Related papers: Noise Thresholds for Higher Dimensional Systems us…
We identify a novel qudit gate which we call the $\sqrt[d]{Z}$ gate. This is an alternate generalization of the qutrit $T$ gate to any odd prime dimension $d$, in the $d^{\text{th}}$ level of the Clifford hierarchy. Using this gate which is…
A significant problem for current quantum computers is noise. While there are many distinct noise channels, the depolarizing noise model often appropriately describes average noise for large circuits involving many qubits and gates. We…
We define several quantitative measures of the robustness of a quantum gate against noise. Exact analytic expressions for the robustness against depolarizing noise are obtained for all unitary quantum gates, and it is found that the…
We construct a polynomial-time classical algorithm that samples from the output distribution of noisy geometrically local Clifford circuits with any product-state input and single-qubit measurements in any basis. Our results apply to…
With the advent of physical qubits exhibiting strong noise bias, it becomes increasingly relevant to identify which quantum gates can be efficiently implemented on error-correcting codes designed to address a single dominant error type.…
Physical Gottesman-Kitaev-Preskill (GKP) states are inherently noisy as ideal ones would require infinite energy. While this is typically considered as a deficiency to be actively corrected, this work demonstrates that imperfect GKP…
Nonlocality is an essential concept that distinguishes quantum from classical models and has been extensively studied in systems of qubits. For higher-dimensional systems, certain results for their two-level counterpart, like Bell…
We analyse a model for fault-tolerant quantum computation with low overhead suitable for situations where the noise is biased. The basis for this scheme is a gadget for the fault-tolerant preparation of magic states that enable universal…
We introduce the qudit Noisy Stabilizer Formalism, a framework for efficiently describing the evolution of stabilizer states in prime-power dimensions subject to generalized Pauli-diagonal noise under Clifford operations and generalized…
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…
Error correcting codes protect quantum information and form the basis of fault tolerant quantum computing. Leading proposals for fault-tolerant quantum computation require codes with an exceedingly rare property, a transverse non-Clifford…
The Gottesman-Knill theorem states that a Clifford circuit acting on stabilizer states can be simulated efficiently on a classical computer. Recently, this result has been generalized to cover inputs that are close to a coherent…
How much noise can a given quantum state tolerate without losing its entanglement? For qudits of arbitrary dimension, I investigate this question for two noise models: Global white noise, where a depolarizing channel is applied to all…
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…
It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical…
Quantum gates executed on physical hardware are inevitably degraded by environmental noise. While state purification effectively distills static quantum resources, the dynamic execution of quantum algorithms requires a higher-order approach…
Determining the best attainable threshold for qudit magic state distillation is directly related to the question of whether or not contextuality is sufficient for universal quantum computation. We show that the performance of a qudit…
The Gottesman-Kitaev-Preskill (GKP) error correcting code uses a bosonic mode to encode a logical qubit, and has the attractive property that its logical Clifford gates can be implemented using Gaussian unitary gates. In contrast, a direct…
Inevitable interactions with the reservoir largely degrade the performance of non-local gates, which hinders practical quantum computation from coming into existence. Here we experimentally demonstrate a 99.920(7)\%-fidelity controlled-NOT…
One of the main challenges in building a quantum processor is to characterize the environmental noise. Noise characterization can be achieved by exploiting different techniques, such as randomization where several sequences of random…