Pretty good state transfer via adaptive quantum error correction

Abstract

We examine the role of quantum error correction (QEC) in achieving pretty good quantum state transfer over a class of 1-d spin Hamiltonians. Recasting the problem of state transfer as one of information transmission over an underlying quantum channel, we identify an adaptive QEC protocol that achieves pretty good state transfer. Using an adaptive recovery and approximate QEC code, we obtain explicit analytical and numerical results for the fidelity of transfer over ideal and disordered 1-d Heisenberg chains. In the case of a disordered chain, we study the distribution of the transition amplitude, which in turn quantifies the stochastic noise in the underlying quantum channel. Our analysis helps us to suitably modify the QEC protocol so as to ensure pretty good state transfer for small disorder strengths and indicates a threshold beyond which QEC does not help in improving the fidelity of state transfer.

Quantum Error Correction: Noise-Adapted Techniques and Applications

“…In this case, the disorder-averaged worst-case fidelity F 2 min δ is the performance metric, and the noise-adapted Petz recovery is constructed in terms of the disorder-averaged transition amplitude f N r,s (t) δ . It is shown both analytically as well as numerically that for small disorder strengths the disorder-averaged transition amplitude is the same as the no-disorder case [72] and the variance in the transition amplitude is vanishingly small. This makes a convincing case for using the noise-adapted Petz recovery to achieve pretty good state transfer over ideal as well as disordered spin chains.…”

“…Since the underlying quantum channel that arises in the context of state transfer over spin chains is typically not of the Pauli form, a natural question to ask is whether noise-adapted QEC may enable information transfer using spin chains over longer distances. This question was addressed recently [72], where it was shown that pretty good state transfer can be achieved using adaptive QEC protocols on spin chains. We will now briefly describe such a noise-adapted protocol for quantum state transfer over a 1-d Heisenberg chain.…”

“…Since the quantum channel E looks very similar to amplitude-damping channel, the adaptive QEC protocol in [72] picks the 4-qubit code in Eq. ( 3) and the Petz recovery map in Eq.…”

Quantum state transmission through a spin chain in finite-temperature heat baths

“…The near perfect state transfer can also be realized if the couplings are weak at the ends [6,7] or the ends can be dynamically controlled [8]. An adaptive quantum error correction protocol that achieves pretty good state transfer has been studied [9]. It has been shown that the fidelity can be improved by encoding the state on multiple spins [8,10,11].…”