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Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is…
We introduce a novel quantum optimization paradigm: the Fixed-Parameter-Count Quantum Approximate Optimization Algorithm (FPC-QAOA). It is a scalable variational framework that maintains a constant number of trainable parameters regardless…
Optimization problems are critical across various domains, yet existing quantum algorithms, despite their great potential, struggle with scalability and accuracy due to excessive reliance on entanglement. To address these limitations, we…
Here we explore which heuristic quantum algorithms for combinatorial optimization might be most practical to try out on a small fault-tolerant quantum computer. We compile circuits for several variants of quantum accelerated simulated…
A pivotal task for quantum computing is to speed up solving problems that are both classically intractable and practically valuable. Among these, combinatorial optimization problems have attracted tremendous attention due to their broad…
Classical optimization problems can be solved by adiabatically preparing the ground state of a quantum Hamiltonian that encodes the problem. The performance of this approach is determined by the smallest gap encountered during the…
The ability to efficiently prepare ground states of quantum Hamiltonians via adiabatic protocols is typically limited by the smallest energy gap encountered during the quantum evolution. This presents a key obstacle for quantum simulation…
We determine the complexity of several constraint satisfaction problems using the quantum adiabatic algorithm in its simplest implementation. We do so by studying the size dependence of the gap to the first excited state of "typical"…
The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. However, the potential of QAOA to tackle classically intractable problems remains unclear. Here,…
Computing using a continuous-time evolution, based on the natural interaction Hamiltonian of the quantum computer hardware, is a promising route to building useful quantum computers in the near-term. Adiabatic quantum computing, quantum…
A major challenge in quantum computing is to solve general problems with limited physical hardware. Here, we implement digitized adiabatic quantum computing, combining the generality of the adiabatic algorithm with the universality of the…
Quantum annealing is a promising algorithm for solving combinatorial optimization problems. It searches for the ground state of the Ising model, which corresponds to the optimal solution of a given combinatorial optimization problem. The…
Local quantum annealing (LQA), an iterative algorithm, is designed to solve combinatorial optimization problems. It draws inspiration from QA, which utilizes adiabatic time evolution to determine the global minimum of a given objective…
We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat…
Variational quantum circuits build the foundation for various classes of quantum algorithms. In a nutshell, the weights of a parametrized quantum circuit are varied until the empirical sampling distribution of the circuit is sufficiently…
In recent years, Variational Quantum Algorithms (VQAs) have emerged as a promising approach for solving optimization problems on quantum computers in the NISQ era. However, one limitation of VQAs is their reliance on fixed-structure…
The real-time simulation of large many-body quantum systems is a formidable task, that may only be achievable with a genuine quantum computational platform. Currently, quantum hardware with a number of qubits sufficient to make classical…
We introduce a simple framework for estimating lower bounds on the runtime of a broad class of adiabatic quantum algorithms. The central formula consists of calculating the variance of the final Hamiltonian with respect to the initial…
Quantum annealers provide an effective framework for solving large-scale combinatorial optimization problems. This work presents a novel methodology for training Variational Quantum Algorithms (VQAs) by reformulating the parameter…
Optimal parameter setting for applications problems embedded into hardware graphs is key to practical quantum annealers (QA). Embedding chains typically crop up as harmful Griffiths phases, but can be used as a resource as we show here: to…