Related papers: Quantum magic dynamics in random circuits
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of every physical quantity is evaluated by means of a probability distribution. We study the possibility to describe pure…
We introduce a notion of chirality for generic quantum states. A chiral state is defined as a state which cannot be transformed into its complex conjugate in a local product basis using local unitary operations. We introduce a number of…
Quantum algorithms for quantum chemistry map the dynamics of electrons in a molecule to the dynamics of a coupled spin system. To reach chemical accuracy for interesting molecules, a large number of quantum gates must be applied which…
Although the similarity between non-stabilizer states -- also known as magic states -- in discrete-variable systems and non-Gaussian states in continuous-variable systems has widely been recognized, the precise connections between these two…
Random quantum circuits continue to inspire a wide range of applications in quantum information science and many-body quantum physics, while remaining analytically tractable through probabilistic methods. Motivated by an interest in…
Many proposals for fault-tolerant quantum computation require injection of 'magic states' to achieve a universal set of operations. Some qubit states are above a threshold fidelity, allowing them to be converted into magic states via 'magic…
Entanglement and magic are fundamental resources that capture the complexity of quantum many-body systems. Non-local magic isolates the irreducible nonstabilizerness intrinsically tied to entanglement. However, evaluating this quantity…
Sums play a prominent role in the formalisms of quantum mechanics, be it for mixing and superposing states, or for composing state spaces. Surprisingly, a conceptual analysis of quantum measurement seems to suggest that quantum mechanics…
Quantum circuit compilation comprises many computationally hard reasoning tasks that nonetheless lie inside #$\mathbf{P}$ and its decision counterpart in $\mathbf{PP}$. The classical simulation of general quantum circuits is a core example.…
The use of quantum information in technology promises to supersede the so-called classical devices used nowadays. Understanding what features are inherently non-classical is crucial for reaching better-than-classical performance. This…
We study the classical simulation complexity in both the weak and strong senses, of matchgate (MG) computations supplemented with all combinations of settings involving inclusion of intermediate adaptive or nonadaptive computational basis…
The dependence of quantum algorithms on state fidelity is difficult to characterize analytically and is best explored experimentally as hardware scales and noisy simulations become intractable. While low fidelity states are often…
The measuring process is an external intervention in the dynamics of a quantum system. It involves a unitary interaction of that system with a measuring apparatus, a further interaction of both with an unknown environment causing…
Magic is a quantum resource essential for universal quantum computation and represents the deviation of quantum states from those that can be simulated efficiently using classical algorithms. Using the Stabilizer R\'enyi Entropy (SRE), we…
Isolated atoms as well as molecules at equilibrium are presumed to be simple from the point of view of quantum computational complexity. Here we show that the process of chemical bond formation is accompanied by a marked increase in the…
The property of non-stabiliserness, or ``magic'', is of interest in quantum computing due to its role in developing fault-tolerant quantum algorithms with genuine computational advantage over classical counterparts. There has been much…
Stabilizer states along with Clifford manipulations (unitary transformations and measurements) thereof -- despite being efficiently simulable on a classical computer -- are an important tool in quantum information processing, with…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…
The central philosophy of statistical mechanics (stat-mech) and random-matrix theory of complex systems is that while individual instances are essentially intractable to simulate, the statistical properties of random ensembles obey simple…