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We propose a modification to Nielsen's circuit complexity for Hamiltonian simulation using the Suzuki-Trotter (ST) method, which provides a network like structure for the quantum circuit. This leads to an optimized gate counting linear in…
Simulating real-time dynamics under a Hamiltonian is a central goal of quantum information science. While numerous Hamiltonian-simulation quantum algorithms have been proposed, the effects of physical noise have rarely been incorporated…
In analogy of classical Kolmogorov complexity we develop a theory of the algorithmic information in bits contained in any one of continuously many pure quantum states: quantum Kolmogorov complexity. Classical Kolmogorov complexity coincides…
The quantum approximate optimization algorithm (QAOA) is a promising method for solving certain classical combinatorial optimization problems on near-term quantum devices. When employing the QAOA to 3-SAT and Max-3-SAT problems, the quantum…
The formula-evaluation problem is defined recursively. A formula's evaluation is the evaluation of a gate, the inputs of which are themselves independent formulas. Despite this pure recursive structure, the problem is combinatorially…
The Boolean constraint satisfaction problem 3-SAT is arguably the canonical NP-complete problem. In contrast, 2-SAT can not only be decided in polynomial time, but in fact in deterministic linear time. In 2006, Bravyi proposed a physically…
In earlier work, we developed an approach for automatic complexity analysis of integer programs, based on an alternating modular inference of upper runtime and size bounds for program parts. In this paper, we show how recent techniques to…
Recent studies have shown that there is a strong interplay between quantum complexity and quantum chaos. In this work, we consider a new method to study geometric complexity for interacting non-Gaussian quantum mechanical systems to…
We investigate the limitations of quantum computers for solving nonlinear dynamical systems. In particular, we tighten the worst-case bounds of the quantum Carleman linearisation (QCL) algorithm [Liu et al., PNAS 118, 2021] answering one of…
Quantum circuit synthesis is the task of decomposing a given quantum operator into a sequence of elementary quantum gates. Since the finite target gate set cannot exactly implement any given operator, approximation is often necessary. Model…
Parity-SAT is the problem of determining whether a given CNF formula has an odd number of satisfying assignments. As a canonical $\oplus$P-complete problem, it represents a fundamental variant of the exact model counting problem (#SAT).…
Quantum simulation has emerged as a key application of quantum computing, with significant progress made in algorithms for simulating both closed and open quantum systems. The simulation of open quantum systems, particularly those governed…
Many computational problems are subject to a quantum speed-up: one might find that a problem having an O(n^3)-time or O(n^2)-time classic algorithm can be solved by a known O(n^1.5)-time or O(n)-time quantum algorithm. The question…
The Boolean satisfiability (SAT) problem lies at the core of many applications in combinatorial optimization, software verification, cryptography, and machine learning. While state-of-the-art solvers have demonstrated high efficiency in…
We propose to use local search algorithms to produce SAT instances which are harder to solve than randomly generated k-CNF formulae. The first results, obtained with rudimentary search algorithms, show that the approach deserves further…
Graph-based representations of images have recently acquired an important role for classification purposes within the context of machine learning approaches. The underlying idea is to consider that relevant information of an image is…
We investigate Clifford+$T$ quantum circuits with a small number of $T$-gates. Using the sparsification lemma, we identify time complexity lower bounds in terms of $T$-gate count below which a strong simulator would improve on the…
Query complexity measures the amount of information an algorithm needs about a problem to compute a solution. On a quantum computer there are different realizations of a query and we will show that these are not always equivalent. Our…
Quantum Approximation Optimization Algorithm (QAOA) is a highly advocated variational algorithm for solving the combinatorial optimization problem. One critical feature in the quantum circuit of QAOA algorithm is that it consists of…
Quantum computational complexity estimates the difficulty of constructing quantum states from elementary operations, a problem of prime importance for quantum computation. Surprisingly, this quantity can also serve to study a completely…