Geometric formalism for constructing arbitrary single-qubit dynamically corrected gates

Abstract

Implementing high-fidelity quantum control and reducing the effect of the coupling between a quantum system and its environment is a major challenge in developing quantum information technologies. Here, we show that there exists a geometrical structure hidden within the time-dependent Schrödinger equation that provides a simple way to view the entire solution space of pulses that suppress noise errors in a system's evolution. In this framework, any single-qubit gate that is robust against quasistatic noise to first order corresponds to a closed three-dimensional space curve, where the driving fields that implement the robust gate can be read off from the curvature and torsion of the space curve. Gates that are robust to second order are in one-to-one correspondence with closed curves whose projections onto three mutually orthogonal planes each enclose a vanishing net area. We use this formalism to derive new examples of dynamically corrected gates generated from smooth pulses. We also show how it can be employed to analyze the noise-cancellation properties of pulses generated from numerical algorithms such as GRAPE. A similar geometrical framework exists for quantum systems of arbitrary Hilbert space dimension.

arXiv commentpublished version

References in corpus (44)

• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• Dynamical suppression of decoherence in two-state quantum systems
• Reliable Quantum Computers
• A Two Qubit Logic Gate in Silicon
• Control of quantum phenomena: Past, present, and future
• A >99.9%-fidelity quantum-dot spin qubit with coherence limited by charge noise
• High-fidelity quantum logic gates using trapped-ion hyperfine qubits
• High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions
• Training Schrödinger's cat: quantum optimal control
• A programmable two-qubit quantum processor in silicon
• Keeping a Quantum Bit Alive by Optimized $\pi$-Pulse Sequences
• Quantum CNOT Gate for Spins in Silicon
• Optimal control technique for Many Body Quantum Systems dynamics
• Chopped random-basis quantum optimization
• Molecular Quantum Computing by an Optimal Control Algorithm for Unitary Transformations
• Robust dynamical decoupling with bounded controls
• Dynamically Error-Corrected Gates for Universal Quantum Computation
• Experimental demonstration of fault-tolerant state preparation with superconducting qubits
• Silicon qubit fidelities approaching incoherent noise limits via pulse engineering
• 1/f Flux Noise in Josephson Phase Qubits
• Decoherence in Solid State Qubits
• Composite pulses for robust universal control of singlet-triplet qubits
• Review of Decoherence Free Subspaces, Noiseless Subsystems, and Dynamical Decoupling
• Universality of Uhrig dynamical decoupling for suppressing qubit pure dephasing and relaxation
• Arbitrarily Accurate Dynamical Control in Open Quantum Systems
• Fidelity of Single Qubit Maps
• Analytically solvable driven time-dependent two-level quantum systems
• Dynamical Quantum Error Correction of Unitary Operations with Bounded Controls
• Noise-resistant control for a spin qubit array
• Robust quantum gates for singlet-triplet spin qubits using composite pulses
• Continuously decoupling single-qubit operations from a perturbing thermal bath of scalar bosons
• Automated Synthesis of Dynamically Corrected Quantum Gates
• The fastest pulses that implement dynamically corrected gates
• Robust quantum control using smooth pulses and topological winding
• Cooperative pulses in robust quantum control: Application to broadband Ramsey-type pulse sequence elements
• General solution to inhomogeneous dephasing and smooth pulse dynamical decoupling
• Exact solution for quantum dynamics of a periodically-driven two-level-system
• Crosstalk error correction through dynamical decoupling of single-qubit gates in capacitively coupled singlet-triplet semiconductor spin qubits
• Dynamically Correcting a CNOT Gate for any Systematic Logical Error
• Pulse sequence designed for robust C-phase gates in SiMOS and Si/SiGe double quantum dots
• Dynamical decoupling of a qubit with always-on control fields
• Error correction for gate operations in systems of exchange-coupled singlet-triplet qubits in double quantum dots
• Conditions allowing error correction in driven qubits
• Geometry of adiabatic Hamiltonians for two-level quantum systems

Cited by in corpus (31)

• Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control
• The SMART protocol -- Pulse engineering of a global field for robust and universal quantum computation
• Doubly geometric quantum control
• Implementation of the SMART protocol for global qubit control in silicon
• Geometrical Formalism for Dynamically Corrected Gates in Multiqubit Systems
• Fast high-fidelity entangling gates for spin qubits in Si double quantum dots
• Robust quantum gates using smooth pulses and physics-informed neural networks
• Analytically parameterized solutions for robust quantum control using smooth pulses
• Fast and Robust Geometric Two-Qubit Gates for Superconducting Qubits and beyond
• Robust Quantum Gates against Correlated Noise in Integrated Quantum Chips
• Phase driving hole spin qubits
• Noise-resistant Landau-Zener sweeps from geometrical curves
• Enhanced-Fidelity Ultrafast Geometric Quantum Computation Using Strong Classical Drives
• Protecting Quantum Information in Quantum Dot Spin Chains by Driving Exchange Interactions Periodically
• Dynamically corrected gates in silicon singlet-triplet spin qubits
• Designing dynamically corrected gates robust to multiple noise sources using geometric space curves
• Designing globally optimal entangling gates using geometric space curves
• Reverse engineering of one-qubit filter functions with dynamical invariants
• A greedy reconstruction algorithm for the identification of spin distribution
• Optimal control and ultimate bounds of 1:2 nonlinear quantum systems
• Designing arbitrary single-axis rotations robust against perpendicular time-dependent noise
• Application of the Pontryagin Maximum Principle to the robust time-optimal control of two-level quantum systems
• Robust population transfer of spin states by geometric formalism
• Geometric correspondence of noisy quantum dynamics and universal robust quantum gates
• Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
• Robust phase-controlled gates for scalable atomic quantum processors using optical standing waves
• Higher-order protection of quantum gates: Hamiltonian engineering coordinated with dynamical decoupling
• Accessing the Full Capabilities of Filter Functions: A Tool for Detailed Noise and Control Susceptibility Analysis
• An automated geometric space curve approach for designing dynamically corrected gates
• Hybrid acousto-optical spin control in quantum dots
• Application of the Small Tip-Angle approximation in the Toggling Frame for the design of analytic robust pulses in Quantum Control