Simulating Hamiltonians in quantum networks: Efficient schemes and complexity bounds

By P. Wocjan, M. Roetteler, Dominik Janzing, T. Beth. 2001

49 citations recorded by the source corpus.

We address the problem of simulating pair-interaction Hamiltonians in n-node quantum networks where the subsystems have arbitrary, possibly different, dimensions. We show that any pair interaction can be used to simulate any other by applying sequences of appropriate local control sequences. Conditions on time optimal simulation are formulated in terms of spectral majorization of matrices characterizing the coupling parameters. Efficient schemes for decoupling and time reversal can be constructed from orthogonal arrays provided that the dimensions of all nodes are equal to the same prime power. Moreover, we consider a specific system of n harmonic oscillators with bilinear interaction. In this case, decoupling can efficiently be achieved using the combinatorial concept of difference schemes. For this type of interaction we present optimal schemes for inversion.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Sahel Ashhab
2. I. Georgescu
3. Franco Nori
4. J. You
5. Shannon Whitlock
6. M. Morgado
7. K. Bliokh
8. Adam Miranowicz

In Computational Theory and Mathematics

1. Sahel Ashhab
2. I. Georgescu
3. Franco Nori

Citations in the corpus

• Quantum Simulation (2013, methodology): “…studied, and several methods have been developed (see, e.g., (Berry et al., 2007; Bravyi et al., 2008; Bremner et al., 2005; Brown et al., 2011; Dodd et al., 2002; Dür et al., 2008; Hastings, 2006; Wang and Zanardi, 2002; Wocjan et al., 2002a,b,c)), but it still remains a difficult problem.”