arXiv subjects

Ashok Ajoy

Publications and source records attributed to Ashok Ajoy.

60 records · Page 4Linked to original sources

arXiv2012

Algorithmic approach to simulate Hamiltonian dynamics and an NMR simulation of Quantum State Transfer

We propose an iterative algorithm to simulate the dynamics generated by any $n$-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator $U$ (unitary) into a product of different time-step unitaries. The algorithm product-decomposes $U$ in a chosen operator basis by identifying a certain symmetry of $U$ that is intimately related to the number of gates in the decomposition. We illustrate the algorithm by first obtaining a polynomial decomposition in the Pauli basis of the $n$-qubit Quantum State Transfer unitary by Di Franco et. al. (Phys. Rev. Lett. 101, 230502 (2008)) that transports quantum information from one end of a spin chain to the other; and then implement it in Nuclear Magnetic Resonance to demonstrate that the decomposition is experimentally viable and well-scaled. We furthur experimentally test the resilience of the state transfer to static errors in the coupling parameters of the simulated Hamiltonian. This is done by decomposing and simulating the corresponding imperfect unitaries.

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arXiv2012

Mixed-state quantum transport in correlated spin networks

Quantum spin networks can be used to transport information between separated registers in a quantum information processor. To find a practical implementation, the strict requirements of ideal models for perfect state transfer need to be relaxed, allowing for complex coupling topologies and general initial states. Here we analyze transport in complex quantum spin networks in the maximally mixed state and derive explicit conditions that should be satisfied by propagators for perfect state transport. Using a description of the transport process as a quantum walk over the network, we show that it is necessary to phase correlate the transport processes occurring along all the possible paths in the network. We provide a Hamiltonian that achieves this correlation, and use it in a constructive method to derive engineered couplings for perfect transport in complicated network topologies.

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arXiv2011

Optimal pulse spacing for dynamical decoupling in the presence of a purely-dephasing spin-bath

Maintaining quantum coherence is a crucial requirement for quantum computation; hence protecting quantum systems against their irreversible corruption due to environmental noise is an important open problem. Dynamical decoupling (DD) is an effective method for reducing decoherence with a low control overhead. It also plays an important role in quantum metrology, where for instance it is employed in multiparameter estimation. While a sequence of equidistant control pulses (CPMG) has been ubiquitously used for decoupling, Uhrig recently proposed that a non-equidistant pulse sequence (UDD) may enhance DD performance, especially for systems where the spectral density of the environment has a sharp frequency cutoff. On the other hand, equidistant sequences outperform UDD for soft cutoffs. The relative advantage provided by UDD for intermediate regimes is not clear. In this paper, we analyze the relative DD performance in this regime experimentally, using solid-state nuclear magnetic resonance. Our system-qubits are 13C nuclear spins and the environment consists of a 1H nuclear spin-bath whose spectral density is close to a normal (Gaussian) distribution. We find that in the presence of such a bath, the CPMG sequence outperforms the UDD sequence. An analogy between dynamical decoupling and interference effects in optics provides an intuitive explanation as to why the CPMG sequence performs superior to any non-equidistant DD sequence in the presence of this kind of environmental noise.

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arXiv2010

Performance comparison of dynamical decoupling sequences for a qubit in a rapidly fluctuating spin-bath

Avoiding the loss of coherence of quantum mechanical states is an important prerequisite for quantum information processing. Dynamical decoupling (DD) is one of the most effective experimental methods for maintaining coherence, especially when one can access only the qubit-system and not its environment (bath). It involves the application of pulses to the system whose net effect is a reversal of the system-environment interaction. In any real system, however, the environment is not static, and therefore the reversal of the system-environment interaction becomes imperfect if the spacing between refocusing pulses becomes comparable to or longer than the correlation time of the environment. The efficiency of the refocusing improves therefore if the spacing between the pulses is reduced. Here, we quantify the efficiency of different DD sequences in preserving different quantum states. We use 13C nuclear spins as qubits and an environment of 1H nuclear spins as the environment, which couples to the qubit via magnetic dipole-dipole couplings. Strong dipole-dipole couplings between the proton spins result in a rapidly fluctuating environment with a correlation time of the order of 100 us. Our experimental results show that short delays between the pulses yield better performance if they are compared with the bath correlation time. However, as the pulse spacing becomes shorter than the bath correlation time, an optimum is reached. For even shorter delays, the pulse imperfections dominate over the decoherence losses and cause the quantum state to decay.

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arXiv2009

Hierarchical Genetic Algorithm Approach to Determine Pulse Sequences in NMR

We develop a new class of genetic algorithm that computationally determines efficient pulse sequences to implement a quantum gate U in a three-qubit system. The method is shown to be quite general, and the same algorithm can be used to derive efficient sequences for a variety of target matrices. We demonstrate this by implementing the inversion-on-equality gate efficiently when the spin-spin coupling constants $J_{12}=J_{23}=J$ and $J_{13}=0$. We also propose new pulse sequences to implement the Parity gate and Fanout gate, which are about 50% more efficient than the previous best efforts. Moreover, these sequences are shown to require significantly less RF power for their implementation. The proposed algorithm introduces several new features in the conventional genetic algorithm framework. We use matrices instead of linear chains, and the columns of these matrices have a well defined hierarchy. The algorithm is a genetic algorithm coupled to a fast local optimizer, and is hence a hybrid GA. It shows fast convergence, and running on a MATLAB platform takes about 20 minutes on a standard personal computer to derive efficient pulse sequences for any target 8X8 matrix $U$.

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arXiv2009

Svetlichny's inequality and genuine tripartite nonlocality in three-qubit pure states

The violation of the Svetlichny's inequality (SI) [Phys. Rev. D, 35, 3066 (1987)] is sufficient but not necessary for genuine tripartite nonlocal correlations. Here we quantify the relationship between tripartite entanglement and the maximum expectation value of the Svetlichny operator (which is bounded from above by the inequality) for the two inequivalent subclasses of pure three-qubit states: the GHZ-class and the W-class. We show that the maximum for the GHZ-class states reduces to Mermin's inequality [Phys. Rev. Lett. 65, 1838 (1990)] modulo a constant factor, and although it is a function of the three tangle and the residual concurrence, large number of states don't violate the inequality. We further show that by design SI is more suitable as a measure of genuine tripartite nonlocality between the three qubits in the the W-class states, and the maximum is a certain function of the bipartite entanglement (the concurrence) of the three reduced states, and only when their certain sum attains a certain threshold value, they violate the inequality.

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