Related papers: Boolean Functions, Projection Operators and Quantu…
Some new inequalities for the norm and the numerical radius of composite operators generated by a pair of operators are given.
I give a pedagogical account of Shor's nine-bit code for correcting arbitrary errors on single qubits, and I review work that determines when it is possible to maintain quantum coherence by reversing the deleterious effects of open-system…
Alternative partial Boolean structures, implicit in the discussion of classical representability of sets of quantum mechanical predictions, are characterized, with definite general conclusions on the equivalence of the approaches going back…
Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales.…
Identifying a full basis of operators to a given order is key to the generality of Effective Field Theory (EFT) and is by now a problem of known solution in terms of the Hilbert series. The present work is concerned with hidden symmetry in…
Bosonic error correcting codes utilize the infinite dimensional Hilbert space of a harmonic oscillator to encode a qubit. Bosonic rotation codes are characterized by a discrete rotation symmetry in their Wigner functions and include codes…
Energy correlators offer a clean probe of quantum chromodynamics, serving as an ideal laboratory to rigorously investigate non-perturbative power corrections. The recent discovery that linear corrections exhibit a universal anomalous…
Quantum correlations are central to the foundations of quantum physics and form the basis of quantum technologies. Here, our goal is to connect quantum correlations and computation: using quantum correlations as a resource for computation -…
Coherence vectors and correlation matrices are important functions frequently used in physics. The numerical calculation of these functions directly from their definitions, which involves Kronecker products and matrix multiplications, may…
After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about…
In this paper we find the optimal error bound (smallest possible estimate, independent of the starting point) for the linear convergence rate of the simultaneous projection method applied to closed linear subspaces in a real Hilbert space.…
Error-correction codes are central for fault-tolerant information processing. Here we develop a rigorous framework to describe various coding models based on quantum resource theory of superchannels. We find, by treating codings as…
Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes which are tailored…
In this article, we present some new general forms of numerical radius inequalities for Hilbert space operators. The significance of these inequalities follow from the way they extend and refine some known results in this field. Among other…
A general `quantum history theory' can be characterised by the space of histories and by the space of decoherence functionals. In this note we consider the situation where the space of histories is given by the lattice of projection…
We study quasi-exact quantum error correcting codes and quantum computation with them. A quasi-exact code is an approximate code such that it contains a finite number of scaling parameters, the tuning of which can flow it to corresponding…
We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This…
We study the convergence of $Q$-learning with linear function approximation. Our key contribution is the introduction of a novel multi-Bellman operator that extends the traditional Bellman operator. By exploring the properties of this…
In the paper titled "Encoding A Qubit In An Oscillator" Gottesman, Kitaev, and Preskill [quant-ph/0008040] described a method to encode a qubit in the continuous Hilbert space of an oscillator's position and momentum variables. This…
We investigate the properties of the simultaneous projection method as applied to countably infinitely many closed and linear subspaces of a real Hilbert space. We establish the optimal error bound for linear convergence of this method,…