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Adiabatic quantum algorithms are characterized by their run time and accuracy. The relation between the two is essential for quantifying adiabatic algorithmic performance, yet is often poorly understood. We study the dynamics of a…
That superpositions of states can be useful for performing tasks in quantum systems has been known since the early days of quantum information, but only recently has quantitative theory of quantum coherence been proposed. Here we apply that…
We present a full implementation and simulation of a novel quantum reinforcement learning method. Our work is a detailed and formal proof of concept for how quantum algorithms can be used to solve reinforcement learning problems and shows…
The application of quantum algorithms to classical problems is generally accompanied by significant bottlenecks when transferring data between quantum and classical states, often negating any intrinsic quantum advantage. Here we address…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
We define and study a new type of quantum oracle, the quantum conditional oracle, which provides oracle access to the conditional probabilities associated with an underlying distribution. Amongst other properties, we (a) obtain speed-ups…
The paper considers the problem of finding a given substring in a text. It is known that the complexity of a classical search query in an unordered database is linear in the length of the text and a given substring. At the same time,…
In classical computation, a problem can be solved in multiple steps where calculated results of each step can be copied and used repeatedly. While in quantum computation, it is difficult to realize a similar multi-step computation process…
We show that quantum oracles provide an advantage over classical oracles for answering classical counterfactual questions in causal models, or equivalently, for identifying unknown causal parameters such as distributions over functional…
We introduce the quantum complexity class FQMA. This class describes the complexity of generating a quantum state that serves as a witness for a given QMA problem. In a certain sense, FQMA is the quantum analogue of FNP (function problems…
We revisit the so-called compressed oracle technique, introduced by Zhandry for analyzing quantum algorithms in the quantum random oracle model (QROM). To start off with, we offer a concise exposition of the technique, which easily extends…
We propose a method for quantum algorithm design assisted by machine learning. The method uses a quantum-classical hybrid simulator, where a "quantum student" is being taught by a "classical teacher." In other words, in our method, the…
The difference between classical and quantum algorithms (QA) is following: problem solved by QA is coded in the structure of the quantum operators. Input to QA in this case is always the same. Output of QA says which problem coded. In some…
We investigate the performance of a quantum algorithm for solving classical 3-SAT problems. A cycle of post-selected measurements drives the computer's register monotonically toward a steady state which is correlated to the classical…
Complexity theory traditionally studies the hardness of solving classical computational problems. In the quantum setting, it is also natural to consider a different notion of complexity, namely the complexity of physically preparing a…
We introduce a versatile method for preparing a quantum state whose amplitudes are given by some known function. Unlike existing approaches, our method does not require handcrafted reversible arithmetic circuits, or quantum table reads, to…
Quantum computing promises to solve difficult optimization problems in chemistry, physics and mathematics more efficiently than classical computers, but requires fault-tolerant quantum computers with millions of qubits. To overcome errors…
Searching and sorting used as a subroutine in many important algorithms. Quantum algorithm can find a target item in a database faster than any classical algorithm. One can trade accuracy for speed and find a part of the database (a block)…
The Traveling Salesman Problem (TSP) is a classical NP-hard problem that plays a crucial role in combinatorial optimization. In this paper, we are interested in the quantum search framework for the TSP because it has robust theoretical…
We establish connections between state tomography, pseudorandomness, quantum state synthesis, and circuit lower bounds. In particular, let $\mathfrak{C}$ be a family of non-uniform quantum circuits of polynomial size and suppose that there…