相关论文: How Much Structure Is Needed for Huge Quantum Spee…
Fast quantum algorithms can solve important computational problems more efficiently than classical algorithms. However, little is known about whether quantum computing can speed up solving geometric problems. This article explores quantum…
Quantifying quantum states' complexity is a key problem in various subfields of science, from quantum computing to black-hole physics. We prove a prominent conjecture by Brown and Susskind about how random quantum circuits' complexity…
In this paper I argue that entanglement is a necessary component for any explanation of quantum speedup and I address some purported counter-examples that some claim show that the contrary is true. In particular, I address Biham et al.'s…
The field of quantum algorithms aims to find ways to speed up the solution of computational problems by using a quantum computer. A key milestone in this field will be when a universal quantum computer performs a computational task that is…
Branch-and-bound is a widely used technique for solving combinatorial optimisation problems where one has access to two procedures: a branching procedure that splits a set of potential solutions into subsets, and a cost procedure that…
One of the outstanding challenges in contemporary science and technology is building a quantum computer that is useful in applications. By starting from an estimate of the algorithm success rate, we can explicitly connect gate fidelity to…
We perform formal verification of quantum circuits by integrating several techniques specialized to particular classes of circuits. Our verification methodology is based on the new notion of a reversible miter that allows one to leverage…
We present a simple theory accounting for two central observations in a recent experiment on quantum coarsening and collective dynamics on a programmable quantum simulator [T. Manovitz et al., Nature \textbf{638}, 86 (2025)]: an apparent…
Quantum circuit complexity is a fundamental concept whose importance permeates quantum information, computation, many-body physics and high-energy physics. While extensively studied in closed systems, its characterization and behaviors in…
Random transformations are typically good at "scrambling" information. Specifically, in the quantum setting, scrambling usually refers to the process of mapping most initial pure product states under a unitary transformation to states which…
Recent works have shown that quantum computers can polynomially speed up certain SAT-solving algorithms even when the number of available qubits is significantly smaller than the number of variables. Here we generalise this approach. We…
We show that quantum computation can be performed in a system at thermal equilibrium if a spontaneous symmetry breaking occurs. The computing process is associated to the time evolution of the statistical average of the qubit coherence…
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…
Near-term quantum devices with limited qubits motivate the study of space-bounded quantum computation in the data stream model. We show that Shannon entropy estimation exhibits an exponential separation between quantum and classical space…
Quantum entanglement is an essential feature of many-body systems that impacts both quantum information processing and fundamental physics. The growth of entanglement is a major challenge for classical simulation methods. In this work, we…
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…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
Motivated by the recent experimental demonstrations of quantum supremacy, proving the hardness of the output of random quantum circuits is an imperative near term goal. We prove under the complexity theoretical assumption of the…
In general relativity space-time ends at singularities. The big bang is considered as the Beginning and the big crunch, the End. However these conclusions are arrived at by using general relativity in regimes which lie well beyond its…
The glued-trees problem is the only example known to date for which quantum annealing provides an exponential speedup, albeit by partly using excited state evolution, in an oracular setting. How robust is this speedup to noise on the…