Error metric for non-trace-preserving quantum operations
arXiv:2110.02290 · doi:10.1103/PhysRevA.108.032609
Abstract
We study the problem of measuring errors in non-trace-preserving quantum operations, with a focus on their impact on quantum computing. We propose an error metric that efficiently provides an upper bound on the trace distance between the normalized output states from imperfect and ideal operations, while remaining compatible with the diamond distance. As a demonstration of its application, we apply our metric in the analysis of a lossy beam splitter and a nondeterministic conditional sign-flip gate, two primary non-trace-preserving operations in the Knill-Laflamme-Milburn protocol. We then turn to the leakage errors of neutral-atom quantum computers, finding that these errors scale worse than previously anticipated, implying a more stringent fault-tolerant threshold. We also assess the quantum Zeno gate's error using our metric. In a broader context, we discuss the potential of our metric to analyze general postselected protocols, where it can be employed to study error propagation and estimate thresholds in fault-tolerant quantum computing. The results highlight the critical role of our proposed error metric in understanding and addressing challenges in practical quantum information processing.
arXiv comment18 pages, 4 figures
References in corpus (66)
- Quantum Teleportation is a Universal Computational Primitive
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Experimental One-Way Quantum Computing
- Quantum Computing with Very Noisy Devices
- Entanglement renormalization
- Universal Linear Optics
- Universal Quantum Computation with Continuous-Variable Cluster States
- Fault-tolerant quantum computation with high threshold in two dimensions
- Simple pulses for elimination of leakage in weakly nonlinear qubits
- Resource-efficient linear optical quantum computation
- Realization of a multi-node quantum network of remote solid-state qubits
- Distance measures to compare real and ideal quantum processes
- Overhead and noise threshold of fault-tolerant quantum error correction
- Quantum Zeno dynamics: mathematical and physical aspects
- Tensor Network Renormalization
- Quantum certification and benchmarking
- Modular Entanglement of Atomic Qubits using both Photons and Phonons
- Linear Optics C-Phase gate made simple
- Deterministic teleportation of a quantum gate between two logical qubits
- Measuring and Suppressing Quantum State Leakage in a Superconducting Qubit
- The XZZX Surface Code
- Microwave Quantum Link between Superconducting Circuits Housed in Spatially Separated Cryogenic Systems
- From three-photon GHZ states to ballistic universal quantum computation
- A Quantum-Logic Gate between Distant Quantum-Network Modules
- Entanglement of trapped-ion qubits separated by 230 meters
- Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays
- Simple Scheme for Efficient Linear Optics Quantum Gates
- Quantum Logic Operations Using Single Photons and the Zeno Effect
- Constrained dynamics via the Zeno effect in quantum simulation: Implementing non-Abelian lattice gauge theories with cold atoms
- Quantum Computing Using Single Photons and the Zeno Effect
- Quantification and Characterization of Leakage Errors
- Quantum gate teleportation between separated qubits in a trapped-ion processor
- Theory of quantum system certification: a tutorial
- Comparing Experiments to the Fault-Tolerance Threshold
- Noise thresholds for optical quantum computers
- Deterministic generation of multiparticle entanglement by quantum Zeno dynamics
- Bounding quantum gate error rate based on reported average fidelity
- Quantum Zeno dynamics of a field in a cavity
- Optically-Heralded Entanglement of Superconducting Systems in Quantum Networks
- Realization of a Knill-Laflamme-Milburn C-NOT gate -a photonic quantum circuit combining effective optical nonlinearities
- Tensor-Network Simulations of the Surface Code under Realistic Noise
- Quantifying error and leakage in an encoded Si/SiGe triple-dot qubit
- Experimental quantum process tomography of non trace-preserving maps
- Understanding the effects of leakage in superconducting quantum error detection circuits
- Teleportation-based realization of an optical quantum two-qubit entangling gate
- Topological Qubit Design and Leakage
- Universal Leakage Elimination
- Experimentally scalable protocol for identification of correctable codes
- Protecting quantum entanglement from leakage and qubit errors via repetitive parity measurements
- Deterministic correction of qubit loss
- Leakage detection for a transmon-based surface code
- Fundamental limitations on distillation of quantum channel resources
- Modeling quantum noise for efficient testing of fault-tolerant circuits
- A hardware-efficient leakage-reduction scheme for quantum error correction with superconducting transmon qubits
- Demonstration of universal control between non-interacting qubits using the Quantum Zeno effect
- Comparing Zeeman qubits to hyperfine qubits in the context of the surface code: Yb and Yb
- Eliminating Leakage Errors in Hyperfine Qubits
- Leakage mitigation for quantum error correction using a mixed qubit scheme
- Handling Leakage with Subsystem Codes
- Quantum Zeno effects across a parity-time symmetry breaking transition in atomic momentum space
- Constructing Functional Braids for Low-Leakage Topological Quantum Computing
- Intrinsic leakage of the Josephson flux qubit and breakdown of the two-level approximation for strong driving
- Fault-Tolerant Quantum Computation for Singlet-Triplet Qubits with Leakage Errors
- A Silicon Surface Code Architecture Resilient Against Leakage Errors
- Tradeoff between Leakage and Dephasing Errors in the Fluxonium Qubit
- Quantum Fourier transform on photonic qubits using cavity QED