Related papers: From Constraint to Code: DQI-Kit -- A Software Fra…
Decoded Quantum Interferometry (DQI) is a recently introduced quantum algorithm that reduces discrete optimization to decoding with potential advantages over the best-known polynomial-time classical algorithms for certain Max-LINSAT…
A recent paper by Jordan et al. introduced Decoded Quantum Interferometry (DQI), a novel quantum algorithm that uses the quantum Fourier transform to reduce linear optimization problems -- max-XORSAT and max-LINSAT -- to decoding problems.…
Attaining a quantum speedup in solving practically useful optimization problems has been one of the holy grails in the field of quantum computing. While prior approaches have demonstrated speedups for certain structured problem classes,…
Achieving superpolynomial speedups for optimization has long been a central goal for quantum algorithms. Here we introduce Decoded Quantum Interferometry (DQI), a quantum algorithm that uses the quantum Fourier transform to reduce…
Decoded Quantum Interferometry (DQI) is a framework for approximating special kinds of discrete optimization problems that relies on problem structure in a way that sets it apart from other classical or quantum approaches. We show that the…
Decoded Quantum Interferometry (DQI) is a recently proposed quantum optimization algorithm that exploits sparsity in the Fourier spectrum of objective functions, with the potential for exponential speedups over classical algorithms on…
Decoded Quantum Interferometry (DQI) is a recently proposed quantum algorithm for approximating solutions to combinatorial optimization problems by reducing instances of linear satisfiability to bounded-distance decoding over superpositions…
Optimization via decoded quantum interferometry (DQI) has recently gained a great deal of attention as a promising avenue for solving optimization problems using quantum computers. In this paper, we apply DQI to an industrial optimization…
We study the complexity of Decoded Quantum Interferometry (DQI), a quantum algorithm for approximate optimization. First, we show that the algorithm resists classical simulation strategies based on locating outputs with large probabilities.…
Recently, Jordan et al. (Nature, 2025) introduced a novel quantum-algorithmic technique called Decoded Quantum Interferometry (DQI) for solving specific combinatorial optimization problems associated with classical codes. They presented a…
Decoded Quantum Interferometry (DQI) promises superpolynomial speedups for structured optimization; however, its practical realization is often hindered by significant sensitivity to hardware noise and spectral dispersion. To bridge this…
Decoded Quantum Interferometry (DQI) provides a framework for superpolynomial quantum speedups by reducing certain optimization problems to reversible decoding tasks. We apply DQI to the Optimal Polynomial Intersection (OPI) problem, whose…
We develop a new benchmarking scheme for the Decoded Quantum Interferometry (DQI) algorithm quantifying the number of quantum gates required to obtain an optimal solution to a problem amenable to DQI. We apply the benchmarking scheme to the…
Decoded Quantum Interferometry (DQI) defines a duality that pairs decoding problems with optimization problems. The original work on DQI considered Reed-Solomon decoding, whose dual optimization problem, called Optimal Polynomial…
We study the performance of Decoded Quantum Interferometry (DQI) on typical instances of MAX-$k$-XOR-SAT when the transpose of the constraint matrix is drawn from a standard ensemble of LDPC parity check matrices. We prove that if the…
Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing…
The Optimal Polynomial Intersection (OPI) problem is the following: Given sets $S_1, \ldots, S_m \subseteq \mathbb{F}$ and evaluation points $a_1, \ldots, a_m \in \mathbb{F}$, find a polynomial $Q \in \mathbb{F}[x]$ of degree less than $n$…
Quantum computing holds great promise for surpassing the limits of classical devices in many fields. Despite impressive developments, however, current research is primarily focused on qubits. At the same time, quantum hardware based on…
Although quantum computing holds promise for solving Combinatorial Optimization Problems (COPs), the limited qubit capacity of NISQ hardware makes large-scale instances intractable. Conventional methods attempt to bridge this gap through…
The deployment of deep neural networks on resource-constrained devices relies on quantization. While static, uniform quantization applies a fixed bit-width to all inputs, it fails to adapt to their varying complexity. Dynamic,…