Related papers: Analysis of the Relation between Quadratic Unconst…
Encoding combinatorial optimization problems into physically meaningful Hamiltonians with tractable energy landscapes forms the foundation of quantum optimization. Numerous works have studied such efficient encodings for the class of…
We show through numerical simulation that the Quantum Approximate Optimization Algorithm (QAOA) for higher-order, random-coefficient, heavy-hex compatible spin glass Ising models has strong parameter concentration across problem sizes from…
Non-commutative polynomial optimization (NPO) problems seek to minimize the state average of a polynomial of some operator variables, subject to polynomial constraints, over all states and operators, as well as the Hilbert spaces where…
The LogQ algorithm encodes Quadratic Unconstrained Binary Optimization (QUBO) problems with exponentially fewer qubits than the Quantum Approximate Optimization Algorithm (QAOA). The advantages of conventional LogQ are accompanied by a…
A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs).…
In the era of quantum computing, the emergence of quantum computers and subsequent advancements have led to the development of various quantum algorithms capable of solving linear equations and eigenvalues, surpassing the pace of classical…
Constraints make hard optimization problems even harder to solve on quantum devices because they are implemented with large energy penalties and additional qubit overhead. The parity mapping, which has been introduced as an alternative to…
Combinatorial optimization problems are one of the target applications of current quantum technology, mainly because of their industrial relevance, the difficulty of solving large instances of them classically, and their equivalence to…
In this paper, we present a brief review and introduction to Quadratic Unconstrained D-ary Optimization (QUDO), Tensor Quadratic Unconstrained D-ary Optimization (T-QUDO) and Higher-Order Unconstrained Binary Optimization (HOBO)…
Diagnosing the minimal set of faults capable of explaining a set of given observations, e.g., from sensor readouts, is a hard combinatorial optimization problem usually tackled with artificial intelligence techniques. We present the mapping…
Quantum Approximate Optimization Algorithm (QAOA) can be used to solve quadratic unconstrained binary optimization (QUBO) problems. However, the size of the solvable problem is limited by the number of qubits. To leverage noisy…
We discuss the computational complexity of random 2D Ising spin glasses, which represent an interesting class of constraint satisfaction problems for black box optimization. Two extremal cases are considered: (1) the +/- J spin glass, and…
Quadratic unconstrained binary optimization (QUBO) tasks are very important in chemistry, finance, job scheduling, and so on, which can be represented using graph structures, with the variables as nodes and the interaction between them as…
The Quantum Approximate Optimization Algorithm (QAOA) and its derived variants are widely in use for approximating combinatorial optimization problem instances on gate-based Noisy Intermediate Scale Quantum (NISQ) computers. Commonly,…
We present benchmarks of the parity transformation for the Quantum Approximate Optimization Algorithm (QAOA). We analyse the gate resources required to implement a single QAOA cycle for real-world scenarios. In particular, we consider…
Combinatorial optimization problems are central to both practical applications and the development of optimization methods. While classical and quantum algorithms have been refined over decades, machine learning--assisted approaches are…
Quantum computers show potential for achieving computational advantage over classical computers, with many candidate applications in combinatorial optimisation. We present an application level benchmarking framework for near-term quantum…
This paper introduces the use of tailored variational forms for variational quantum eigensolver that have properties of representing certain constraints on the search domain of a linear constrained quadratic binary optimization problem…
To run an algorithm on a quantum computer, one must choose an assignment from logical qubits in a circuit to physical qubits on quantum hardware. This task of initial qubit placement, or qubit allocation, is especially important on…
This article describes how to solve Sudoku puzzles using Quadratic Unconstrained Binary Optimization (QUBO). To this end, a QUBO instance with 729 variables is constructed, encoding a Sudoku grid with all constraints in place, which is then…