English
Related papers

Related papers: Constant-Soundness Interactive Proofs for Local Ha…

200 papers

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.,…

Quantum Hamiltonian complexity studies computational complexity aspects of local Hamiltonians and ground states; these questions can be viewed as generalizations of classical computational complexity problems related to local constraint…

Quantum Physics · Physics 2015-03-17 Dorit Aharonov , Itai Arad , Zeph Landau , Umesh Vazirani

A frustration-free local Hamiltonian has the property that its ground state minimises the energy of all local terms simultaneously. In general, even deciding whether a Hamiltonian is frustration-free is a hard task, as it is closely related…

Quantum Physics · Physics 2017-12-15 András Gilyén , Or Sattath

We provide several advances to the understanding of the class of Quantum Merlin-Arthur proof systems (QMA), the quantum analogue of NP. Our central contribution is proving a longstanding conjecture that the Consistency of Local Density…

Quantum Physics · Physics 2022-10-13 Anne Broadbent , Alex B. Grilo

I present a quick and sound method for the robustness verification of a sort of quantum classifiers who are Linear Sound. Since quantum machine learning has been put into practice in relevant fields and Linear Sound Property, LSP is a…

Quantum Physics · Physics 2023-03-10 Su Bonan

We study 'Merlinized' versions of the recently defined Guided Local Hamiltonian problem, which we call 'Guidable Local Hamiltonian' problems. Unlike their guided counterparts, these problems do not have a guiding state provided as a part of…

Quantum Physics · Physics 2024-06-11 Jordi Weggemans , Marten Folkertsma , Chris Cade

The quantum analogue of a constraint satisfaction problem is a sum of local Hamiltonians - each local Hamiltonian specifies a local constraint whose violation contributes to the energy of the given quantum state. Formalizing the intuitive…

Quantum Physics · Physics 2008-11-25 Dorit Aharonov , Itai Arad , Zeph Landau , Umesh Vazirani

The k-local Hamiltonian problem is a natural complete problem for the complexity class QMA, the quantum analog of NP. It is similar in spirit to MAX-k-SAT, which is NP-complete for k<=2. It was known that the problem is QMA-complete for any…

Quantum Physics · Physics 2007-05-23 Julia Kempe , Alexei Kitaev , Oded Regev

An important task in quantum physics is the estimation of local quantities for ground states of local Hamiltonians. Recently, [Ambainis, CCC 2014] defined the complexity class P^QMA[log], and motivated its study by showing that the physical…

Quantum Physics · Physics 2020-04-09 Sevag Gharibian , Justin Yirka

We analyze the complexity of classically simulating continuous-time dynamics of locally interacting quantum spin systems with a constant rate of entanglement breaking noise. We prove that a polynomial time classical algorithm can be used to…

Quantum Physics · Physics 2022-11-11 Rahul Trivedi , J. Ignacio Cirac

Many-body open quantum systems, described by Lindbladian master equations, are a rich class of physical models that display complex equilibrium and out-of-equilibrium phenomena which remain to be understood. In this paper, we theoretically…

Quantum Physics · Physics 2025-07-15 Vikram Kashyap , Georgios Styliaris , Sara Mouradian , Juan Ignacio Cirac , Rahul Trivedi

Low degree tests play an important role in classical complexity theory, serving as basic ingredients in foundational results such as $\mathsf{MIP} = \mathsf{NEXP}$ [BFL91] and the PCP theorem [AS98,ALM+98]. Over the last ten years, versions…

Quantum Physics · Physics 2020-11-21 Zhengfeng Ji , Anand Natarajan , Thomas Vidick , John Wright , Henry Yuen

Interactive proof systems whose verifiers are constant-space machines have interesting features that do not have counterparts in the better studied case where the verifiers operate under reasonably large space bounds. The language…

Computational Complexity · Computer Science 2025-12-17 M. Utkan Gezer , A. C. Cem Say

We present upper and lower bounds of the computational complexity of the two-way communication model of multiple-prover quantum interactive proof systems whose verifiers are limited to measure-many two-way quantum finite automata. We prove…

Quantum Physics · Physics 2015-08-25 Tomoyuki Yamakami

In this paper we consider quantum interactive proof systems, i.e., interactive proof systems in which the prover and verifier may perform quantum computations and exchange quantum messages. It is proved that every language in PSPACE has a…

Computational Complexity · Computer Science 2007-05-23 John Watrous

The calculation of ground-state energies of physical systems can be formalised as the k-local Hamiltonian problem, which is the natural quantum analogue of classical constraint satisfaction problems. One way of making the problem more…

Quantum Physics · Physics 2016-03-29 Toby Cubitt , Ashley Montanaro

A central question in quantum information theory and computational complexity is how powerful nonlocal strategies are in cooperative games with imperfect information, such as multi-prover interactive proof systems. This paper develops a new…

Quantum Physics · Physics 2008-04-11 Tsuyoshi Ito , Hirotada Kobayashi , Daniel Preda , Xiaoming Sun , Andrew C. -C. Yao

Achieving quantum computational advantage requires solving a classically intractable problem on a quantum device. Natural proposals rely upon the intrinsic hardness of classically simulating quantum mechanics; however, verifying the output…

Hamiltonian learning is an important procedure in quantum system identification, calibration, and successful operation of quantum computers. Through queries to the quantum system, this procedure seeks to obtain the parameters of a given…

Quantum Physics · Physics 2023-08-25 Arkopal Dutt , Edwin Pednault , Chai Wah Wu , Sarah Sheldon , John Smolin , Lev Bishop , Isaac L. Chuang

A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify the quantum advantage of an untrusted prover. That is, a quantum prover can correctly answer the verifier's challenges and…

Quantum Physics · Physics 2022-09-21 Zhenning Liu , Alexandru Gheorghiu