Related papers: A New Quantum Lower Bound Method, with Application…

Advances in quantum algorithms suggest a tentative scaling advantage on certain combinatorial optimization problems. Recent work, however, has also reinforced the idea that barren plateaus render variational algorithms ineffective on large…

Branching programs are quite popular for studying time-space lower bounds. Bera et al. recently introduced the model of generalized quantum branching program aka. GQBP that generalized two earlier models of quantum branching programs. In…

We prove a very general lower bound technique for quantum and randomized query complexity, that is easy to prove as well as to apply. To achieve this, we introduce the use of Kolmogorov complexity to query complexity. Our technique…

The problem of finding a local minimum of a black-box function is central for understanding local search as well as quantum adiabatic algorithms. For functions on the Boolean hypercube {0,1}^n, we show a lower bound of Omega(2^{n/4}/n) on…

The goal of the ordered search problem is to find a particular item in an ordered list of n items. Using the adversary method, Hoyer, Neerbek, and Shi proved a quantum lower bound for this problem of (1/pi) ln n + Theta(1). Here, we find…

We introduce a protocol addressing the conformance test problem, which consists in determining whether a process under test conforms to a reference one. We consider a process to be characterized by the set of end-product it produces, which…

We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where…

We prove lower bounds on the error probability of a quantum algorithm for searching through an unordered list of N items, as a function of the number T of queries it makes. In particular, if T=O(sqrt{N}) then the error is lower bounded by a…

Local Search problem, which finds a local minimum of a black-box function on a given graph, is of both practical and theoretical importance to combinatorial optimization, complexity theory and many other areas in theoretical computer…

Although a quantum state requires exponentially many classical bits to describe, the laws of quantum mechanics impose severe restrictions on how that state can be accessed. This paper shows in three settings that quantum messages have only…

Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact,…

We provide simple but surprisingly useful direct product theorems for proving lower bounds on online algorithms with a limited amount of advice about the future. As a consequence, we are able to translate decades of research on randomized…

This article presents the first complete application of a quantum time-marching algorithm for simulating multidimensional linear transport phenomena with arbitrary boundaries, whereby the success probabilities are problem intrinsic. The…

We examine the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}^N in the black-box model. We show that, in the black-box model, the exponential quantum speed-up obtained for partial functions…

The Quantum Approximate Optimization Algorithm (QAOA) uses a quantum computer to implement a variational method with $2p$ layers of alternating unitary operators, optimized by a classical computer to minimize a cost function. While rigorous…

Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…

Several combinatorial optimization problems can be solved with NISQ devices once that a corresponding quadratic unconstrained binary optimization (QUBO) form is derived. The aim of this work is to drastically reduce the variables needed for…

We show tight lower bounds for the entire trade-off between space and query time for the Approximate Near Neighbor search problem. Our lower bounds hold in a restricted model of computation, which captures all hashing-based approaches. In…

A common situation in quantum many-body physics is that the underlying theories are known but too complicated to solve efficiently. In such cases one usually builds simpler effective theories as low-energy or large-scale alternatives to the…

Real-world optimization problems must undergo a series of transformations before becoming solvable on current quantum hardware. Even for a fixed problem, the number of possible transformation paths -- from industry-relevant formulations…