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 $\pm XX$-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 $XX$-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.
Highlights
Quantum annealing exploits quantum-mechanical fluctuations to solve combinatorial optimization problems [1,2,3,4,5,6,7,8]
In a typical formulation, the combinatorial optimization problem one wants to solve is expressed as an Ising model, represented in terms of the z components of the Pauli matrices, and quantum fluctuations are introduced as a transverse field, the sum of the x components of the Pauli matrices over all sites
We study the effects of nonstoquastic X X catalysts on the phase transition of the frustrated Ising ladder, and the stoquastic case is treated for completeness
Summary
Quantum annealing exploits quantum-mechanical fluctuations to solve combinatorial optimization problems [1,2,3,4,5,6,7,8]. On another aspect, namely, that a certain set of nonstoquastic catalysts of the X X type is known to reduce the order of quantum phase transitions from first to second [16,17,19,21,22,23] This means that adiabatic evolution converges to the ground state of the final Hamiltonian in quantum annealing with an exponential speedup relative to the stoquastic case. It does not guarantee a quantum speedup relative to classical solution methods, and in addition examples are known where X X -type nonstoquastic catalysts do not lead to performance improvements [20,23,25,26]. This section describes the definition of the model and its basic properties in the case without X X interactions, and is largely a recapitulation of Ref. [11]
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