Related papers: Exact Non-identity check is NQP-complete

Whether the class QMA (Quantum Merlin Arthur) is equal to QMA1, or QMA with one-sided error, has been an open problem for years. This note helps to explain why the problem is difficult, by using ideas from real analysis to give a "quantum…

The counterfeit coin problem requires us to find all false coins from a given bunch of coins using a balance scale. We assume that the balance scale gives us only ``balanced'' or ``tilted'' information and that we know the number k of false…

Quantum computers are on the brink of surpassing the capabilities of even the most powerful classical computers. This naturally raises the question of how one can trust the results of a quantum computer when they cannot be compared to…

Authentication provides the trust people need to engage in transactions. The advent of physical keys that are impossible to copy promises to revolutionize this field. Up to now, such keys have been verified by classical challenge-response…

Continuous time quantum walks on exponentially large, sparse graphs form a powerful paradigm for quantum computing: On the one hand, they can be efficiently simulated on a quantum computer. On the other hand, they are themselves…

The accurate identification of faulty hardware is a fundamental requirement for reliable quantum information processing. We address this problem in a quantum setting, where a series of $n$ devices is intended to apply the same unitary…

An exact quantization rule for the Schr\"{o}dinger equation is presented. In the exact quantization rule, in addition to $N\pi$, there is an integral term, called the quantum correction. For the exactly solvable systems we find that the…

Based on the standard transfer matrix, a formally exact quantization condition for arbitrary potentials, which outflanks and unifies the historical approaches, is derived. It can be used to find the exact bound-state energy eigenvalues of…

We propose the idea of a Quantum Cheque Scheme, a cryptographic protocol in which any legitimate client of a trusted bank can issue a cheque, that cannot be counterfeited or altered in anyway, and can be verified by a bank or any of its…

Verification of quantum computation is a task to efficiently check whether an output given from a quantum computer is correct. Existing verification protocols conducted between a quantum computer to be verified and a verifier necessitate…

A quantum algorithm is exact if it always produces the correct answer, on any input. Coming up with exact quantum algorithms that substantially outperform the best classical algorithm has been a quite challenging task. In this paper, we…

We study the problem of encrypting and authenticating quantum data in the presence of adversaries making adaptive chosen plaintext and chosen ciphertext queries. Classically, security games use string copying and comparison to detect…

For typical first-order logical theories, satisfying assignments have a straightforward finite representation that can directly serve as a certificate that a given assignment satisfies the given formula. For non-linear real arithmetic…

We solve the problem of the classification of perfect quantum codes. We prove that the only nontrivial perfect quantum codes are those with the parameters . There exist no other nontrivial perfect quantum codes.

Specific quantum algorithms exist to-in theory-break elliptic curve cryptographic protocols. Implementing these algorithms requires designing quantum circuits that perform elliptic curve arithmetic. To accurately judge a cryptographic…

In the exact quantum query model a successful algorithm must always output the correct function value. We investigate the function that is true if exactly $k$ or $l$ of the $n$ input bits given by an oracle are 1. We find an optimal…

Secure computation of equivalence has fundamental application in many different areas, including healthcare. We study this problem in the context of matching an individual identity to link medical records across systems. We develop an…

We formulate and study, in general terms, the problem of quantum system identification, i.e., the determination (or estimation) of unknown quantum channels through their action on suitably chosen input density operators. We also present a…

A reliable method for characterizing quantum operations that is suitable for improving and validating their accuracies is indispensable for realizing a practical quantum computer. Known methods are still not sufficient because they lack…

Equivalence checking of hybrid quantum circuits is of primary importance, given that quantum circuit transformations are omnipresent along the quantum compiler chain. While some approaches exist for automating this task, most focus on the…