Building a fault-tolerant quantum computer using concatenated cat codes

Abstract

We present a comprehensive architectural analysis for a proposed fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes. For the physical hardware, we propose a system of acoustic resonators coupled to superconducting circuits with a two-dimensional layout. Using estimated physical parameters for the hardware, we perform a detailed error analysis of measurements and gates, including CNOT and Toffoli gates. Having built a realistic noise model, we numerically simulate quantum error correction when the outer code is either a repetition code or a thin rectangular surface code. Our next step toward universal fault-tolerant quantum computation is a protocol for fault-tolerant Toffoli magic state preparation that significantly improves upon the fidelity of physical Toffoli gates at very low qubit cost. To achieve even lower overheads, we devise a new magic-state distillation protocol for Toffoli states. Combining these results together, we obtain realistic full-resource estimates of the physical error rates and overheads needed to run useful fault-tolerant quantum algorithms. We find that with around 1,000 superconducting circuit components, one could construct a fault-tolerant quantum computer that can run circuits which are currently intractable for classical computers. Hardware with 18,000 superconducting circuit components, in turn, could simulate the Hubbard model in a regime beyond the reach of classical computing.

arXiv comment117 pages (main text 32 pages), 62 figures, 15 tables. Comments welcome! V2 adds additional appendices and conforms to journal specifications

References in corpus (109)

• Surface codes: Towards practical large-scale quantum computation
• Circuit Quantum Electrodynamics
• A Quantum Engineer's Guide to Superconducting Qubits
• Introduction to Quantum Noise, Measurement and Amplification
• Topological quantum memory
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• State preservation by repetitive error detection in a superconducting quantum circuit
• Fault-tolerant quantum computation with high threshold in two dimensions
• High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions
• High-fidelity quantum logic gates using trapped-ion hyperfine qubits
• Dynamically protected cat-qubits: a new paradigm for universal quantum computation
• Roads towards fault-tolerant universal quantum computation
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Surface code quantum computing by lattice surgery
• Qubit architecture with high coherence and fast tunable coupling
• Confining the state of light to a quantum manifold by engineered two-photon loss
• Macroscopically distinct quantum superposition states as a bosonic code for amplitude damping
• The Kerr-Cat Qubit: Stabilization, Readout, and Gates
• Fast Scalable State Measurement with Superconducting Qubits
• Effective Hamiltonian Theory and Its Applications in Quantum Information
• Efficient Quantum Computation using Coherent States
• A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
• Magic state distillation with low overhead
• Quantum computing with nearest neighbor interactions and error rates over 1%
• Black-box superconducting circuit quantization
• Engineering the quantum states of light in a Kerr-nonlinear resonator by two-photon driving
• Performance and structure of single-mode bosonic codes
• Trading classical and quantum computational resources
• Low-distance Surface Codes under Realistic Quantum Noise
• Effective operator formalism for open quantum systems
• Simulation of quantum circuits by low-rank stabilizer decompositions
• Phononic bandgap nano-acoustic cavity with ultralong phonon lifetime
• Halving the cost of quantum addition
• Rapid high-fidelity multiplexed readout of superconducting qubits
• Tracking Photon Jumps with Repeated Quantum Non-Demolition Parity Measurements
• Continuous quantum error correction via quantum feedback control
• Realization of high-fidelity CZ and ZZ-free iSWAP gates with a tunable coupler
• Exponential suppression of bit-flips in a qubit encoded in an oscillator
• Universal fault-tolerant quantum computation with only transversal gates and error correction
• Suppression of Qubit Crosstalk in a Tunable Coupling Superconducting Circuit
• Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network: Toward quantum soft computing
• 3-Wave Mixing Josephson Dipole Element
• Magic State Distillation: Not as Costly as You Think
• Ultrahigh Error Threshold for Surface Codes with Biased Noise
• Measurement-induced state transitions in a superconducting qubit: Beyond the rotating wave approximation
• Novel constructions for the fault-tolerant Toffoli gate
• Fault-tolerant quantum computation against biased noise
• Efficient Bayesian Phase Estimation
• Bias-preserving gates with stabilized cat qubits
• Fast quantum non-demolition readout from longitudinal qubit-oscillator interaction
• Resolving the energy levels of a nanomechanical oscillator
• Topological and subsystem codes on low-degree graphs with flag qubits
• Repetition Cat Qubits for Fault-Tolerant Quantum Computation
• Hardware-efficient quantum random access memory with hybrid quantum acoustic systems
• Fault-tolerant conversion between the Steane and Reed-Muller quantum codes
• Low rank representations for quantum simulation of electronic structure
• Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization
• Quantum computation with realistic magic state factories
• Designing quantum memories with embedded control: photonic circuits for autonomous quantum error correction
• Coherent oscillations inside a quantum manifold stabilized by dissipation
• Stabilized Cat in Driven Nonlinear Cavity: A Fault-Tolerant Error Syndrome Detector
• Unfolding the color code
• Entangling Bosonic Modes via an Engineered Exchange Interaction
• Efficient magic state factories with a catalyzed |CCZ> to 2|T> transformation
• Effective fault-tolerant quantum computation with slow measurements
• Schrodinger's catapult: Launching multiphoton quantum states from a microwave cavity memory
• Flag fault-tolerant error correction with arbitrary distance codes
• Random access quantum information processors
• Multilevel distillation of magic states for quantum computing
• Improving wafer-scale Josephson junction resistance variation in superconducting quantum coherent circuits
• Tailoring surface codes for highly biased noise
• Fault-tolerant thresholds for the surface code in excess of 5% under biased noise
• Universal quantum computation with a nonlinear oscillator network
• Symmetry breaking and error correction in open quantum systems
• Quantum theory of a bandpass Purcell filter for qubit readout
• Time Averaged Quantum Dynamics and the Validity of the Effective Hamiltonian Model
• Surface code implementation of block code state distillation
• A unified framework for magic state distillation and multi-qubit gate-synthesis with reduced resource cost
• Programmable interference between two microwave quantum memories
• Triangular color codes on trivalent graphs with flag qubits
• Lattice Surgery with a Twist: Simplifying Clifford Gates of Surface Codes
• High-fidelity measurement of qubits encoded in multilevel superconducting circuits
• Fault-tolerant magic state preparation with flag qubits
• Codes and Protocols for Distilling $T$, controlled-$S$, and Toffoli Gates
• Toward fault-tolerant quantum computation without concatenation
• Engineering bilinear mode coupling in circuit QED: Theory and experiment
• Superconducting circuit quantum computing with nanomechanical resonators as storage
• Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits
• Continuous quantum error correction by cooling
• Applying quantum algorithms to constraint satisfaction problems
• Magic State Distillation with Low Space Overhead and Optimal Asymptotic Input Count
• Low overhead quantum computation using lattice surgery
• Distillation with sublogarithmic overhead
• Code Deformation and Lattice Surgery Are Gauge Fixing
• Error Rates and Resource Overheads of Repetition Cat Qubits
• Proof of finite surface code threshold for matching
• Unifying gate-synthesis and magic state distillation
• Fault-Tolerant Quantum Computing in the Pauli or Clifford Frame with Slow Error Diagnostics
• Fault-tolerant quantum computation with asymmetric Bacon-Shor codes
• Distilling one-qubit magic states into Toffoli states
• 2-D Compass Codes
• Structural instability of driven Josephson circuits prevented by an inductive shunt
• Loss channels affecting lithium niobate phononic crystal resonators at cryogenic temperature
• Millimeter-wave interconnects for microwave-frequency quantum machines
• An efficient magic state approach to small angle rotations
• Prospects for quantum acoustics with phononic crystal devices
• Robust readout of bosonic qubits in the dispersive coupling regime
• Fault-tolerant Compass Codes
• Collapse and Revival of an Artificial Atom Coupled to a Structured Photonic Reservoir

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