Related papers: Approximate traces on groups and the quantum compl…
We survey a number of incompleteness results in operator algebras stemming from the recent undecidability result in quantum complexity theory known as $\operatorname{MIP}^*=\operatorname{RE}$, the most prominent of which is the G\"odelian…
Instantaneous quantum polynomial-time (IQP) computation is a class of quantum computation consisting only of commuting two-qubit gates and is not universal in the sense of standard quantum computation. Nevertheless, it has been shown that…
We identify a formal connection between physical problems related to the detection of separable (unentangled) quantum states and complexity classes in theoretical computer science. In particular, we show that to nearly every quantum…
We present a Coq formalization of the Quantified Reflection Calculus with one modality, or $\mathsf{QRC}_1$. This is a decidable, strictly positive, and quantified modal logic previously studied for its applications in proof theory. The…
We initiate the study of quantum Interactive Oracle Proofs (qIOPs), a generalization of both quantum Probabilistically Checkable Proofs and quantum Interactive Proofs, as well as a quantum analogue of classical Interactive Oracle Proofs. In…
By leveraging quantum-mechanical properties like superposition, entanglement, and interference, quantum computing (QC) offers promising solutions for problems that classical computing has not been able to solve efficiently, such as drug…
Modeling and reasoning about concurrent quantum systems is very important both for distributed quantum computing and for quantum protocol verification. As a consequence, a general framework describing formally the communication and…
We introduce the notion of integrable modules over $\imath$quantum groups (a.k.a. quantum symmetric pair coideal subalgebras). After determining a presentation of such modules, we prove that each integrable module over a quantum group is…
Distinguishing logarithmic depth quantum circuits on mixed states is shown to be complete for QIP, the class of problems having quantum interactive proof systems. Circuits in this model can represent arbitrary quantum processes, and thus…
The goal of the presented paper is to provide an introduction to the basic computational models used in quantum information theory. We review various models of quantum Turing machine, quantum circuits and quantum random access machine…
We use modular invariant theory to establish a complete set of relations of the mod $p$ homology of $\{QS^k\}_{k\geq0}$, for $p$ odd, as a ring object in the category of coalgebras (also known as a coalgebraic ring or a Hopf ring). We also…
We provide a necessary condition that a quantum measurement can be implemented by the class of protocols known as Local Operations and Classical Communication, or LOCC, including when an error is allowed but must vanish in the limit of an…
We review recent progress made in quantum information processing (QIP) which can be applied in the simulation of quantum systems and chemical phenomena. The review is focused on quantum algorithms which are useful for quantum simulation of…
We formulate a systematic construction of commuting quantum traces for reflection algebras. This is achieved by introducing two sets of generalized reflection equations with associated consistent fusion procedures. Products of their…
The correspondence principle asserts that quantum mechanics resembles classical mechanics in the high-quantum-number limit. In the past few years many papers have been published on the extension of both quantum mechanics and classical…
We study the Moore complex of a simplicial cocommutative Hopf algebra through Hopf kernels. The most striking result to emerge from this construction is the coherent definition of 2-crossed modules of cocommutative Hopf algebras. This…
We introduce two modal natural deduction systems that are suitable to represent and reason about transformations of quantum registers in an abstract, qualitative, way. Quantum registers represent quantum systems, and can be viewed as the…
We present a generic compiler that converts any $\mathsf{MIP}^{*}$ protocol into a succinct interactive argument where the communication and the verifier are classical, and where post-quantum soundness relies on the post-quantum…
A quantum compiler is a critical piece in the quantum computing pipeline since it allows an abstract quantum circuit to be run on a physical quantum computer. One extremely important subproblem in quantum compilation is the generation of a…
We prove that QIP(2), the class of problems having two-message quantum interactive proof systems, is a subset of PSPACE. This relationship is obtained by means of an efficient parallel algorithm, based on the multiplicative weights update…