Role of Non-stoquastic Catalysts in Quantum Adiabatic Optimization

Abstract

The viability of non-stoquastic catalyst Hamiltonians to deliver consistent quantum speedups in quantum adiabatic optimization remains an open question. The infinite-range ferromagnetic $p$-spin model is a rare example exhibiting an exponential advantage for non-stoquastic catalysts over its stoquastic counterpart. We revisit this model and note how the incremental changes in the ground state wavefunction give an indication of how the non-stoquastic catalyst provides an advantage. We then construct two new examples that exhibit an advantage for non-stoquastic catalysts over stoquastic catalysts. The first is another infinite range model that is only 2-local but also exhibits an exponential advantage, and the second is a geometrically local Ising example that exhibits a growing advantage up to the maximum system size we study.

v1: 8 pages, 10 figures. v2. Expanded presentation, including a new example. 12 pages, 20 figures. v3: Updated to published version

References in corpus (18)

• Bounds for the adiabatic approximation with applications to quantum computation
• Decoherence in adiabatic quantum computation
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
• Quantum annealing with antiferromagnetic fluctuations
• Noise resistance of adiabatic quantum computation using random matrix theory
• Decoherence in a scalable adiabatic quantum computer
• Exponential Enhancement of the Efficiency of Quantum Annealing by Non-Stochastic Hamiltonians
• Many-body transverse interactions in the quantum annealing of the p-spin ferromagnet
• Quantum Adiabatic Evolution Algorithms with Different Paths
• An Elementary Proof of the Quantum Adiabatic Theorem
• Adiabatic Markovian Dynamics
• Analog Errors in Ising Machines
• The quantum adiabatic search with decoherence in the instantaneous energy eigenbasis
• Adiabatic optimization versus diffusion Monte Carlo
• The adiabatic theorem in the presence of noise
• Quantum Speed-Up at Zero Temperature via Coherent Catalysis
• Decoherence induced deformation of the ground state in adiabatic quantum computation
• Total suppression of a large spin tunneling barrier in quantum adiabatic computation

Cited by in corpus (39)

• Perspectives of quantum annealing: Methods and implementations
• Differentiable Quantum Architecture Search
• Prospects for Quantum Enhancement with Diabatic Quantum Annealing
• Quantum annealing with longitudinal bias fields
• Digitized Adiabatic Quantum Factorization
• Variationally Scheduled Quantum Simulation
• De-Signing Hamiltonians for Quantum Adiabatic Optimization
• Effective Hamiltonians for interacting superconducting qubits -- local basis reduction and the Schrieffer-Wolff transformation
• Circumventing superexponential runtimes for hard instances of quantum adiabatic optimization
• Standard quantum annealing outperforms adiabatic reverse annealing with decoherence
• The Effects of the Problem Hamiltonian Parameters on the Minimum Spectral Gap in Adiabatic Quantum Optimization
• A Quantum N-Queens Solver
• Speedup of the Quantum Adiabatic Algorithm using Delocalization Catalysis
• Permutation Matrix Representation Quantum Monte Carlo
• Mean-Field Solution of the Weak-Strong Cluster Problem for Quantum Annealing with Stoquastic and Non-Stoquastic Catalysts
• Diagonal Catalysts in Quantum Adiabatic Optimization
• Deep learning optimal quantum annealing schedules for random Ising models
• Superconducting qubit circuit emulation of a vector spin-1/2
• Symmetry-Protected Quantum Adiabatic Evolution in Spontaneous Symmetry-Breaking Transitions
• Effective spin models of Kerr-nonlinear parametric oscillators for quantum annealing
• Quantum annealing with twisted fields
• Stoquasticity in circuit QED
• Phase transitions in the frustrated Ising ladder with stoquastic and nonstoquastic catalysts
• Bounding first-order quantum phase transitions in adiabatic quantum computing
• The quantum annealing gap and quench dynamics in the exact cover problem
• Improving nonstoquastic quantum annealing with spin-reversal transformations
• Quantum annealing sampling with a bias field
• Nonstoquastic catalyst for bifurcation-based quantum annealing of ferromagnetic $p$-spin model
• Investigating the potential for a limited quantum speedup on protein lattice problems
• Quantum Annealing with chaotic driver Hamiltonians
• Validating a Two Qubit Non-Stoquastic Hamiltonian in Quantum Annealing
• Fighting Exponentially Small Gaps by Counterdiabatic Driving
• Ultrastrong capacitive coupling of flux qubits
• Effect of Quantum Statistics on Computational Power of Atomic Quantum Annealers
• Analog Errors in Quantum Annealing: Doom and Hope
• Convergence condition of simulated quantum annealing with a non-stoquastic catalyst
• Proof of avoidability of the quantum first-order transition in transverse magnetization in quantum annealing of finite-dimensional spin glasses
• Essentiality of the Non-stoquastic Hamiltonians and Driver Graph Design in Quantum Optimization Annealing
• Three-Josephson Junctions Flux Qubit Couplings