Related papers: Characterizing error propagation in quantum circui…
Leakage errors arise when the quantum state leaks out of some subspace of interest, for example, the two-level subspace of a multi-level system defining a computational `qubit' or the logical code space defined by some quantum…
These notes introduce quantum computation and quantum error correction, emphasising the importance of stabilisers and the mathematical foundations in basic Lie theory. We begin by using the double cover map $\mathrm{SU}_2 \rightarrow…
Incoherence in the controlled Hamiltonian is an important limitation on the precision of coherent control in quantum information processing. Incoherence can typically be modelled as a distribution of unitary processes arising from slowly…
Using nuclear magnetic resonance techniques, we experimentally investigated the effects of applying a two bit phase error detection code to preserve quantum information in nuclear spin systems. Input states were stored with and without…
We study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum…
Hardware crosstalk in multi-tenant superconducting quantum computers constitutes a significant security threat, enabling adversaries to inject targeted errors across tenant boundaries. We present the first end-to-end framework for mapping…
Numerical solutions to hyperbolic partial differential equations, involving wave propagations in one direction, are subject to several specific errors, such as numerical dispersion, dissipation or aliasing. In multi-dimensions, where the…
We analyze the notion of quantum coherence in an interference experiment. We let the phase shifts fluctuate according to a given statistical distribution and introduce a decoherence parameter, defined in terms of a generalized visibility of…
Noisy Intermediate-Scale Quantum (NISQ) hardware has unavoidable noises, and crosstalk error is a significant error source. When multiple quantum operations are executed simultaneously, the quantum state can be corrupted due to the…
In this paper, we address the problem of state communication in finite-level quantum systems through noise-affected channels. Our approach is based on a self-consistent theory of decoding inner products associated with the code and error…
Noisy and Intermediate-Scale Quantum, or NISQ, processors are sensitive to noise, prone to quantum decoherence, and are not yet capable of continuous quantum error correction for fault-tolerant quantum computation. Hence, quantum algorithms…
We present a theoretical framework for state-adaptive quantum error correction that bridges the gap between quantum computing and error correction paradigms. By incorporating knowledge of quantum states into the error correction process, we…
The central challenge in building a quantum computer is error correction. Unlike classical bits, which are susceptible to only one type of error, quantum bits ("qubits") are susceptible to two types of error, corresponding to flips of the…
A new pure quantum state, isotropic in spin variables, is defined in an extended spin phase space beyond standard quantum mechanics. It allows to represent the entangled singlet state in separable form. The statistical correlations between…
Error models for quantum computing processors describe their deviation from ideal behavior and predict the consequences in applications. But those processors' experimental behavior -- the observed outcome statistics of quantum circuits --…
The competition between interactions and dissipative processes in a quantum many-body system can drive phase transitions of different order. Exploiting a combination of cluster methods and quantum trajectories, we show how the systematic…
The states needed in a quantum computation are extremely affected by decoherence. Several methods have been proposed to control error spreading. They use two main tools: fault-tolerant constructions and concatenated quantum error correcting…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…
This paper introduces a process framework for debugging quantum circuits, focusing on three distinct types of circuit blocks: Amplitude Permutation, Phase Modulation, and Amplitude Redistribution circuit blocks. Our research addresses the…
We introduce a quasi-probability phase space distribution with two pairs of azimuthal-angular coordinates. This representation is well adapted to describe quantum systems with discrete symmetry. Quantum error correction of states encoded in…