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arXiv:2201.11666

Efficient transfer of entanglement along a qubit chain in the presence of thermal fluctuations

Gourab Das, Rangeet Bhattacharyya

Published Jan 27, 2022• 0 citations
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Abstract

Quantum communications require efficient implementations of quantum state transportation with high fidelity. Here, we consider the transport of entanglement along a chain of qubits. A series of SWAP operations involving successive pairs of qubits can transport entanglement along the chain. We report that the fidelity of the abovementioned gate has a maximum value corresponding to an optimum value of the drive amplitude in the presence of drive-induced decoherence. To incorporate environmental effect, we use a previously reported fluctuation-regulated quantum master equation [A. Chakrabarti and R. Bhattacharyya, Phys. Rev. A 97, 063837 (2018)]. The existence of an optimum drive amplitude implies that these series of SWAP operations on open quantum systems would have an optimal transfer speed of the entanglement.

DOI
10.48550/arxiv.2201.11666

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Quantum communications require efficient implementations of quantum state transportation with high fidelity. Here, we consider the transport of entanglement along a chain of qubits. A series of SWAP operations involving successive pairs of qubits can transport entanglement along the chain. We report that the fidelity of the abovementioned gate has a maximum value corresponding to an optimum value of the drive amplitude in the presence of drive-induced decoherence. To incorporate environmental effect, we use a previously reported fluctuation-regulated quantum master equation [A. Chakrabarti and R. Bhattacharyya, Phys. Rev. A 97, 063837 (2018)]. The existence of an optimum drive amplitude implies that these series of SWAP operations on open quantum systems would have an optimal transfer speed of the entanglement.
Efficient implementation of quantum algorithms requires single- or multiple-qubit gates with high fidelity. Here we report that the fidelity of gate operations on open quantum systems has a maximum value corresponding to an optimum value of the drive amplitude in the presence of drive-induced decoherence. To demonstrate this, we use a previously reported fluctuation-regulated quantum master equation [A. Chakrabarti and R. Bhattacharyya, Phys. Rev. A 97, 063837 (2018)]. The fidelity is found to be a function of the drive-induced dissipative terms as well as the relaxation terms arising from the qubit-environment coupling; as a result, it behaves nonmonotonically with the drive amplitude. The existence of an optimum drive amplitude implies that the qubit gate operations on open quantum systems would have an optimal clock speed. We demonstrate the universality of the results for the gate operations on single- and multiple-qubit gates.
Efficient implementation of quantum algorithms requires single- or multi-qubit gates with high fidelity. We use a recently reported thermal fluctuation-regulated quantum master equation to estimate the fidelity of single-qubit gates on open quantum systems. We show that the fidelity is a function of the drive-induced dissipative terms as well as the relaxation terms arising from the qubit-environment coupling; as a result, it behaves non-monotonically with the drive-amplitude. The calculated fidelity is found to have a maximum corresponding to an optimum value of the drive-amplitude. Therefore, the highest fidelity of the single-qubit operations on open quantum systems would require an optimal clock speed. The arguments are also extended to multi-qubit systems.
We investigate the fidelity of Grover's search algorithm by implementing it on an open quantum system. In particular, we study with what accuracy one can estimate that the algorithm would deliver the searched state. In reality, every system has some influence of its environment. We include the environmental effects on the system dynamics by using a recently reported fluctuation-regulated quantum master equation (FRQME). The FRQME indicates that in addition to the regular relaxation due to system-environment coupling, the applied drive also causes dissipation in the system dynamics. As a result, the fidelity is found to depend on both the drive-induced dissipative terms and the relaxation terms and we find that there exists a competition between them, leading to an optimum value of the drive amplitude for which the fidelity becomes maximum. For efficient implementation of the search algorithm, precise knowledge of this optimum drive amplitude is essential.
We consider the ``transport'' of the state of a spin across a Heisenberg-coupled spin chain via the use of repeated SWAP gates, starting with one of two states---one in which the leftmost spin is down and the others up, and one in which the leftmost two spins are in a singlet state (i.e., they are entangled), and the others are again all up. More specifically, we transport the state of the leftmost spin in the first case and the next-to-leftmost spin in the second to the other end of the chain, and then back again. We accomplish our SWAP operations here by increasing the exchange coupling between the two spins that we operate on from a base value JJJ to a larger value JSWAP{J}_{\text{SWAP}}JSWAP​ for a time $t=\ensuremath{\pi}\ensuremath{\hbar}/4{J}_{\text{SWAP}}$. We determine the fidelity of this sequence of operations in a number of situations---one in which only nearest-neighbor coupling exists between spins and there is no magnetic dipole-dipole coupling or noise (the most ideal case), one in which we introduce next-nearest-neighbor coupling, but none of the other effects, and one in which all of these effects are present. In the last case, the noise is assumed to be quasistatic, i.e., the exchange couplings are each drawn from a Gaussian distribution, truncated to only nonnegative values. We plot the fidelity as a function of JSWAP{J}_{\text{SWAP}}JSWAP​ to illustrate various effects, namely crosstalk due to coupling to other spins, as well as noise, that are detrimental to our ability to perform a SWAP operation. Our theory should be useful to the ongoing experimental efforts in building semiconductor-based spin quantum computer architectures.
We consider the transfer of continuous-variable entangled states in coupled oscillator chains embedded in a generic environment. We demonstrate high-fidelity transfer via optimal control in two configurations-a linear chain and an X-shaped chain. More specifically, we use the Krotov optimization algorithm to design control fields that achieve the desired state transfer. Under environmental memory effects, the Krotov algorithm needs to be modified, since the dissipative terms in non-Markovian dynamics are generally governed by the time-dependent system Hamiltonian. Remarkably, we can achieve high-fidelity transfer by simply tuning the frequencies of the oscillators while keeping the coupling strength constant, even in the presence of open-system effects. For the system under consideration, we find that quantum memory effects can aid in the transfer of entanglement and show improvement over the memoryless case. In addition, it is possible to target a range of entangled states, making it unnecessary to know the parameters of the initial state beforehand.
High-quality quantum-state and entanglement transfer can be achieved in an unmodulated spin bus operating in the ballistic regime, which occurs when the endpoint qubits A and B are nonperturbatively coupled to the chain by a suitable exchange interaction j 0 . Indeed, the transition amplitude characterizing the transfer quality exhibits a maximum for a finite optimal value j opt 0 ( N ), where N is the channel length. We show that j opt 0 ( N ) scales as N −1/6 for large N and that it ensures a high-quality entanglement transfer even in the limit of arbitrarily long channels, almost independently of the channel initialization. For instance, for any chain length the average quantum-state transmission fidelity exceeds 90% and decreases very little in a broad neighbourhood of j opt 0 ( N ). We emphasize that, taking the reverse point of view, should j 0 be experimentally constrained, high-quality transfer can still be obtained by adjusting the channel length to its optimal value.