Perils of Embedding for Quantum Sampling

Abstract

Given quantum hardware that enables sampling from a family of natively implemented Hamiltonians, how well can one use that hardware to sample from a Hamiltonian outside that family? A common approach is to minor embed the desired Hamiltonian in a native Hamiltonian. In Phys. Rev. Research 2, 023020 (2020) it was shown that minor embedding can be detrimental for classical thermal sampling. Here, we generalize these results by considering quantum thermal sampling in the transverse-field Ising model, i.e. sampling a Hamiltonian with non-zero off diagonal terms. To study these systems numerically we introduce a modification to standard cluster update quantum Monte-Carlo (QMC) techniques, which allows us to much more efficiently obtain thermal samples of an embedded Hamiltonian, enabling us to simulate systems of much larger sizes and larger transverse-field strengths than would otherwise be possible. Our numerics focus on models that can be implemented on current quantum devices using planar two-dimensional lattices, which exhibit finite-temperature quantum phase transitions. Our results include: i) An estimate on the probability to sample the logical subspace directly as a function of transverse-field, temperature, and total system size, which agrees with QMC simulations. ii) We show that typically measured observables (diagonal energy and magnetization) are biased by the embedding process, in the regime of intermediate transverse field strength, meaning that the extracted values are not the same as in the native model. iii) By considering individual embedding realizations akin to 'realizations of disorder', we provide numerical evidence suggesting that as the embedding size is increased, the critical point shifts to increasingly large values of the transverse-field.

arXiv comment11+5 pages, 16 Figures. V2: updated to published version, including new results by averaging over embedding realizations

References in corpus (29)

• Quantum Annealing in the Transverse Ising Model
• Error mitigation for short-depth quantum circuits
• Quantum annealing with more than one hundred qubits
• Efficient variational quantum simulator incorporating active error minimisation
• A blueprint for demonstrating quantum supremacy with superconducting qubits
• Quantum Boltzmann Machine
• Observation of topological phenomena in a programmable lattice of 1,800 qubits
• Estimation of effective temperatures in quantum annealers for sampling applications: A case study with possible applications in deep learning
• Application of Quantum Annealing to Training of Deep Neural Networks
• Quantum Variational Autoencoder
• Scaling advantage in quantum simulation of geometrically frustrated magnets
• Probing quantum information propagation with out-of-time-ordered correlators
• Quantum-Assisted Learning of Hardware-Embedded Probabilistic Graphical Models
• Digital-Analog Quantum Computation
• Estimating errors reliably in Monte Carlo simulations of the Ehrenfest model
• Non-ergodic delocalized states for efficient population transfer within a narrow band of the energy landscape
• Simulating the Shastry-Sutherland Ising Model using Quantum Annealing
• Quantum annealing correction at finite temperature: ferromagnetic $p$-spin models
• Emulating the one-dimensional Fermi-Hubbard model by a double chain of qubits
• Mean Field Analysis of Quantum Annealing Correction
• Path integral Monte Carlo ground state approach: Formalism, implementation, and applications
• Improved Boltzmann machines with error corrected quantum annealing
• Quantum-assisted associative adversarial network: Applying quantum annealing in deep learning
• Griffiths-McCoy singularity on the diluted Chimera graph: Monte Carlo simulations and experiments on the quantum hardware
• Nested Quantum Annealing Correction at Finite Temperature: $p$-spin models
• Testing a quantum annealer as a quantum thermal sampler
• Perils of Embedding for Sampling Problems
• Can quantum Monte Carlo simulate quantum annealing?
• Restricted Boltzmann Machines for galaxy morphology classification with a quantum annealer

Cited by in corpus (4)

• Solving Larger Maximum Clique Problems Using Parallel Quantum Annealing
• Comparing Three Generations of D-Wave Quantum Annealers for Minor Embedded Combinatorial Optimization Problems
• Advantage of pausing: parameter setting for quantum annealers
• Mapping State Transition Susceptibility in Quantum Annealing