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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…

Quantum Physics · Physics 2025-06-02 Giulio Malavolta , Tamer Mour

It is known that the group non-membership problem is in QMA relative to any group oracle and in ${\rm SPP}\cap{\rm BQP}$ relative to group oracles for solvable groups. We consider a modified version of the group non-membership problem where…

Quantum Physics · Physics 2021-10-05 Tomoyuki Morimae , Harumichi Nishimura , Francois Le Gall

Testing efficiently whether a finite set with a binary operation over it, given as an oracle, is a group is a well-known open problem in the field of property testing. Recently, Friedl, Ivanyos and Santha have made a significant step in the…

Quantum Physics · Physics 2021-10-05 Yoshifumi Inui , Francois Le Gall

We explore the space "just above" BQP by defining a complexity class PDQP (Product Dynamical Quantum Polynomial time) which is larger than BQP but does not contain NP relative to an oracle. The class is defined by imagining that quantum…

Quantum Physics · Physics 2014-12-22 Scott Aaronson , Adam Bouland , Joseph Fitzsimons , Mitchell Lee

A proof of quantumness is a method for provably demonstrating (to a classical verifier) that a quantum device can perform computational tasks that a classical device with comparable resources cannot. Providing a proof of quantumness is the…

Quantum Physics · Physics 2020-05-12 Zvika Brakerski , Venkata Koppula , Umesh Vazirani , Thomas Vidick

One can fix the randomness used by a randomized algorithm, but there is no analogous notion of fixing the quantumness used by a quantum algorithm. Underscoring this fundamental difference, we show that, in the black-box setting, the…

Computational Complexity · Computer Science 2024-04-26 Scott Aaronson , DeVon Ingram , William Kretschmer

A test of quantumness is a protocol that allows a classical verifier to certify (only) that a prover is not classical. We show that tests of quantumness that follow a certain template, which captures recent proposals such as (Kalai et al.,…

In computer science, many search problems are reducible to decision problems, which implies that finding a solution is as hard as deciding whether a solution exists. A quantum analogue of search-to-decision reductions would be to ask…

Quantum Physics · Physics 2025-02-05 Jordi Weggemans

Quantum Merlin-Arthur proof systems are believed to be stronger than both their classical counterparts and ``stand-alone'' quantum computers when Arthur is assumed to operate in $\Omega(\log n)$ space. No hint of such an advantage over…

Computational Complexity · Computer Science 2025-05-14 A. C. Cem Say

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…

Quantum Physics · Physics 2024-05-27 Petia Arabadjieva , Alexandru Gheorghiu , Victor Gitton , Tony Metger

We give a comprehensive characterization of the computational power of shallow quantum circuits combined with classical computation. Specifically, for classes of search problems, we show that the following statements hold, relative to a…

The main promise of quantum computing is to efficiently solve certain problems that are prohibitively expensive for a classical computer. Most problems with a proven quantum advantage involve the repeated use of a black box, or oracle,…

We investigate the structure of quantum proof systems by establishing collapse results that reveal simplifications in their complexity landscape. By extending classical theorems such as the Karp-Lipton theorem to quantum settings and…

Quantum Physics · Physics 2025-07-08 Kartik Anand , Kabgyun Jeong , Junseo Lee

Recently Chen and Movassagh proposed the quantum Merkle tree, which is a quantum analogue of the well-known classical Merkle tree. It gives a succinct verification protocol for quantum state commitment. Although they only proved security…

Quantum Physics · Physics 2023-03-01 Lijie Chen , Ramis Movassagh

The universality of quantum theory has been questioned ever since it was proposed. Key to this long-unsolved question is to test whether a given physical system has non-classical features. Here we connect recently proposed witnesses of…

This paper positively solves the quantum subroutine problem for fully quantum oracles. The quantum subroutine problem asks whether a quantum computer with an efficiently computable oracle can be efficiently simulated by a non-oracle quantum…

Quantum Physics · Physics 2007-05-23 Harumichi Nishimura , Masanao Ozawa

Identifying non-classicality unambiguously and inexpensively is a long-standing open challenge in physics. The No-Signalling-In-Time protocol was developed as an experimental test for macroscopic realism, and serves as a witness of quantum…

Quantum Physics · Physics 2018-11-28 George C. Knee , Max Marcus , Luke D. Smith , Animesh Datta

The research described in this note aims at solving the constructive membership problem for the class of quasisimple classical groups. Our algorithms are developed in the black-box group model; that is, they do not require specific…

Group Theory · Mathematics 2010-07-01 Sophie Ambrose , Scott H. Murray , Cheryl E. Praeger , Csaba Schneider

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,…

Quantum Physics · Physics 2012-03-24 Alina Dubrovska Vasilieva

QMA (Quantum Merlin Arthur) is the class of problems which, though potentially hard to solve, have a quantum solution which can be verified efficiently using a quantum computer. It thus forms a natural quantum version of the classical…

Quantum Physics · Physics 2016-03-02 Tomoyuki Morimae , Daniel Nagaj , Norbert Schuch