Related papers: Advice Coins for Classical and Quantum Computation
Although polynomial-time probabilistic Turing machines can utilize uncomputable transition probabilities to recognize uncountably many languages with bounded error when allowed to use logarithmic space, it is known that such "magic coins"…
We examine the characteristic features of reversible and quantum computations in the presence of supplementary external information, known as advice. In particular, we present a simple, algebraic characterization of languages recognized by…
Advice is supplementary information that enhances the computational power of an underlying computation. This paper focuses on advice that is given in the form of a pure quantum state and examines the influence of such advice on the…
Although a quantum state requires exponentially many classical bits to describe, the laws of quantum mechanics impose severe restrictions on how that state can be accessed. This paper shows in three settings that quantum messages have only…
In this thesis, we introduce a new quantum Turing machine (QTM) model that supports general quantum operators, together with its pushdown, counter, and finite automaton variants, and examine the computational power of classical and quantum…
In this paper, we consider a new direction of computation, which we call computation with large advice. We mainly consider constant space computation with large advice in Turing machines, and prove the following facts: (i) The class of…
In this paper, we study the relationship between advice in the form of a training set and classical advice. We do this by analyzing the class $\mathsf{BPP/samp}$ and certain variants of it. Specifically, our main result demonstrates that…
This article traces a brief history of the use of single electron spins to compute. In classical computing schemes, a binary bit is represented by the spin polarization of a single electron confined in a quantum dot. If a weak magnetic…
This paper furthers existing evidence that quantum computers are capable of computations beyond classical computers. Specifically, we strengthen the collapse of the polynomial hierarchy to the second level if: (i) Quantum computers with…
Extracting classical information from quantum systems is of fundamental importance, and classical shadows allow us to extract a large amount of information using relatively few measurements. Conventional shadow estimators are unbiased and…
While it is well known that a Turing machine equipped with the ability to flip a fair coin cannot compute more that a standard Turing machine, we show that this is not true for a biased coin. Indeed, any oracle set $X$ may be coded as a…
We consider the scenario where Alice wants to send a secret (classical) $n$-bit message to Bob using a classical key, and where only one-way transmission from Alice to Bob is possible. In this case, quantum communication cannot help to…
Given a random permutation $f: [N] \to [N]$ as a black box and $y \in [N]$, we want to output $x = f^{-1}(y)$. Supplementary to our input, we are given classical advice in the form of a pre-computed data structure; this advice can depend on…
Relational problems (those with many possible valid outputs) are different from decision problems, but it is easy to forget just how different. This paper initiates the study of FBQP/qpoly, the class of relational problems solvable in…
We show the following: a randomly chosen pure state as a resource for measurement-based quantum computation, is - with overwhelming probability - of no greater help to a polynomially bounded classical control computer, than a string of…
Aaronson and Drucker (2011) asked whether there exists a quantum finite automaton that can distinguish fair coin tosses from biased ones by spending significantly more time in accepting states, on average, given an infinite sequence of…
Quantum computers are believed to bring computational advantages in simulating quantum many body systems. However, recent works have shown that classical machine learning algorithms are able to predict numerous properties of quantum systems…
We consider the task of verifying the correctness of quantum computation for a restricted class of circuits which contain at most two basis changes. This contains circuits giving rise to the second level of the Fourier Hierarchy, the lowest…
Coin flipping is a cryptographic primitive for which strictly better protocols exist if the players are not only allowed to exchange classical, but also quantum messages. During the past few years, several results have appeared which give a…
This paper presents two unconventional links between quantum and classical physics. The first link appears in the study of quantum cryptography. In the presence of a spy, the quantum correlations shared by Alice and Bob are imperfect. One…