Exploring the trade-off between fidelity- and time-optimal control of quantum unitary transformations

Abstract

Generating a unitary transformation in the shortest possible time is of practical importance to quantum information processing because it helps to reduce decoherence effects and improve robustness to additive control field noise. Many analytical and numerical studies have identified the minimum time necessary to implement a variety of quantum gates on coupled-spin qubit systems. This work focuses on exploring the Pareto front that quantifies the trade-off between the competitive objectives of maximizing the gate fidelity $\mathcal{F}$ and minimizing the control time $T$. In order to identify the critical time $T^{\ast }$, below which the target transformation is not reachable, as well as to determine the associated Pareto front, we introduce a numerical method of Pareto front tracking (PFT). We consider closed two- and multi-qubit systems with constant inter-qubit coupling strengths and each individual qubit controlled by a separate time-dependent external field. Our analysis demonstrates that unit fidelity (to a desired numerical accuracy) can be achieved at any $T\ge T^{\ast }$ in most cases. However, the optimization search effort rises superexponentially as $T$ decreases and approaches $T^{\ast }$. Furthermore, a small decrease in control time incurs a significant penalty in fidelity for $T<T^{\ast }$, indicating that it is generally undesirable to operate below the critical time. We investigate the dependence of the critical time $T^{\ast }$ on the coupling strength between qubits and the target gate transformation. Practical consequences of these findings for laboratory implementation of quantum gates are discussed.

23 pages, 11 figures

References in corpus (40)

• Control of quantum phenomena: Past, present, and future
• Time Optimal Control in Spin Systems
• A geometric theory of non-local two-qubit operations
• Molecular Quantum Computing by an Optimal Control Algorithm for Unitary Transformations
• Optimal control theory for unitary transformations
• Quantum Computation with Vibrationally Excited Molecules
• Comparing, Optimising and Benchmarking Quantum Control Algorithms in a Unifying Programming Framework
• Sub-Riemannian Geometry and Time Optimal Control of Three Spin Systems: Quantum Gates and Coherence Transfer
• Quantum Control Landscapes
• Optimal Control-Based Efficient Synthesis of Building Blocks of Quantum Algorithms Seen in Perspective from Network Complexity towards Time Complexity
• An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation
• Optimal control, geometry, and quantum computing
• Robust optimal quantum gates for Josephson charge qubits
• Time Optimal Unitary Operations
• Optimal Control for Generating Quantum Gates in Open Dissipative Systems
• Optimal Control of Coupled Josephson Qubits
• Scalable quantum computation via local control of only two qubits
• Optimal control of quantum gates and suppression of decoherence in a system of interacting two-level particles
• Optimal control of entangling operations for trapped ion quantum computing
• Speeding up critical system dynamics through optimized evolution
• Quantum Control Landscapes: A Closer Look
• The Quantum Speed Limit of Optimal Controlled Phasegates for Trapped Neutral Atoms
• Efficient Algorithms for Optimal Control of Quantum Dynamics: The "Krotov'' Method unencumbered
• Search complexity and resource scaling for the quantum optimal control of unitary transformations
• Exploring Quantum Control Landscapes: Topology, Features, and Optimization Scaling
• Environment-invariant measure of distance between evolutions of an open quantum system
• Implications of Simultaneous Requirements for Low Noise Exchange Gates in Double Quantum Dots
• Optimized single-qubit gates for Josephson phase qubits
• Optimal Control for Open Quantum Systems: Qubits and Quantum Gates
• Implementation of Quantum Gates via Optimal Control
• Quantum Pareto Optimal Control
• Implementing Quantum Gates by Optimal Control with Doubly Exponential Convergence
• Optimized pulses for the control of uncertain qubits
• Fidelity of optimally controlled quantum gates with randomly coupled multiparticle environments
• Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain
• High Fidelity Quantum Gates in the Presence of Dispersion
• Time complexity and gate complexity
• Optimal control of the silicon-based donor electron spin quantum computing
• Correcting errors in a quantum gate with pushed ions via optimal control
• Encoding a qubit into multilevel subspaces

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• Exact solutions for time-optimal control of spin I=1 by NMR
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• Error-budgeting for a controlled-phase gate with strontium-88 Rydberg atoms
• Group Sparse Matrix Optimization for Efficient Quantum State Transformation
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• Optimization of the ionization time of an atom with tailored laser pulses: a theoretical study
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