Related papers: A Menagerie of Symmetry Testing Quantum Algorithms
Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this paper, we propose quantum algorithms capable of testing whether a Hamiltonian…
Symmetry is a unifying concept in physics. In quantum information and beyond, it is known that quantum states possessing symmetry are not useful for certain information-processing tasks. For example, states that commute with a Hamiltonian…
In quantum computing, knowing the symmetries a given system or state obeys or disobeys is often useful. For example, Hamiltonian symmetries may limit allowed state transitions or simplify learning parameters in machine learning…
Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the…
Symmetry is an important and unifying notion in many areas of physics. In quantum mechanics, it is possible to eliminate degrees of freedom from a system by leveraging symmetry to identify the possible physical transitions. This allows us…
Symmetry is fundamental in the description and simulation of quantum systems. Leveraging symmetries in classical simulations of many-body quantum systems can results in significant overhead due to the exponentially growing size of some…
This paper investigates symmetric composite binary quantum hypothesis testing (QHT), where the goal is to determine which of two uncertainty sets contains an unknown quantum state. While asymptotic error exponents for this problem are…
Identifying symmetries in quantum dynamics, such as identity or time-reversal invariance, is a crucial challenge with profound implications for quantum technologies. We introduce a unified framework combining group representation theory and…
Symmetry is a guiding principle in physics that allows to generalize conclusions between many physical systems. In the ongoing search for new topological phases of matter, symmetry plays a crucial role because it protects topological…
A quantum walker on a graph, prepared in the state $| \psi_{\rm in} \rangle$, e.g. initially localized at node $r_{\rm in}$, is repeatedly probed, with fixed frequency $1/\tau$, to test its presence at some target node $r_{\rm d}$ until the…
The problem of discriminating between many quantum channels with certainty is analyzed under the assumption of prior knowledge of algebraic relations among possible channels. It is shown, by explicit construction of a novel family of…
Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…
The mixedness of one share of a pure bipartite state determines whether the overall state is a separable, unentangled state. Here we consider quantum computational tests of mixedness, and we derive an exact expression of the acceptance…
In this thesis we describe methods for avoiding the detrimental effects of decoherence while at the same time still allowing for computation of the quantum information. The philosophy of the method discussed in the first part of this thesis…
Quantum circuits consisting of random unitary gates and subject to local measurements have been shown to undergo a phase transition, tuned by the rate of measurement, from a state with volume-law entanglement to an area-law state. From a…
Symmetry adaptation, universality, and gate efficiency are central but often competing requirements in quantum algorithms for electronic structure and many-body physics. For example, fully symmetry-adapted universal operator pools typically…
The notion of symmetry is shown to be at the heart of all error correction/avoidance strategies for preserving quantum coherence of an open quantum system S e.g., a quantum computer. The existence of a non-trivial group of symmetries of the…
Group theory is extremely successful in characterizing the symmetries in quantum systems, which greatly simplifies and unifies our treatments of quantum systems. Here we introduce the concept of the symmetry for a quantum Boltzmann machine…
Quantum states may exhibit asymmetry with respect to the action of a given group. Such an asymmetry of states can be considered as a resource in applications such as quantum metrology, and it is a concept that encompasses quantum coherence…
We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better…