Speed limits for two-qubit gates with weakly anharmonic qubits

Abstract

We consider the implementation of two-qubit gates when the physical systems used to realize the qubits possess additional quantum states in the accessible energy range. We use optimal control theory to determine the maximum achievable gate speed for two-qubit gates in the qubit subspace of the many-level Hilbert space, and we analyze the effect of the additional quantum states on the gate speed. We identify two competing mechanisms. On one hand, higher energy levels are generally more strongly coupled to each other. Under suitable conditions, this stronger coupling can be utilized to make two-qubit gates significantly faster than the reference value based on simple qubits. On the other hand, a weak anharmonicity constrains the speed at which the system can be adequately controlled: according to the intuitive picture, faster operations require stronger control fields, which are more likely to excite higher levels in a weakly anharmonic system, which in turn leads to faster decoherence and uncontrolled leakage outside the qubit space. In order to account for this constraint, we modify the pulse optimization algorithm to avoid pulses that lead to appreciable population of the higher levels. In this case we find that the presence of the higher levels can lead to a significant reduction in the maximum achievable gate speed. We also compare the optimal-control gate speeds with those obtained using the cross-resonance/selective-darkening gate protocol. We find that the latter, with some parameter optimization, can be used to achieve a relatively fast implementation of the CNOT gate. These results can help the search for optimized gate implementations in realistic quantum computing architectures, such as those based on superconducting circuits. They also provide guidelines for desirable conditions on anharmonicity that allow optimal utilization of the higher levels to achieve fast quantum gates.

arXiv comment14 pages (two-column), 6 figures

References in corpus (39)

• Quantum Computing
• Charge insensitive qubit design derived from the Cooper pair box
• Superconducting Qubits: Current State of Play
• Demonstration of Two-Qubit Algorithms with a Superconducting Quantum Processor
• Control of quantum phenomena: Past, present, and future
• Simple pulses for elimination of leakage in weakly nonlinear qubits
• Fluxonium: single Cooper pair circuit free of charge offsets
• Coherent Josephson qubit suitable for scalable quantum integrated circuits
• Natural and artificial atoms for quantum computation
• The Flux Qubit Revisited to Enhance Coherence and Reproducibility
• Complete universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits
• Implementing a Universal Gate Set on a Logical Qubit Encoded in an Oscillator
• Demonstration of quantum error correction and universal gate set on a binomial bosonic logical qubit
• Low-decoherence flux qubit
• Monotonically convergent optimization in quantum control using Krotov's method
• Quantum logic gates for coupled superconducting phase qubits
• Effective Hamiltonian models of the cross-resonance gate
• Optimal Control of Coupled Josephson Qubits
• High coherence hybrid superconducting qubit
• Selective darkening of degenerate transitions demonstrated with two superconducting quantum bits
• Operation and intrinsic error budget of a two-qubit cross-resonance gate
• Speed limits for quantum gates in multi-qubit systems
• Implementation of a Walsh-Hadamard gate in a superconducting qutrit
• High-fidelity CZ gate for resonator-based superconducting quantum computers
• Charting the circuit QED design landscape using optimal control theory
• Optimal control of a leaking qubit
• Optimizing for an arbitrary perfect entangler: I. Functionals
• High-fidelity software-defined quantum logic on a superconducting qudit
• Optimized cross-resonance gate for coupled transmon systems
• Optimizing for an arbitrary perfect entangler. II. Application
• Characterization of Control in a Superconducting Qutrit Using Randomized Benchmarking
• Microwave-Activated Controlled-Z Gate for Fixed-Frequency Fluxonium Qubits
• Optimal control for fast and high-fidelity quantum gates in coupled superconducting flux qubits
• Selective darkening of degenerate transitions for implementing quantum controlled-NOT gates
• Two-qubit gate operations in superconducting circuits with strong coupling and weak anharmonicity
• Optimal generation of Fock states in a weakly nonlinear oscillator
• Quantum computing with superconducting circuits in the picosecond regime
• Optimization of Controlled-Z Gate with Data-Driven Gradient Ascent Pulse Engineering in a Superconducting Qubit System
• Excitation spectrum as a resource for efficient two-qubit entangling gates

Cited by in corpus (10)

• Scalable and robust quantum computing on qubit arrays with fixed coupling
• Numerical analysis of quantum circuits for state preparation and unitary operator synthesis
• Implementing two-qubit gates at the quantum speed limit
• Protocol for generating an arbitrary quantum state of the magnetization in cavity magnonics
• Reinforcement learning pulses for transmon qubit entangling gates
• Quantum circuit synthesis via a random combinatorial search
• Universal Control in Bosonic Systems with Weak Kerr Nonlinearities
• Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
• Parallel Driving for Fast Quantum Computing Under Speed Limits
• Automated discovery and optimization of autonomous quantum error correction codes for a general open quantum system