Numerical Gate Synthesis for Quantum Heuristics on Bosonic Quantum Processors

Abstract

There is a recent surge of interest and insights regarding the interplay of quantum optimal control and variational quantum algorithms. We study the framework in the context of qudits which are, for instance, definable as controllable electromagnetic modes of a superconducting cavity system coupled to a transmon. By employing recent quantum optimal control approaches described in (Petersson and Garcia, 2021), we showcase control of single-qudit operations up to eight states, and two-qutrit operations, mapped respectively onto a single mode and two modes of the resonator. We discuss the results of numerical pulse engineering on the closed system for parametrized gates useful to implement Quantum Approximate Optimization Algorithm (QAOA) for qudits. The results show that high fidelity ($>$ 0.99) is achievable with sufficient computational effort for most cases under study, and extensions to multiple modes and open, noisy systems are possible. The tailored pulses can be stored and used as calibrated primitives for a future compiler in circuit quantum electrodynamics (cQED) systems.

arXiv comment11 pages, 4 figures. To appear

References in corpus (39)

• Quantum Computing in the NISQ era and beyond
• Variational Quantum Algorithms
• Circuit Quantum Electrodynamics
• Two-Bit Gates are Universal for Quantum Computation
• From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
• Quantum Annealing and Analog Quantum Computation
• Qudits and high-dimensional quantum computing
• Molecular Quantum Computing by an Optimal Control Algorithm for Unitary Transformations
• Black-box superconducting circuit quantization
• Implementing a Universal Gate Set on a Logical Qubit Encoded in an Oscillator
• Quantum Information Scrambling in a Superconducting Qutrit Processor
• Cavity State Manipulation Using Photon-Number Selective Phase Gates
• Three-dimensional superconducting resonators at $T<20$ mK with the photon lifetime up to $\tau =2$ seconds
• Fast Universal Control of an Oscillator with Weak Dispersive Coupling to a Qubit
• Optimizing Variational Quantum Algorithms using Pontryagin's Minimum Principle
• Resource-efficient digital quantum simulation of $d$-level systems for photonic, vibrational, and spin-$s$ Hamiltonians
• Asymptotically Optimal Quantum Circuits for d-level Systems
• Compiling quantum circuits to realistic hardware architectures using temporal planners
• Experimental Deep Reinforcement Learning for Error-Robust Gateset Design on a Superconducting Quantum Computer
• Quantum control of bosonic modes with superconducting circuits
• From pulses to circuits and back again: A quantum optimal control perspective on variational quantum algorithms
• Maximizing the Hilbert space for a finite number of distinguishable quantum states
• A volumetric framework for quantum computer benchmarks
• Quantum-optimal-control-inspired ansatz for variational quantum algorithms
• Efficient encoding of the weighted MAX k-CUT on a quantum computer using QAOA
• Prospects for Simulating a Qudit Based Model of (1+1)d Scalar QED
• Steering random spin systems to speed up the quantum adiabatic algorithm
• Intrinsic mechanisms for drive-dependent Purcell decay in superconducting quantum circuits
• The Snake Optimizer for Learning Quantum Processor Control Parameters
• Quantum computing hardware for HEP algorithms and sensing
• Impacts of Noise and Structure on Quantum Information Encoded in a Quantum Memory
• Discrete Adjoints for Accurate Numerical Optimization with Application to Quantum Control
• Optimal Control of Closed Quantum Systems via B-Splines with Carrier Waves
• Noise Improvements in Quantum Simulations of sQED using Qutrits
• Effective spin models of Kerr-nonlinear parametric oscillators for quantum annealing
• Quantum annealing in spin-boson model: from a perturbative to a ultrastrong mediated coupling
• Unraveling the origin of higher success probabilities in quantum versus semi-classical annealing
• Neural network accelerator for quantum control
• Efficient cavity control with SNAP gates

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• Dynamics of qudit gates and effects of spectator modes on optimal control pulses
• Performance evaluation of variational quantum eigensolver and quantum dynamics algorithms on the advection-diffusion equation