Related papers: Quantum independent set problem and non-abelian ad…
Existing quantum algorithms for quantum chemistry work well near the equilibrium geometry of molecules, but the results can become unstable when the chemical bonds are broken at large atomic distances. For any adiabatic approach, this…
Using a quantum processor to embed and process classical data enables the generation of correlations between variables that are inefficient to represent through classical computation. A fundamental question is whether these correlations…
The graph isomorphism problem remains a fundamental challenge in computer science, driving the search for efficient decision algorithms. Due to its ambiguous computational complexity, heuristic approaches such as simulated annealing are…
Quantum computing employs controllable interactions to perform sequences of logical gates and entire algorithms on quantum registers. This paradigm has been widely explored, e.g., for simulating dynamics of manybody systems by decomposing…
A finite discrete graph is turned into a quantum (metric) graph once a finite length is assigned to each edge and the one-dimensional Laplacian is taken to be the operator. We study the dependence of the spectral gap (the first positive…
Recent experiments have successfully realized multi-band non-Abelian topological insulators with parity-time symmetry. Their topological classification transcends the conventional ten-fold classification, necessitating the use of…
Adiabatic quantum programming defines the time-dependent mapping of a quantum algorithm into an underlying hardware or logical fabric. An essential step is embedding problem-specific information into the quantum logical fabric. We present…
Quantum-classical hybrid algorithms offer a promising strategy for tackling computationally challenging problems, such as the maximum independent set (MIS) problem that plays a crucial role in areas like network design and data analysis.…
We construct models of exactly solvable two-particle quantum graphs with certain non-local two-particle interactions, establishing appropriate boundary conditions via suitable self-adjoint realisations of the two-particle Laplacian. Showing…
We develop a unified quantum geometric framework to understand reactive quantum dynamics. The critical roles of the quantum geometry of adiabatic electronic states in both adiabatic and non-adiabatic quantum dynamics are unveiled. A…
We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of…
In the continuum limit (large number of qubits), adiabatic quantum algorithms display a remarkable similarity to sweeps through quantum phase transitions. We find that transitions of second or higher order are advantageous in comparison to…
In this paper we consider the problem of testing whether two finite groups are isomorphic. Whereas the case where both groups are abelian is well understood and can be solved efficiently, very little is known about the complexity of…
We propose a new adiabatic algorithm for the unsorted database search problem. This algorithm saves two thirds of qubits than Grover's algorithm in realizations. Meanwhile, we analyze the time complexity of the algorithm by both…
Understanding how non-adiabatic terms affect quantum dynamics is fundamental to improving various protocols for quantum technologies. We present a novel approach to computing the Adiabatic Gauge Potential (AGP), which gives information on…
We introduce a novel quantum algorithm for determining graph connectedness using a constant number of measurements. The algorithm can be extended to find connected components with a linear number of measurements. It relies on non-unitary…
We study the problem of estimating the number of edges in an unknown graph. We consider a hybrid model in which an algorithm may issue independent set, degree, and neighbor queries. We show that this model admits strictly more efficient…
Quantum information processing is likely to have far-reaching impact in the field of artificial intelligence. While the race to build an error-corrected quantum computer is ongoing, noisy, intermediate-scale quantum (NISQ) devices provide…
Neutral atom arrays have emerged as a versatile platform towards scalable quantum computation and optimization. In this paper we present demonstrations of solving maximum weighted independent set problems on a Rydberg atom array using…
We introduce a class of quantum adiabatic evolutions that we claim may be interpreted as the equivalents of the unitary gates of the quantum gate model. We argue that these gates form a universal set and may therefore be used as building…