Geometric correspondence of noisy quantum dynamics and universal robust quantum gates

Abstract

Quantum information processing faces a significant hurdle: noise. Different noise sources induce varying errors in quantum operations depending on the underlying dynamics. To gain a deeper understanding of these error mechanisms, we introduce the concept of Quantum Error Evolution Diagrams (QEED). These QEEDs establish a dual correspondence between driven noisy quantum dynamics and geometric space curves, offering quantitative geometric metrics to assess the severity of these errors. This theory provides a framework for designing universal robust quantum gates to correct the errors induced by generic noises. Furthermore, we present a protocol for constructing a universal set of single- and two-qubit robust quantum gates. These gates, designed with simple and smooth control pulses of arbitrary length, achieve fidelities exceeding 99.99\% across a wide range of noise strengths. This geometric approach offers significant advantages over existing methods. Overall, our work provides new insights into the geometric nature of noisy quantum dynamics and paves the way for the development of approaches to dynamically correct quantum errors.

16 pages, 11 figures

References in corpus (51)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Circuit Quantum Electrodynamics
• A Quantum Engineer's Guide to Superconducting Qubits
• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• The Magnus expansion and some of its applications
• Strong quantum computational advantage using a superconducting quantum processor
• Suppressing quantum errors by scaling a surface code logical qubit
• Simple pulses for elimination of leakage in weakly nonlinear qubits
• High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions
• High-fidelity quantum logic gates using trapped-ion hyperfine qubits
• Training Schrödinger's cat: quantum optimal control
• Stabilizer Codes and Quantum Error Correction
• Realizing Repeated Quantum Error Correction in a Distance-Three Surface Code
• Computing with spin qubits at the surface code error threshold
• Fast universal quantum control above the fault-tolerance threshold in silicon
• Universal control of a six-qubit quantum processor in silicon
• Chopped random-basis quantum optimization
• Experimental Realization of Universal Geometric Quantum Gates with Solid-State Spins
• Fidelity benchmarks for two-qubit gates in silicon
• Fidelity of quantum operations
• Decoherence benchmarking of superconducting qubits
• Controlling open quantum systems: Tools, achievements, and limitations
• Dynamically Error-Corrected Gates for Universal Quantum Computation
• Realization of high-fidelity CZ and ZZ-free iSWAP gates with a tunable coupler
• Precision tomography of a three-qubit donor quantum processor in silicon
• Geometric Quantum Computation
• Suppression of Qubit Crosstalk in a Tunable Coupling Superconducting Circuit
• High-fidelity, high-scalability two-qubit gate scheme for superconducting qubits
• Silicon qubit fidelities approaching incoherent noise limits via pulse engineering
• Bosonic quantum error correction codes in superconducting quantum circuits
• Tunable Coupling Architecture for Fixed-frequency Transmons
• Demonstration of a High-Fidelity CNOT for Fixed-Frequency Transmons with Engineered ZZ Suppression
• Electric field spectroscopy of material defects in transmon qubits
• Towards Scalable Bosonic Quantum Error Correction
• Arbitrary quantum control of qubits in the presence of universal noise
• Experimental implementation of universal nonadiabatic geometric quantum gates in a superconducting circuit
• High-fidelity quantum gates in Si/SiGe double quantum dots
• Suppression of Unwanted $ZZ$ Interactions in a Hybrid Two-Qubit System
• Quantum crosstalk analysis for simultaneous gate operations on superconducting qubits
• Error-corrected gates on an encoded qubit
• Quantum crosstalk cancellation for fast entangling gates and improved multi-qubit performance
• Quantum manipulation of two-electron spin states in metastable double quantum dots
• Benchmarking Coherent Errors in Controlled-Phase Gates due to Spectator Qubits
• Quantum Crosstalk Robust Quantum Control
• Geometric formalism for constructing arbitrary single-qubit dynamically corrected gates
• Introduction to quantum non-reciprocal interactions: from non-Hermitian Hamiltonians to quantum master equations and quantum feedforward schemes
• Systematic Magnus-based approach for suppressing leakage and non-adiabatic errors in quantum dynamics
• General solution to inhomogeneous dephasing and smooth pulse dynamical decoupling
• Optimizing quantum control pulses with complex constraints and few variables through Tensorflow
• A simultaneous feedback and feed-forward control and its application to realize a random walk on the Bloch sphere in a superconducting Xmon-qubit system