Phase transitions in the frustrated Ising ladder with stoquastic and nonstoquastic catalysts
arXiv:2012.07144 · doi:10.1103/PhysRevResearch.3.043013
Abstract
The role of nonstoquasticity in the field of quantum annealing and adiabatic quantum computing is an actively debated topic. We study a strongly-frustrated quasi-one-dimensional quantum Ising model on a two-leg ladder to elucidate how a first-order phase transition with a topological origin is affected by interactions of the -type. Such interactions are sometimes known as stoquastic (negative sign) and nonstoquastic (positive sign) "catalysts". Carrying out a symmetry-preserving real-space renormalization group analysis and extensive density-matrix renormalization group computations, we show that the phase diagrams obtained by these two methods are in qualitative agreement with each other and reveal that the first-order quantum phase transition of a topological nature remains stable against the introduction of both -type catalysts. This is the first study of the effects of nonstoquasticity on a first-order phase transition between topologically distinct phases. Our results indicate that nonstoquastic catalysts are generally insufficient for removing topological obstacles in quantum annealing and adiabatic quantum computing.
arXiv comment31 pages, 16 figures. v2: plots added in Fig. 4, Fig. 5 added, references updated, and minor revisions
References in corpus (45)
- The density-matrix renormalization group
- Quantum Annealing in the Transverse Ising Model
- A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
- Adiabatic Quantum Computing
- Theory of Quantum Annealing of an Ising Spin Glass
- Perspectives of quantum annealing: Methods and implementations
- Mathematical Foundation of Quantum Annealing
- Bounds for the adiabatic approximation with applications to quantum computation
- Entanglement-assisted local manipulation of pure quantum states
- New Trends in Density Matrix Renormalization
- Observation of topological phenomena in a programmable lattice of 1,800 qubits
- Reverse Quantum Annealing Approach to Portfolio Optimization Problems
- Simple proof of equivalence between adiabatic quantum computation and the circuit model
- Realizable Hamiltonians for Universal Adiabatic Quantum Computers
- Application of Quantum Annealing to Nurse Scheduling Problem
- Prospects for Quantum Enhancement with Diabatic Quantum Annealing
- Quantum annealing with antiferromagnetic fluctuations
- Power of Pausing: Advancing Understanding of Thermalization in Experimental Quantum Annealers
- Reverse annealing for the fully connected -spin model
- Modernizing Quantum Annealing using Local Searches
- Nonstoquastic Hamiltonians and Quantum Annealing of an Ising Spin Glass
- Quantum renormalization group of XYZ model in a transverse magnetic field
- Exponential Enhancement of the Efficiency of Quantum Annealing by Non-Stochastic Hamiltonians
- Exponential Speedup of Quantum Annealing by Inhomogeneous Driving of the Transverse Field
- Dynamics of reverse annealing for the fully-connected -spin model
- The quantum adiabatic algorithm and scaling of gaps at first order quantum phase transitions
- Many-body transverse interactions in the quantum annealing of the p-spin ferromagnet
- Does Adiabatic Quantum Optimization Truly Fail for NP-complete problems?
- Reverse quantum annealing of the -spin model with relaxation
- Quantum annealing of the -spin model under inhomogeneous transverse field driving
- Phase diagram of the anti-ferromagnetic xxz model in the presence of an external magnetic field
- On the Computational Complexity of Curing the Sign Problem
- Role of Non-stoquastic Catalysts in Quantum Adiabatic Optimization
- Improving quantum annealing of the ferromagnetic -spin model through pausing
- Universal adiabatic quantum computation via the space-time circuit-to-Hamiltonian construction
- QMA-complete problems for stoquastic Hamiltonians and Markov matrices
- Algorithmic approach to adiabatic quantum optimization
- Why and when is pausing beneficial in quantum annealing?
- Mean field analysis of reverse annealing for code-division multiple-access multiuser detection
- Variationally Scheduled Quantum Simulation
- Energy gap at first-order quantum phase transitions: An anomalous case
- De-Signing Hamiltonians for Quantum Adiabatic Optimization
- Experimental and Theoretical Study of Thermodynamic Effects in a Quantum Annealer
- Engineering non-equilibrium quantum phase transitions via causally gapped Hamiltonians
- Mean-Field Solution of the Weak-Strong Cluster Problem for Quantum Annealing with Stoquastic and Non-Stoquastic Catalysts