相关论文: A sharp interaction-degree threshold for simulatin…

We consider the power of local algorithms for approximately solving Max $k$XOR, a generalization of two constraint satisfaction problems previously studied with classical and quantum algorithms (MaxCut and Max E3LIN2). In Max $k$XOR each…

We propose and study Th-QAOA (pronounced Threshold QAOA), a variation of the Quantum Alternating Operator Ansatz (QAOA) that replaces the standard phase separator operator, which encodes the objective function, with a threshold function…

We study numerical integration on $[0,1]$ by quantum amplitude estimation (QAE), focusing on the cost of constructing the amplitude oracle. Although QAE improves the statistical component of the integration error, this advantage is relevant…

We generalize Farhi et al.'s 0.6924-approximation result technique of the Max-Cut Quantum Approximate Optimization Algorithm (QAOA) on 3-regular graphs to obtain provable lower bounds on the approximation ratio for warm-started QAOA. Given…

The Quantum Approximate Optimization Algorithm (QAOA) is widely studied for combinatorial optimization and has achieved significant advances both in theoretical guarantees and practical performance, yet for general combinatorial…

The Quantum Approximate Optimization Algorithm, QAOA, uses a shallow depth quantum circuit to produce a parameter dependent state. For a given combinatorial optimization problem instance, the quantum expectation of the associated cost…

We study the classical simulatability of commuting quantum circuits with n input qubits and O(log n) output qubits, where a quantum circuit is classically simulatable if its output probability distribution can be sampled up to an…

The classical simulation of quantum circuits is of central importance for benchmarking near-term quantum devices. The fact that gates belonging to the Clifford group can be simulated efficiently on classical computers has motivated a range…

We prove a new version of the quantum threshold theorem that applies to concatenation of a quantum code that corrects only one error, and we use this theorem to derive a rigorous lower bound on the quantum accuracy threshold epsilon_0. Our…

The binary paint shop problem (BPSP) is an APX-hard optimization problem of the automotive industry. In this work, we show how to use the Quantum Approximate Optimization Algorithm (QAOA) to find solutions of the BPSP and demonstrate that…

The problem of learning threshold functions is a fundamental one in machine learning. Classical learning theory implies sample complexity of $O(\xi^{-1} \log(1/\beta))$ (for generalization error $\xi$ with confidence $1-\beta$). The private…

The quantum approximate optimization algorithm (QAOA) promises to solve classically intractable computational problems in the area of combinatorial optimization. A growing amount of evidence suggests that the originally proposed form of the…

We introduce the Constraint-Enhanced Quantum Approximate Optimization Algorithm (CE-QAOA), a shallow, constraint-aware ansatz that operates inside the one-hot product space [n]^m, where m is the number of blocks and each block is…

Understanding the benefits of quantum computing for solving combinatorial optimization problems (COPs) remains an open research question. In this work, we extend and analyze algorithms that solve COPs by recursively shrinking them. The…

The quantum approximate optimization algorithm (QAOA) has become a cornerstone of contemporary quantum applications development. Here we show that the \emph{density} of problem constraints versus problem variables acts as a performance…

Quantum Simulation-based Optimization (QuSO) is a recently proposed class of optimization problems that entails industrially relevant problems characterized by cost functions or constraints that depend on summary statistic information about…

We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…

Quantum computing may provide advantage in solving classical optimization problems. One promising algorithm is the quantum approximate optimization algorithm (QAOA). There have been many proposals for improving this algorithm, such as using…

The Quantum Approximate Optimisation Algorithm is a $p$ layer, time-variable split operator method executed on a quantum processor and driven to convergence by classical outer loop optimisation. The classical co-processor varies individual…

While the ultimate goal of solving computationally intractable problems is to find a provably optimal solutions, practical constraints of real-world scenarios often necessitate focusing on efficiently obtaining high-quality, near-optimal…