Related papers: Complexity of quantum circuits via sensitivity, ma…
Quantum computation provides great speedup over its classical counterpart for certain problems. One of the key challenges for quantum computation is to realize precise control of the quantum system in the presence of noise. Control of the…
Quantum Parametric Circuits are constructed as an alternative to reduce the size of quantum circuits, meaning to decrease the number of quantum gates and, consequently, the depth of these circuits. However, determining the optimal circuit…
The theory of matchgates is of interest in various areas in physics and computer science. Matchgates occur in e.g. the study of fermions and spin chains, in the theory of holographic algorithms and in several recent works in quantum…
Recently, the dynamics of quantum systems that involve both unitary evolution and quantum measurements have attracted attention due to the exotic phenomenon of measurement-induced phase transitions. The latter refers to a sudden change in a…
We investigate the emergence of quantum complexity and chaos in doped Clifford circuits acting on qudits of odd prime dimension $d$. Using doped Clifford Weingarten calculus and a replica tensor network formalism, we derive exact results…
Quantum coherence is a central ingredient in quantum physics with several theoretical and technological ramifications. In this work we consider a figure of merit encoding the information on how the coherence generated on average by a…
Gate-based universal quantum computation is formulated in terms of two types of operations: local single-qubit gates, which are typically easily implementable, and two-qubit entangling gates, whose faithful implementation remains one of the…
Matchgates are an especially multiflorous class of two-qubit nearest neighbour quantum gates, defined by a set of algebraic constraints. They occur for example in the theory of perfect matchings of graphs, non-interacting fermions, and…
In this work, we explore the effects of a quantum quench on the circuit complexity for a quenched quantum field theory having weakly coupled quartic interaction. We use the invariant operator method, under a perturbative framework, for…
Quantum magic is a necessary resource for quantum computers to be not efficiently simulable by classical computers. Previous results have linked the amount of quantum magic, characterized by the number of $T$ gates or stabilizer rank, to…
The problem of simulatability of quantum processes using classical resources plays a cornerstone role for quantum computing. Quantum circuits can be simulated classically, e.g., using Monte Carlo sampling techniques applied to…
Entanglement is the defining characteristic of quantum mechanics. Bipartite entanglement is characterized by the von Neumann entropy. Entanglement is not just described by a number, however; it is also characterized by its level of…
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum…
Quantum computers hold unprecedented potentials for machine learning applications. Here, we prove that physical quantum circuits are PAC (probably approximately correct) learnable on a quantum computer via empirical risk minimization: to…
Fault-tolerant quantum computers compose elements of a discrete gate set in order to approximate a target unitary. The problem of minimising the number of gates is known as gate-synthesis. The approximation error is a form of coherent…
We describe a scheme of quantum computation with magic states on qubits for which contextuality is a necessary resource possessed by the magic states. More generally, we establish contextuality as a necessary resource for all schemes of…
Magic refers to the degree of "quantumness" in a system that cannot be fully described by stabilizer states and Clifford operations alone. In quantum computing, stabilizer states and Clifford operations can be efficiently simulated on a…
We introduce the magic hierarchy, a quantum circuit model that alternates between arbitrary-sized Clifford circuits and constant-depth circuits with two-qubit gates ($\textsf{QNC}^0$). This model unifies existing circuit models, such as…
As quantum computing resources remain scarce and error rates high, minimizing the resource consumption of quantum circuits is essential for achieving practical quantum advantage. Here we consider the natural problem of, given a circuit $C$,…
Magic describes the distance of a quantum state to its closest stabilizer state. It is -- like entanglement -- a necessary resource for a potential quantum advantage over classical computing. We study magic, quantified by stabilizer…