Related papers: A new sibling of BQP

The tight-binding model of quantum particles on a honeycomb lattice is investigated in the presence of homogeneous magnetic field. Provided the magnetic flux per unit hexagon is rational of the elementary flux, the one-particle Hamiltonian…

The natural Hilbert Space of quantum particles can implement maximum-likelihood (ML) decoding of classical information. The 'Quantum Product Algorithm' (QPA) is computed on a Factor Graph, where function nodes are unitary matrix operations…

I study the class of problems efficiently solvable by a quantum computer, given the ability to "postselect" on the outcomes of measurements. I prove that this class coincides with a classical complexity class called PP, or Probabilistic…

We describe certain quiver Hopf algebras by parameters. This leads to the classification of multiple Taft algebras as well as pointed Yetter-Drinfeld modules and their corresponding Nichols algebras. In particular, when the ground-field $k$…

Ever since entanglement was identified as a computational and cryptographic resource, researchers have sought efficient ways to tell whether a given density matrix represents an unentangled, or separable, state. This paper gives the first…

We present a compact quantum circuit for factoring a large class of integers, including some whose classical hardness is expected to be equivalent to RSA (but not including RSA integers themselves). Most notably, we factor $n$-bit integers…

One-way puzzles (OWPuzzs) introduced by Khurana and Tomer [STOC 2024] are a natural quantum analogue of one-way functions (OWFs), and one of the most fundamental primitives in ''Microcrypt'' where OWFs do not exist but quantum cryptography…

In this paper we present several multipartite quantum systems featuring the same type of genuine (tripartite) entanglement. Based on a geometric interpretation of the so-called $|W\rangle$ and $|GHZ\rangle$ states we show that the…

Query complexity is a model of computation in which we have to compute a function $f(x_1, \ldots, x_N)$ of variables $x_i$ which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes.…

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…

The complexity class $PSPACE$ includes all computational problems that can be solved by a classical computer with polynomial memory. All $PSPACE$ problems are known to be solvable by a quantum computer too with polynomial memory and are,…

Quantum signal processing (QSP) provides a representation of scalar polynomials of degree $d$ as products of matrices in $\mathrm{SU}(2)$, parameterized by $(d+1)$ real numbers known as phase factors. QSP is the mathematical foundation of…

Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central problem solved by Shor's factoring algorithm. We suggest an…

A new quantum algorithm for a search problem and its computational complexity are discussed. It is shown in the search problem containing 2^n objects that our algorithm runs in polynomial time.

In order to establish the computational equivalence between quantum Turing machines (QTMs) and quantum circuit families (QCFs) using Yao's quantum circuit simulation of QTMs, we previously introduced the class of uniform QCFs based on an…

We give a comprehensive characterization of the computational power of shallow quantum circuits combined with classical computation. Specifically, for classes of search problems, we show that the following statements hold, relative to a…

An open question in quantum complexity theory is whether or not the class $\operatorname{MIP}^{co}$, consisting of languages that can be efficiently verified using interacting provers sharing quantum resources according to the quantum…

The "quantum complexity" of a unitary operator measures the difficulty of its construction from a set of elementary quantum gates. While the notion of quantum complexity was first introduced as a quantum generalization of the classical…

We introduce a new quantized enveloping superalgebra $\mathfrak{U}_q{\mathfrak{p}}_n$ attached to the Lie superalgebra ${\mathfrak{p}}_n$ of type $P$. The superalgebra $\mathfrak{U}_q{\mathfrak{p}}_n$ is a quantization of a Lie…

A sufficient condition for a quantum state of a system of spin-1/2 particles (spin-1/2s) to admit a local hidden variable (LHV) description i.e. to be classical is the separability of the density matrix characterizing its state, but not all…