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This paper studies whether quantum proofs are more powerful than classical proofs, or in complexity terms, whether QMA=QCMA. We prove three results about this question. First, we give a "quantum oracle separation" between QMA and QCMA. More…

Quantum Physics · Physics 2020-09-30 Scott Aaronson , Greg Kuperberg

As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available…

Algorithms with unitary oracles can be nested, which makes them extremely versatile. An example is the phase estimation algorithm used in many candidate algorithms for quantum speed-up. The search for new quantum algorithms benefits from…

Quantum Physics · Physics 2024-04-01 Zuzana Gavorová , Matan Seidel , Yonathan Touati

In the standard oracle model, an oracle efficiently evaluates an unknown classical function independent of the quantum algorithm itself. Quantum algorithms have a complex interrelationship to their oracles; for example the possibility of…

Quantum Physics · Physics 2022-06-29 Cica Gustiani , David P. DiVincenzo

Faster algorithms, novel cryptographic mechanisms, and alternative methods of communication become possible when the model underlying information and computation changes from a classical mechanical model to a quantum mechanical one. Quantum…

Quantum Physics · Physics 2009-12-29 Eleanor G. Rieffel

Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…

Quantum Physics · Physics 2017-08-23 Wim van Dam , Yoshitaka Sasaki

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

A quantum computer has now solved a specialized problem believed to be intractable for supercomputers, suggesting that quantum processors may soon outperform supercomputers on scientifically important problems. But flaws in each quantum…

Quantum Physics · Physics 2022-01-21 Timothy Proctor , Kenneth Rudinger , Kevin Young , Erik Nielsen , Robin Blume-Kohout

This paper explores the problem of quantum measurement complexity. In computability theory, the complexity of a problem is determined by how long it takes an effective algorithm to solve it. This complexity may be compared to the difficulty…

Quantum Physics · Physics 2014-10-27 Subhash Kak

Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…

Quantum Physics · Physics 2024-11-14 E. M. Stoudenmire , Xavier Waintal

In this note we study the power of so called query-limited computers. We compare the strength of a classical computer that is allowed to ask two questions to an NP-oracle with the strength of a quantum computer that is allowed only one such…

Quantum Physics · Physics 2007-05-23 Wim van Dam

We study how the choices made when designing an oracle affect the complexity of quantum property testing problems defined relative to this oracle. We encode a regular graph of even degree as an invertible function $f$, and present $f$ in…

Quantum Physics · Physics 2023-11-23 Roozbeh Bassirian , Bill Fefferman , Kunal Marwaha

The driving force in the pursuit for quantum computation is the exciting possibility that quantum algorithms can be more efficient than their classical analogues. Research on the subject has unraveled several aspects of how that can happen.…

Quantum Physics · Physics 2011-02-11 Apoorva Patel

We present a quantum algorithm which identifies with certainty a hidden subgroup of an arbitrary finite group G in only a polynomial (in log |G|) number of calls to the oracle. This is exponentially better than the best classical algorithm.…

Quantum Physics · Physics 2016-12-30 Mark Ettinger , Peter Hoyer , Emanuel Knill

Natural frequencies and normal modes are basic properties of a structure which play important roles in analyses of its vibrational characteristics. As their computation reduces to solving eigenvalue problems, it is a natural arena for…

Quantum Physics · Physics 2023-08-29 Yasunori Lee , Keita Kanno

Quantum query complexity studies the number of queries needed to learn some property of a black box. A closely related question is how well an algorithm can succeed with this learning task using only a fixed number of queries. In this work,…

Several benchmarks have been proposed to holistically measure quantum computing performance. While some have focused on the end user's perspective (e.g., in application-oriented benchmarks), the real industrial value taking into account the…

Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. In effect, they follow the same logical paradigm as (multi-particle)…

Quantum Physics · Physics 2007-05-23 R. Cleve , A. Ekert , L. Henderson , C. Macchiavello , M. Mosca

Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…

Quantum Physics · Physics 2010-01-19 Andrew M. Childs , Wim van Dam

Quantum algorithms are typically understood in terms of the evolution of a multi-qubit quantum system under a prescribed sequence of unitary transformations. The input to the algorithm prescribes some of the unitary transformations in the…

Quantum Physics · Physics 2015-05-13 David Collins