Related papers: Negative Quasi-Probability as a Resource for Quant…
We propose a method for classical simulation of finite-dimensional quantum systems, based on sampling from a quasiprobability distribution, i.e., a generalized Wigner function. Our construction applies to all finite dimensions, with the…
Recent results on the non-universality of fault-tolerant gate sets underline the critical role of resource states, such as magic states, to power scalable, universal quantum computation. Here we develop a resource theory, analogous to the…
Consumption of magic states promotes the stabilizer model of computation to universal quantum computation. Here, we propose three different classical algorithms for simulating such universal quantum circuits, and characterize them by…
Identifying necessary and sufficient conditions for universal quantum computing is a long-standing open problem for which contextuality is, perhaps, the only promising solution [Howard et al., Nature 510, 351 (2014)]. To justify this…
Magic state distillation is an important primitive in fault-tolerant quantum computation. The magic states are pure non-stabilizer states which can be distilled from certain mixed non-stabilizer states via Clifford group operations alone.…
Importance sampling based on quasi-probability decomposition is the backbone of many widely used techniques, such as error mitigation, circuit knitting, and, more generally, virtual quantum resource distillation, as it allows one to…
We present the generalization of the CNC formalism, based on closed and noncontextual sets of Pauli observables, to the setting of odd-prime-dimensional qudits. By introducing new CNC-type phase space point operators, we construct a…
Magic states are key ingredients in schemes to realize universal fault-tolerant quantum computation. Theories of magic states attempt to quantify this computational element via monotones and determine how these states may be efficiently…
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…
Negativity in certain quasiprobability representations is a necessary condition for a quantum computational advantage. Here we define a quasiprobability representation exhibiting this property with respect to quantum computations in the…
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…
In [Phys. Rev. A 70, 062101 (2004)] Gibbons et al. defined a class of discrete Wigner functions W to represent quantum states in a finite Hilbert space dimension d. I characterize a set C_d of states having non-negative W simultaneously in…
A web of cohomological facts relates quantum error correction, measurement-based quantum computation, symmetry protected topological order and contextuality. Here we extend this web to quantum computation with magic states. In this…
We establish lower-bounds on the number of resource states, also known as magic states, needed to perform various quantum computing tasks, treating stabilizer operations as free. Our bounds apply to adaptive computations using measurements…
A unification of the set of quasiprobability representations using the mathematical theory of frames was recently developed for quantum systems with finite-dimensional Hilbert spaces, in which it was proven that such representations require…
Quantum computers will provide considerable speedups with respect to their classical counterparts. However, the identification of the innately quantum features that enable these speedups is challenging. In the continuous-variable setting -…
Classical computers can simulate models of quantum computation with restricted input states. The identification of such states can sharpen the boundary between quantum and classical computations. Previous works describe simulable states of…
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 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…
Quantum channels underlie the dynamics of quantum systems, but in many practical settings it is the channels themselves that require processing. We establish universal limitations on the processing of both quantum states and channels,…