Related papers: Explicit States with Two-sided Long-Range Magic
We introduce the Iterative Clifford Circuit Renormalization (ICCR), a novel technique designed to efficiently handle the dynamics of non-stabilizerness (a.k.a. quantum magic) in generic quantum circuits. ICCR iteratively adjusts the…
Equilibrium statistical ensembles impose stringent constraints on phases of quantum matter. For example, the Mermin-Wagner theorem prohibits long-range order in low-dimensional systems beyond the ground state. Here, we show that quantum…
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…
We study a non-stabilizerness resource theory for operators, which is dual to that describing states. We identify that the stabilizer R\'enyi entropy analog in operator space is a good magic monotone satisfying the usual conditions while…
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…
Quantum Fourier analysis is an important topic in mathematical physics. We introduce a systematic protocol for testing and measuring ``magic'' in quantum states and gates, using a quantum Fourier approach. Magic, as a quantum resource, is…
We introduce a novel measure for the quantum property of nonstabilizerness - commonly known as "magic" - by considering the R\'enyi entropy of the probability distribution associated to a pure quantum state given by the square of the…
We propose a new family of error detecting stabilizer codes with an encoding rate 1/3 that permit a transversal implementation of the pi/8-rotation $T$ on all logical qubits. The new codes are used to construct protocols for distilling…
In this paper, we study the problem of learning an unknown quantum circuit of a certain structure. If the unknown target is an $n$-qubit Clifford circuit, we devise an efficient algorithm to reconstruct its circuit representation by using…
We present exact, closed-form results for the non-stabilizerness of random pure states subject to a U(1) symmetry constraint. Using stabilizer entropy as our non-stabilizerness monotone, we derive the average and the variance for…
In fault-tolerant quantum computing with the surface code, non-Clifford gates are crucial for universal computation. However, implementing these gates using methods like magic state distillation and code switching requires significant…
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…
A fundamental problem in fault-tolerant quantum computation is the tradeoff between universality and dimensionality, exemplified by the the Bravyi-K\"onig bound for $n$-dimensional topological stabilizer codes. In this work, we extend…
Many-body quantum dynamics defined on a spatial lattice and in discrete time -- either as stroboscopic Floquet systems or quantum circuits -- has been an active area of research for several years. Being discrete in space and time, a natural…
The stabiliser formalism plays a central role in quantum computing, error correction, and fault tolerance. Conversions between and verifications of different specifications of stabiliser states and Clifford gates are important components of…
Non-stabilizerness is a key resource for fault-tolerant quantum computation, yet its interplay with entanglement in dynamical settings remains underexplored. We address this by analyzing a well-controlled, analytically tractable setup,…
We investigate the problem of evaluating the output probabilities of Clifford circuits with nonstabilizer product input states. First, we consider the case when the input state is mixed, and give an efficient classical algorithm to…
We present an algorithm for efficiently simulating a quantum circuit in the graph formalism. In the graph formalism, we represent states as a linear combination of graphs with Clifford operations on their vertices. We show how a…
The essence of the famed long-range entanglement as revealed in topologically ordered state is the paradoxical coexistence of short-range correlation and nonlocal information that cannot be removed through constant-depth local quantum…
We introduce a monotone to quantify the amount of non-stabilizerness (or magic for short), in an arbitrary quantum state. The monotone gives a necessary and sufficient criterion for detecting the presence of magic for both pure and mixed…