Related papers: Efficient classical simulation of Clifford circuit…
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…
Motivated by their necessity for most fault-tolerant quantum computation schemes, we formulate a resource theory for magic states. We first show that robustness of magic is a well-behaved magic monotone that operationally quantifies the…
Quantum error correction and fault-tolerance have provided the possibility for large scale quantum computations without a detrimental loss of quantum information. A very natural class of gates for fault-tolerant quantum computation is the…
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…
Stabilizer states, which are also known as the Clifford states, have been commonly utilized in quantum information, quantum error correction, and quantum circuit simulation due to their simple mathematical structure. In this work, we apply…
The study of the boundary between classically simulable and computationally complex quantum dynamics is fundamental to understanding which physical resources may enable enhanced information-processing capabilities. We investigate this…
Nonstabilizerness, or `magic', is a critical quantum resource that, together with entanglement, characterizes the non-classical complexity of quantum states. Here, we address the problem of quantifying the average nonstabilizerness of…
We provide practical and powerful schemes for learning many properties of an unknown n-qubit quantum state using a sparing number of copies of the state. Specifically, we present a depth-modulated randomized measurement scheme that…
The approximate stabilizer rank of a quantum state is the minimum number of terms in any approximate decomposition of that state into stabilizer states. Bravyi and Gosset showed that the approximate stabilizer rank of a so-called "magic"…
A defining feature in the field of quantum computing is the potential of a quantum device to outperform its classical counterpart for a specific computational task. By now, several proposals exist showing that certain sampling problems can…
Non-stabilizerness, alongside entanglement, is a crucial ingredient for fault-tolerant quantum computation and achieving a genuine quantum advantage. Despite recent progress, a complete understanding of the generation and thermalization of…
While quantum computing can accomplish tasks that are classically intractable, the presence of noise may destroy this advantage in the absence of fault tolerance. In this work, we present a classical algorithm that runs in…
We introduce the Clifford entropy, a measure of how close an arbitrary unitary is to a Clifford unitary, which generalizes the stabilizer entropy for states. We show that this quantity vanishes if and only if a unitary is Clifford, is…
We investigate the dynamics of nonstabilizerness - also known as `magic' - in monitored quantum circuits composed of random Clifford unitaries and local projective measurements. For measurements in the computational basis, we derive an…
Random quantum circuits are commonly viewed as hard to simulate classically. In some regimes this has been formally conjectured, and there had been no evidence against the more general possibility that for circuits with uniformly random…
Improving the simulation of quantum circuits on classical computers is important for understanding quantum advantage and increasing development speed. In this paper, we explore a new way to express stabilizer states and further improve the…
Understanding the boundary between classical simulatability and the power of quantum computation is a fascinating topic. Direct simulation of noisy quantum computation requires solving an open quantum many-body system, which is very costly.…
Quasiprobability representation is an important tool for analyzing a quantum system, such as a quantum state or a quantum circuit. In this work, we propose classical algorithms specialized for approximating outcome probabilities of a linear…
We devise a classical algorithm which efficiently computes the quantum expectation values arising in a class of continuous variable quantum circuits wherein the final quantum observable | after the Heisenberg evolution associated with the…
In this work, we introduce a new circuit optimization technique to reduce the number of T gates in Clifford+T circuits by treating T gates conjugated by Clifford gates as $\frac{\pi}{4}$-rotations around Pauli operators. The tested…