Related papers: Non-Universality from Conserved Superoperators in …
Quantum circuits with gates (local unitaries) respecting a global symmetry have broad applications in quantum information science and related fields, such as condensed matter theory and quantum thermodynamics. However, despite their…
A problem of universality in simulation of evolution of quantum system and in theory of quantum computations is related with the possibility of expression or approximation of arbitrary unitary transformation by composition of specific…
According to a fundamental result in quantum computing, any unitary transformation on a composite system can be generated using so-called 2-local unitaries that act only on two subsystems. Beyond its importance in quantum computing, this…
According to a well-known result in quantum computing, any unitary transformation on a composite system can be generated using $2$-local unitaries. Interestingly, this universality need not hold in the presence of symmetries. In this paper,…
In this work, we study distributions of unitaries generated by random quantum circuits containing only symmetry-respecting gates. We develop a unified approach applicable to all symmetry groups and obtain an equation that determines the…
Global control offers a promising route to scalable quantum computing. A recent conjecture by Hu et al. (arXiv:2508.19075) proposes that any connected qubit graph equipped with global Ising-type interactions and tunable global transverse…
Universality of local unitary transformations is one of the cornerstones of quantum computing with many applications and implications that go beyond this field. However, it has been recently shown that this universality does not hold in the…
For numerous applications of quantum theory it is desirable to be able to apply arbitrary unitary operations on a given quantum system. However, in particular situations only a subset of unitary operations is easily accessible. This raises…
This paper explores the connection between causality and many-body dynamics by studying the algebraic structure of tri-partite unitaries ('walls') which permanently arrest local operator spreading in their time-periodic evolution. We show…
We study bipartite unitary operators which stay invariant under the local actions of diagonal unitary and orthogonal groups. We investigate structural properties of these operators, arguing that the diagonal symmetry makes them suitable for…
Quantum algorithms may be described by sequences of unitary transformations called quantum gates and measurements applied to the quantum register of n quantum bits, qubits. A collection of quantum gates is called universal if it can be used…
Unitarity of the global evolution is an extremely stringent condition on finite state models in discrete spacetime. Quantum cellular automata, in particular, are tightly constrained. In previous work we proved a simple No-go Theorem which…
Quantum circuits with symmetry-respecting gates have attracted broad interest in quantum information science. While recent work has developed a theory for circuits with Abelian symmetries, revealing important distinctions between Abelian…
We study the apparent tension between locality and unitarity for symmetries in quantum field theory. This emerges in the context of categorical symmetries where symmetry operators are generically non-invertible. We argue that locality…
A quantum circuit is generalized to a nonunitary one whose constituents are nonunitary gates operated by quantum measurement. It is shown that a specific type of one-qubit nonunitary gates, the controlled-NOT gate, as well as all one-qubit…
Any unitary transformation of quantum computational networks is explicitly decomposed, in an exact and unified form, into a sequence of a limited number of one-qubit quantum gates and the two-qubit diagonal gates that have diagonal unitary…
We study the Universality and Membership Problems for gate sets consisting of a finite number of quantum gates. Our approach relies on the techniques from compact Lie groups theory. We also introduce an auxiliary problem called Subgroup…
To generate arbitrary one- and two-qubit gates, the universal decompositions are usually used in quantum computing, and the universality of these decompositions has been demonstrated. However, in realistic experiments, gate errors may…
We revisit the question of universality in quantum computing and propose a new paradigm. Instead of forcing a physical system to enact a predetermined set of universal gates (e.g., single-qubit operations and CNOT), we focus on the…
We present a criterion that serves as the basis for a polynomial-time algorithm to decide whether a finite set of qudit gates exponentiated by some Hamiltonians is universal. Our approach formulates universality in Lie algebraic terms and…