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- ArticleMay 2024
Interactive Oracle Arguments in the QROM and Applications to Succinct Verification of Quantum Computation
AbstractThis work is motivated by the following question: can an untrusted quantum server convince a classical verifier of the answer to an efficient quantum computation using only polylogarithmic communication? We show how to achieve this in the quantum ...
- research-articleJanuary 2022
QMA-Hardness of Consistency of Local Density Matrices with Applications to Quantum Zero-Knowledge
SIAM Journal on Computing (SICOMP), Volume 51, Issue 4Pages 1400–1450https://doi.org/10.1137/21M140729XWe provide several advances to the understanding of the class of quantum Merlin--Arthur (QMA) proof systems, the quantum analogue of NP. Our central contribution is proving a longstanding conjecture that the consistency of local density matrices (CLDM) ...
- ArticleAugust 2020
Non-interactive Zero-Knowledge Arguments for QMA, with Preprocessing
AbstractA non-interactive zero-knowledge (NIZK) proof system for a language allows a prover (who is provided with an instance , and a witness w for x) to compute a classical certificate for the claim that such that has the following properties: 1) can ...
- research-articleJanuary 2020
Zero-Knowledge Proof Systems for QMA
SIAM Journal on Computing (SICOMP), Volume 49, Issue 2Pages 245–283https://doi.org/10.1137/18M1193530Prior work has established that all problems in NP admit classical zero-knowledge proof systems, and under reasonable hardness assumptions for quantum computations, these proof systems can be made secure against quantum attacks. We prove a result ...
- articleNovember 2017
Robustness of QMA against witness noise
Using the tool of concatenated stabilizer coding, we prove that the complexity class QMA remains unchanged even if every witness qubit is disturbed by constant noise. This result may not only be relevant for physical implementations of verifying ...
- articleJanuary 2016
Complexity of the XY antiferromagnet at fixed magnetization
We prove that approximating the ground energy of the antiferromagnetic XY model on a simple graph at fixed magnetization (given as part of the instance specification) is QMA-complete. To show this, we strengthen a previous result by establishing QMA-...
- articleNovember 2015
Quantum merlin-arthur with clifford arthur
We show that the class QMA does not change even if we restrict Arthur's computing ability to only Clifford gate operations (plus classical XOR gate). The idea is to use the fact that the preparation of certain single-qubit states, so called magic states,...
- articleSeptember 2015
An almost sudden jump in quantum complexity
The Quantum Satisfiability problem (QSAT) is the generalization of the canonical NP-complete problem - Boolean Satisfiability. (k, s)-QSAT is the following variant of the problem: given a set of projectors of rank 1, acting non-trivially on k qubits out ...
- articleApril 2014
QMA-complete problems
In this paper we give an overview of the quantum computational complexity class QMA and a description of known QMA-complete problems to date. Such problems are believed to be difficult to solve, even with a quantum computer, but have the property that ...
- articleJanuary 2013
QMA variants with polynomially many provers
We study three variants of multi-prover quantum Merlin-Arthur proof systems. We first show that the class of problems that can be efficiently verified using polynomially many quantum proofs, each of logarithmic-size, is exactly MQA (also known as QCMA), ...
- articleJuly 2012
On QMA protocols with two short quantum proofs
This paper gives a QMA (Quantum Merlin-Arthur) protocol for 3-SAT with two logarithmic-size quantum proofs (that are not entangled with each other) such that the gap between the completeness and the soundness is Ω(1/npolylog(n)). This improves the best ...
- articleJanuary 2012
Impossibility of succinct quantum proofs for collision-freeness
We show that any quantum algorithm to decide whether a function f : [n] → [n] is a permutation or far from a permutation must make Ω (n1/3/w) queries to f, even if the algorithm is given a w-qubit quantum witness in support of f being a permutation. ...
- articleNovember 2009
Fast amplification of QMA
Quantum Information & Computation (QIC), Volume 9, Issue 11Pages 1053–1068Given a verifier circuit for a problem in QMA, we show how to exponentially amplifythe gap between its acceptance probabilities in the 'yes' and 'no' cases, with a methodthat is quadratically faster than the procedure given by Marriott and Watrous [1]. ...
- research-articleMay 2009
The detectability lemma and quantum gap amplification
STOC '09: Proceedings of the forty-first annual ACM symposium on Theory of computingPages 417–426https://doi.org/10.1145/1536414.1536472The quantum analogue of the constraint satisfaction problem is the fundamental physics question of finding the minimal energy state of a local Hamiltonian --- each term of the Hamiltonian specifies a local constraint whose violation contributes to the ...
- ArticleJune 2008
The Power of Unentanglement
CCC '08: Proceedings of the 2008 IEEE 23rd Annual Conference on Computational ComplexityPages 223–236https://doi.org/10.1109/CCC.2008.5The class QMA(k), introduced by Kobayashi et al., consists of all languages that can be verified using k unentangled quantum proofs. Many of the simplest questions about this class have remained embarrassingly open: for example, can we give any evidence ...
- articleMay 2003
3-local Hamitonian is QMA-complete
It has been shown by Kitaev that the 5-LOCAL HAMILTONIAN problem is QMA-complete. Here we reduce the locality of the problem by showing that 3-LOCAL HAMILTONIAN is already QMA-complete.