Limitations of optimization algorithms on noisy quantum devices

Abstract

Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is whether their noise can be overcome or it fundamentally restricts any potential quantum advantage. We present a transparent way of comparing classical algorithms to quantum ones running on near-term quantum devices for a large family of problems that include optimization problems and approximations to the ground state energy of Hamiltonians. Our approach is based on the combination of entropic inequalities that determine how fast the quantum computation state converges to the fixed point of the noise model, together with established classical methods of Gibbs state sampling. The approach is extremely versatile and allows for its application to a large variety of problems, noise models and quantum computing architectures. We use our result to provide estimates for a variety of problems and architectures that have been the focus of recent experiments, such as quantum annealers, variational quantum eigensolvers, and quantum approximate optimization. The bounds we obtain indicate that substantial quantum advantages are unlikely for classical optimization unless the current noise rates are decreased by orders of magnitude or the topology of the problem matches that of the device. This is the case even if the number of qubits increases substantially. We reach similar but less stringent conclusions for quantum Hamiltonian problems.

arXiv comment19 pages, 3 figures

References in corpus (33)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• A variational eigenvalue solver on a quantum processor
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Ising formulations of many NP problems
• Adiabatic Quantum Computing
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Quantum optimization using variational algorithms on near-term quantum devices
• Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model
• Variational ansatz-based quantum simulation of imaginary time evolution
• Quantum Approximate Optimization of Non-Planar Graph Problems on a Planar Superconducting Processor
• Variational quantum algorithms for discovering Hamiltonian spectra
• Minimally entangled typical quantum states at finite temperature
• Accelerated Variational Quantum Eigensolver
• Variational Quantum State Diagonalization
• Achieving quantum supremacy with sparse and noisy commuting quantum computations
• Numerical Linked-Cluster Approach to Quantum Lattice Models
• Decoherence in adiabatic quantum computation
• Optimized simulated annealing for Ising spin glasses
• Approximating Gibbs states of local Hamiltonians efficiently with PEPS
• Quantum logarithmic Sobolev inequalities and rapid mixing
• Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithms
• A Short Introduction to Numerical Linked-Cluster Expansions
• Scalable Semidefinite Programming
• Clustering of conditional mutual information for quantum Gibbs states above a threshold temperature
• Relative Entropy Convergence for Depolarizing Channels
• Classical algorithms, correlation decay, and complex zeros of partition functions of quantum many-body systems
• On the modified logarithmic Sobolev inequality for the heat-bath dynamics for 1D systems
• Online Learning of Quantum States
• Efficient online quantum state estimation using a matrix-exponentiated gradient method
• Robust entanglement renormalization on a noisy quantum computer
• Quantum Subdivision Capacities and Continuous-time Quantum Coding
• Upper bounds on fault tolerance thresholds of noisy Clifford-based quantum computers

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