18,322 research outputs found
A decoupling approach to the quantum capacity
We give a short proof that the coherent information is an achievable rate for
the transmission of quantum information through a noisy quantum channel. Our
method is to produce random codes by performing a unitarily covariant
projective measurement on a typical subspace of a tensor power state. We show
that, provided the rank of each measurement operator is sufficiently small, the
transmitted data will with high probability be decoupled from the channel's
environment. We also show that our construction leads to random codes whose
average input is close to a product state and outline a modification yielding
unitarily invariant ensembles of maximally entangled codes.Comment: 13 pages, published versio
a lattice perspective
We examine general Gottesman-Kitaev-Preskill (GKP) codes for continuous-variable quantum error correction, including concatenated GKP codes, through the lens of lattice theory, in order to better understand the structure of this class of stabilizer codes. We derive formal bounds on code parameters, show how different decoding strategies are precisely related, propose new ways to obtain GKP codes by means of glued lattices and the tensor product of lattices and point to natural resource savings that have remained hidden in recent approaches. We present general results that we illustrate through examples taken from different classes of codes, including scaled self-dual GKP codes and the concatenated surface-GKP code
Parallel quantum simulation of large systems on small NISQ computers
Tensor networks permit computational and entanglement resources to be concentrated in interesting regions of Hilbert space. Implemented on NISQ machines they allow simulation of quantum systems that are much larger than the computational machine itself. This is achieved by parallelising the quantum simulation. Here, we demonstrate this in the simplest case; an infinite, translationally invariant quantum spin chain. We provide Cirq and Qiskit code that translates infinite, translationally invariant matrix product state (iMPS) algorithms to finite-depth quantum circuit machines, allowing the representation, optimisation and evolution of arbitrary one-dimensional systems. The illustrative simulated output of these codes for achievable circuit sizes is given
Quantum Block and Convolutional Codes from Self-orthogonal Product Codes
We present a construction of self-orthogonal codes using product codes. From
the resulting codes, one can construct both block quantum error-correcting
codes and quantum convolutional codes. We show that from the examples of
convolutional codes found, we can derive ordinary quantum error-correcting
codes using tail-biting with parameters [[42N,24N,3]]_2. While it is known that
the product construction cannot improve the rate in the classical case, we show
that this can happen for quantum codes: we show that a code [[15,7,3]]_2 is
obtained by the product of a code [[5,1,3]]_2 with a suitable code.Comment: 5 pages, paper presented at the 2005 IEEE International Symposium on
Information Theor
Codes for the Quantum Erasure Channel
The quantum erasure channel (QEC) is considered. Codes for the QEC have to
correct for erasures, i. e., arbitrary errors at known positions. We show that
four qubits are necessary and sufficient to encode one qubit and correct one
erasure, in contrast to five qubits for unknown positions. Moreover, a family
of quantum codes for the QEC, the quantum BCH codes, that can be efficiently
decoded is introduced.Comment: 6 pages, RevTeX, no figures, submitted to Physical Review A, code
extended to encode 2 qubits, references adde
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