Related papers: On Perfect Completeness for QMA
We consider a finite universe U (more exactly - a family U of them) and second order quantifiers Q_K, where for each U this means quantifying over a family of n(K)-place relations closed under permuting U. We define some natural orders and…
Enhancing classical machine learning (ML) algorithms through quantum kernels is a rapidly growing research topic in quantum machine learning (QML). A key challenge in using kernels -- both classical and quantum -- is that ML workflows…
Classical matching theory can be defined in terms of matrices with nonnegative entries. The notion of Positive operator, central in Quantum Theory, is a natural generalization of matrices with nonnegative entries. Based on this point of…
We study the precise computational complexity of deciding satisfiability of first-order quantified formulas over the theory of fixed-size bit-vectors with binary-encoded bit-widths and constants. This problem is known to be in EXPSPACE and…
Let L be a language decided by a constant-round quantum Arthur-Merlin (QAM) protocol with negligible soundness error and all but possibly the last message being classical. We prove that if this protocol is zero knowledge with a black-box,…
Quantum metrology concerns improving the estimation of an unknown parameter using an optimal measurement scheme on the quantum system. More the optimality of the measurement, the better will be the improvement in sensing the value of the…
To explore the limitation of a class of quantum algorithms originally proposed for the Hilbert's tenth problem, we consider two further classes of mathematically non-decidable problems, those of a modified version of the Hilbert's tenth…
Large language models are playing an increasingly significant role in molecular research, yet existing models often generate erroneous information, posing challenges to accurate molecular comprehension. Traditional evaluation metrics for…
This paper studies complexity theoretic aspects of quantum refereed games, which are abstract games between two competing players that send quantum states to a referee, who performs an efficiently implementable joint measurement on the two…
The standard inputs given to a quantum machine are classical binary strings. In this view, any quantum complexity class is a collection of subsets of $\{0,1\}^{*}$. However, a quantum machine can also accept quantum states as its input. T.…
The class of languages having polynomial-time classical or quantum interactive proof systems ($\mathsf{IP}$ or $\mathsf{QIP}$, respectively) is identical to $\mathsf{PSPACE}$. We show that $\mathsf{PSPACE}$ (and so $\mathsf{QIP}$) is subset…
It is often assumed that the ancilla qubits required for encoding a qubit in quantum error correction (QEC) have to be in pure states, $|00...0>$ for example. In this letter, we seek an encoding scheme, in which the ancillae may be in a…
The best mathematical arguments against a realistic interpretation of quantum mechanics - that gives definite but partially unknown values to all observables - are analysed and shown to be based on reasoning that is not compelling. This…
Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact,…
Because the subject of relativistic quantum field theory (QFT) contains all of non-relativistic quantum mechanics, we expect quantum field computation to contain (non-relativistic) quantum computation. Although we do not yet have a quantum…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
Formulations of quantum mechanics can be characterized as realistic, operationalist, or a combination of the two. In this paper a realistic theory is defined as describing a closed system entirely by means of entities and concepts…
We investigate the difficulties that undergraduate students in quantum mechanics courses have in transferring learning from previous courses or within the same course from one context to another by administering written tests and conducting…
Classical satisfiability (SAT) and quantum satisfiability (QSAT) are complete problems for the complexity classes NP and QMA which are believed to be intractable for classical and quantum computers, respectively. Statistical ensembles of…
We consider quantum versions of two well-studied classical learning models: Angluin's model of exact learning from membership queries and Valiant's Probably Approximately Correct (PAC) model of learning from random examples. We give…