2,677 research outputs found
Multi-Error-Correcting Amplitude Damping Codes
We construct new families of multi-error-correcting quantum codes for the
amplitude damping channel. Our key observation is that, with proper encoding,
two uses of the amplitude damping channel simulate a quantum erasure channel.
This allows us to use concatenated codes with quantum erasure-correcting codes
as outer codes for correcting multiple amplitude damping errors. Our new codes
are degenerate stabilizer codes and have parameters which are better than the
amplitude damping codes obtained by any previously known construction.Comment: 5 pages. Submitted to ISIT 201
Optimal quantum codes for preventing collective amplitude damping
Collective decoherence is possible if the departure between quantum bits is
smaller than the effective wave length of the noise field. Collectivity in the
decoherence helps us to devise more efficient quantum codes. We present a class
of optimal quantum codes for preventing collective amplitude damping to a
reservoir at zero temperature. It is shown that two qubits are enough to
protect one bit quantum information, and approximately qubits are enough to protect qubit information when is large.
For preventing collective amplitude damping, these codes are much more
efficient than the previously-discovered quantum error correcting or avoiding
codes.Comment: 14 pages, Late
Permutation-invariant constant-excitation quantum codes for amplitude damping
The increasing interest in using quantum error correcting codes in practical devices has heightened the need for designing quantum error correcting codes that can correct against specialized errors, such as that of amplitude damping errors which model photon loss. Although considerable research has been devoted to quantum error correcting codes for amplitude damping, not so much attention has been paid to having these codes simultaneously lie within the decoherence free subspace of their underlying physical system. One common physical system comprises of quantum harmonic oscillators, and constant-excitation quantum codes can be naturally stabilized within them. The purpose of this paper is to give constant-excitation quantum codes that not only correct amplitude damping errors, but are also immune against permutations of their underlying modes. To construct such quantum codes, we use the nullspace of a specially constructed matrix based on integer partitions
Approximate quantum error correction for generalized amplitude damping errors
We present analytic estimates of the performances of various approximate
quantum error correction schemes for the generalized amplitude damping (GAD)
qubit channel. Specifically, we consider both stabilizer and nonadditive
quantum codes. The performance of such error-correcting schemes is quantified
by means of the entanglement fidelity as a function of the damping probability
and the non-zero environmental temperature. The recovery scheme employed
throughout our work applies, in principle, to arbitrary quantum codes and is
the analogue of the perfect Knill-Laflamme recovery scheme adapted to the
approximate quantum error correction framework for the GAD error model. We also
analytically recover and/or clarify some previously known numerical results in
the limiting case of vanishing temperature of the environment, the well-known
traditional amplitude damping channel. In addition, our study suggests that
degenerate stabilizer codes and self-complementary nonadditive codes are
especially suitable for the error correction of the GAD noise model. Finally,
comparing the properly normalized entanglement fidelities of the best
performant stabilizer and nonadditive codes characterized by the same length,
we show that nonadditive codes outperform stabilizer codes not only in terms of
encoded dimension but also in terms of entanglement fidelity.Comment: 44 pages, 8 figures, improved v
Linear programming bounds for quantum amplitude damping codes
Given that approximate quantum error-correcting (AQEC) codes have a
potentially better performance than perfect quantum error correction codes, it
is pertinent to quantify their performance. While quantum weight enumerators
establish some of the best upper bounds on the minimum distance of quantum
error-correcting codes, these bounds do not directly apply to AQEC codes.
Herein, we introduce quantum weight enumerators for amplitude damping (AD)
errors and work within the framework of approximate quantum error correction.
In particular, we introduce an auxiliary exact weight enumerator that is
intrinsic to a code space and moreover, we establish a linear relationship
between the quantum weight enumerators for AD errors and this auxiliary exact
weight enumerator. This allows us to establish a linear program that is
infeasible only when AQEC AD codes with corresponding parameters do not exist.
To illustrate our linear program, we numerically rule out the existence of
three-qubit AD codes that are capable of correcting an arbitrary AD error.Comment: 5 page
New class of quantum error-correcting codes for a bosonic mode
We construct a new class of quantum error-correcting codes for a bosonic mode
which are advantageous for applications in quantum memories, communication, and
scalable computation. These 'binomial quantum codes' are formed from a finite
superposition of Fock states weighted with binomial coefficients. The binomial
codes can exactly correct errors that are polynomial up to a specific degree in
bosonic creation and annihilation operators, including amplitude damping and
displacement noise as well as boson addition and dephasing errors. For
realistic continuous-time dissipative evolution, the codes can perform
approximate quantum error correction to any given order in the timestep between
error detection measurements. We present an explicit approximate quantum error
recovery operation based on projective measurements and unitary operations. The
binomial codes are tailored for detecting boson loss and gain errors by means
of measurements of the generalized number parity. We discuss optimization of
the binomial codes and demonstrate that by relaxing the parity structure, codes
with even lower unrecoverable error rates can be achieved. The binomial codes
are related to existing two-mode bosonic codes but offer the advantage of
requiring only a single bosonic mode to correct amplitude damping as well as
the ability to correct other errors. Our codes are similar in spirit to 'cat
codes' based on superpositions of the coherent states, but offer several
advantages such as smaller mean number, exact rather than approximate
orthonormality of the code words, and an explicit unitary operation for
repumping energy into the bosonic mode. The binomial quantum codes are
realizable with current superconducting circuit technology and they should
prove useful in other quantum technologies, including bosonic quantum memories,
photonic quantum communication, and optical-to-microwave up- and
down-conversion.Comment: Published versio
High Performance Single-Error-Correcting Quantum Codes for Amplitude Damping
Original manuscript July 29, 2009We construct families of high performance quantum amplitude damping codes. All of our codes are nonadditive and most modestly outperform the best possible additive codes in terms of encoded dimension. One family is built from nonlinear error-correcting codes for classical asymmetric channels, with which we systematically construct quantum amplitude damping codes with parameters better than any prior construction known for any block length n ≥ 8 except n=2r-1. We generalize this construction to employ classical codes over GF(3) with which we numerically obtain better performing codes up to length 14. Because the resulting codes are of the codeword stabilized (CWS) type, conceptually simple (though potentially computationally expensive) encoding and decoding circuits are available
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