14 Structure of quantum memory channels

Tomáš Rybár, Mário Ziman, Vladimír Bu_ek

Tomáš Rybár, Mário Ziman, Vladimír Bužek

Durgun Duran, Abdullah Verçin

Yu-Juan Sun, Wei-Min Zhang

It is known that the opening or closing mechanism of a voltage-gated ion channel is triggered by the potential difference across the cell membrane in the nervous system. Based on this picture, we model the ion channel as a nanoscale two-terminal ionic tunneling junction. We apply an external time-varying voltage on the junction to mimic the membrane potential difference in the stimulation of neurons. We derive the non-Markovian quantum Langevin equation from the first principle of quantum mechanics for the ion transport in ion channels, and obtain the ion transport current in terms of quantum tunnelings of ions controlled by the time-varying voltage. We find that the time-varying voltage induces an effective magnetic flux, which causes quantum coherence in ion tunnelings. This effective magnetic flux induces further an oscillatory component to the spectral structure of the ion system, forming a time-dependent quantum memory. Such voltage-induced memory is defined as the active quantum memory, which manifests in the system with a regular oscillatory sideband structure in the ion transport current. The sideband structure demonstrates a multicrossing hysteresis in the current-voltage ( I − V ) curve, responding to the variation of the time-varying voltage (membrane potential difference). We also find that the strength of active quantum memory can be described by the ratio of amplitude and frequency of the time-varying voltage, and can be quantitatively measured through the number of nonzero cross points in the I − V hysteresis and conductance-voltage diagram. Additionally, we explore the temperature dependence of the active quantum memory in such a system. Further, we apply this model to the ion channel system on the biological energy scale. The description of these active quantum memory characteristics provides a quantum mechanical understanding to the underlying mechanism of ion channel dynamics.

Tomáš Rybár

Abstract Quantum memory channels represent a very general, yet simple and comprehensible model for causal processes. As such they have attracted considerable research interest, mostly aimed on their transfer capabilities and structure properties. Most notably it was shown that memory channels can be implemented via physically naturally motivated collision models. We also define the concept of repeatable channels and show that only unital channels can be implemented repeatably with pure memory channels. In the special case of qubit channels we also show that every unital qubit channel has a repeatable implementation. We also briefly explore the possibilities of stroboscopical simulation of channels and show that all random unitary channels can be stroboscopically simulated. Particularly in qubit case, all indivisible qubit channels are also random unitary, hence for qubit all indivisible channels can be stroboscopically simulated. Memory channels also naturally capture the framework of correlated experiments. We develop methods to gather and interpret data obtained in such setting and in detail examine the two qubit case. We also show that for control unitary interactions the measured data will never contradict a simple unitary evolution. Thus no memory effects can be spotted then.

Sitan Chen, Weiyuan Gong

In this work, we consider one of the prototypical tasks for characterizing the structure of noise in quantum devices: estimating eigenvalues of an n -qubit Pauli noise channel. Prior work [Chen , Phys. Rev. A 105, 032435 (2022)] has proved no-go theorems for this task in the practical regime in which one has a limited amount of quantum memory; i.e., any protocol with ≤ 0.99 n ancilla qubits of quantum memory must make exponentially many measurements, provided that it is . Such protocols can only interact with the channel by repeatedly preparing a state, passing it through the channel, and measuring immediately afterward. Surprisingly, in this work we show that protocols with an extremely small amount of quantum memory achieve an exponential advantage for this task. We give a protocol that can estimate any prescribed set of eigenvalues A of a Pauli channel to error ε using only O ( log  log  ( | A | ) / ε 2 ) ancilla qubits, O ~ ( n 2 / ε 2 ) measurements, and O ( n 2 | A | / ε 2 ) queries to the Pauli channel. In contrast, we show that any protocol with zero ancilla—even a concatenating one—must make Ω ( 2 n / ε 2 ) measurements. We also prove that the number of queries cannot be improved significantly: with k ancilla qubits, Ω ( 2 ( n − k ) / 3 ) queries to the channel are necessary to learn all eigenvalues, even for concatenating protocols.