Related papers: Classical verification of quantum circuits contain…
We present a formalism that captures the process of proving quantum superiority to skeptics as an interactive game between two agents, supervised by a referee. Bob, is sampling from a classical distribution on a quantum device that is…
Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…
A proof of quantumness is an efficiently verifiable interactive test that an efficient quantum computer can pass, but all efficient classical computers cannot (under some cryptographic assumption). Such protocols play a crucial role in the…
We present two verification protocols where the correctness of a "target" computation is checked by means of "trap" computations that can be efficiently simulated on a classical computer. Our protocols rely on a minimal set of noise-free…
Quantum processes, such as quantum circuits, quantum memories, and quantum channels, are essential ingredients in almost all quantum information processing tasks. However, the characterization of these processes remains a daunting task due…
Shor's algorithms for factorization and discrete logarithms on a quantum computer employ Fourier transforms preceding a final measurement. It is shown that such a Fourier transform can be carried out in a semi-classical way in which a…
Realizing a conceptual quantum algorithm on an actual physical device necessitates the algorithm's quantum circuit description to undergo certain transformations in order to adhere to all constraints imposed by the hardware. In this regard,…
Let $f$ denote length preserving function on words. A classical algorithm can be considered as $T$ iterated applications of black box representing $f$, beginning with input word $x$ of length $n$. It is proved that if $T=O(2^{n/(7+e)}), e…
A quantum position-verification scheme attempts to verify the spatial location of a prover. The prover is issued a challenge with quantum and classical inputs and must respond with appropriate timings. We consider two well-studied…
We establish the first general connection between the design of quantum algorithms and circuit lower bounds. Specifically, let $\mathfrak{C}$ be a class of polynomial-size concepts, and suppose that $\mathfrak{C}$ can be PAC-learned with…
This paper describes the verification of the classical software and hardware stack that is used to control cold atom- and superconducting-based quantum computing hardware. The paper serves both as an introduction to quantum computing and to…
We define a class of stochastic processes based on evolutions and measurements of quantum systems, and consider the complexity of predicting their long-term behavior. It is shown that a very general class of decision problems regarding…
A proof of quantumness (PoQ) allows a classical verifier to efficiently test if a quantum machine is performing a computation that is infeasible for any classical machine. In this work, we propose a new approach for constructing PoQ…
Many interesting computational problems can be reformulated in terms of decision trees. A natural classical algorithm is to then run a random walk on the tree, starting at the root, to see if the tree contains a node n levels from the root.…
The quantum Fourier transform (QFT) is sometimes said to be the source of various exponential quantum speed-ups. In this paper we introduce a class of quantum circuits which cannot outperform classical computers even though the QFT…
Uncertainty principle forbids one to determine which of the two paths a quantum system has travelled, unless interference between the alternatives had been destroyed by a measuring device, e.g., by a pointer. One can try to weaken the…
Quantum algorithm is constructed which verifies the formulas of predicate calculus in time $O(\sqrt N)$ with bounded error probability, where $N$ is the time required for classical algorithms. This algorithm uses the polynomial number of…
Coverage criteria play a central role in assessing test adequacy in classical software, yet their effectiveness for quantum programs remains poorly understood and largely unexplored. In this paper, we propose six quantum-tailored criteria -…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
We initiate the study of parameterized complexity of $\textsf{QMA}$ problems in terms of the number of non-Clifford gates in the problem description. We show that for the problem of parameterized quantum circuit satisfiability, there exists…