Related papers: Lower Bounds for Parallel Quantum Counting

We give a careful proof that a parallelized version of adiabatic quantum computation can efficiently simulate universal gate model quantum computation. The proof specifies an explicit parameter-dependent Hamiltonian $H({\lambda})$ that is…

In this note, we show that quantum lower bounds obtained using the adversary method hold in the Hamiltonian oracle model.

Ben Reichardt showed in a series of results that the general adversary bound of a function characterizes its quantum query complexity. This survey seeks to aggregate the background and definitions necessary to understand the proof. Notable…

We present a new method for proving lower bounds on quantum query algorithms. The new method is an extension of adversary method, by analyzing the eigenspace structure of the problem. Using the new method, we prove a strong direct product…

Quantum counting is the task of determining the dimension of the subspace of states that are accepted by a quantum verifier circuit. It is the quantum analog of counting the number of valid solutions to NP problems -- a problem well-studied…

Notwithstanding interest and excitement building around quantum computing in the last decades, a concise statement saying where this computing can truly help is still missing. As it is shown in the present paper, equal cost of computation…

Quantum resources outperform classical ones for certain communication and computational tasks. Remarkably, in some cases, the quantum advantage cannot be improved using hypothetical postquantum resources. A class of tasks with this property…

Classical optimization algorithms in machine learning often take a long time to compute when applied to a multi-dimensional problem and require a huge amount of CPU and GPU resource. Quantum parallelism has a potential to speed up machine…

Commutativity has the same inherent limitations as compatibility. Then, it is worth conceiving simple concurrency control techniques. We propose a restricted form of commutativity which increases parallelism without incurring a higher…

We study parallel comparison-based algorithms for finding all equivalence classes of a set of $n$ elements, where sorting according to some total order is not possible. Such scenarios arise, for example, in applications, such as in…

This note complements the paper "One-Way Ticket to Las Vegas and the Quantum Adversary" (arxiv:2301.02003). I develop the ideas behind the adversary bound - universal algorithm duality therein in a different form, using the same perspective…

We study the question of whether parallelization in the exploration of the feasible set can be used to speed up convex optimization, in the local oracle model of computation. We show that the answer is negative for both deterministic and…

We observe that fault-tolerant quantum computers have an optimal advantage over classical computers in approximating solutions to many NP optimization problems. This observation however gives nothing in practice.

Adversarial learning is one of the most successful approaches to modelling high-dimensional probability distributions from data. The quantum computing community has recently begun to generalize this idea and to look for potential…

We show how phase and amplitude estimation algorithms can be parallelized. This can reduce the gate depth of the quantum circuits to that of a single Grover operator with a small overhead. Further, we show that for quantum amplitude…

We prove inequalities involving greatest common divisors of functions at integral points with respect to numerically parallel divisors, generalizing a result of Wang and Yasufuku (after work of Bugeaud-Corvaja-Zannier, Corvaja-Zannier, and…

Quantum classifiers are vulnerable to adversarial attacks that manipulate their input classical or quantum data. A promising countermeasure is adversarial training, where quantum classifiers are trained by using an attack-aware, adversarial…

We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. This model is in part motivated by the fact that decoherence times of qubits are typically small, so it makes sense to parallelize quantum…

We show that a separation between the class of all problems that can efficiently be solved on a quantum computer and those solvable using probabilistic classical algorithms in polynomial time implies the generalized contextuality of quantum…

Many problems of industrial interest are NP-complete, and quickly exhaust resources of computational devices with increasing input sizes. Quantum annealers (QA) are physical devices that aim at this class of problems by exploiting quantum…