dimensions
• Universal fault-tolerant gates on concatenated stabilizer codes
• Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits
• Fault-tolerant quantum computation with asymmetric Bacon-Shor codes
• A State Distillation Protocol to Implement Arbitrary Single-qubit Rotations
• Reducing the quantum computing overhead with complex gate distillation
• Efficient simulation of quantum error correction under coherent error based on non-unitary free-fermionic formalism
• Error rates and resource overheads of encoded three-qubit gates

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• Combined Dissipative and Hamiltonian Confinement of Cat Qubits
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• A circuit-level protocol and analysis for twist-based lattice surgery
• Introduction to Quantum Error Correction and Fault Tolerance
• Two-photon driven Kerr quantum oscillator with multiple spectral degeneracies
• Quantum computation with cat qubits
• Performance of teleportation-based error correction circuits for bosonic codes with noisy measurements
• High-Fidelity Magic-State Preparation with a Biased-Noise Architecture
• LDPC-cat codes for low-overhead quantum computing in 2D
• Fault-tolerant quantum computation by hybrid qubits with bosonic cat-code and single photons
• Tailored cluster states with high threshold under biased noise
• High-performance repetition cat code using fast noisy operations
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• Designing High-Fidelity Zeno Gates for Dissipative Cat Qubits
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• A cellular automaton decoder for a noise-bias tailored color code
• Closest lattice point decoding for multimode Gottesman-Kitaev-Preskill codes
• Adaptive variational low-rank dynamics for open quantum systems
• Analog information decoding of bosonic quantum LDPC codes
• Hybrid cat-transmon architecture for scalable, hardware-efficient quantum error correction
• Preserving phase coherence and linearity in cat qubits with exponential bit-flip suppression
• Surface Code with Imperfect Erasure Checks
• Dynamic compensation for pump-induced frequency shift in Kerr-cat qubit initialization
• Bit-flip errors in dissipative cat qubits: second-order perturbation theory
• Engineering the Nonlinearity of Bosonic Modes with a Multi-loop SQUID
• Single-shot quantum error correction with the three-dimensional subsystem toric code
• Practical quantum error correction with the XZZX code and Kerr-cat qubits
• Mitigating Temporal Fragility in the XY Surface Code
• Unfolded distillation: very low-cost magic state preparation for biased-noise qubits