Abstract
The production of quantum states required for use in quantum protocols & technologies is studied by developing the tools to re-engineer a perfect state transfer spin chain so that a separable input excitation is output over multiple sites. We concentrate in particular on cases where the excitation is superposed over a small subset of the qubits on the spin chain, known as fractional revivals, demonstrating that spin chains are capable of producing a far greater range of fractional revivals than previously known, at high speed. We also provide a numerical technique for generating chains that produce arbitrary single-excitation states, such as the W state.
Highlights
The task of quantum state synthesis lies at the heart of quantum technologies – before any quantum protocol can be run, be it a Bell test [1], quantum key distribution [2], quantum cloning [3,4,5], random number generation [6] or quantum computation [7], a non-trivial quantum resource, such as a Bell state, W -state or GHZ state must be prepared
As perfect state transfer is a special case of state synthesis, with |ψT = |N, it is clear that these conditions are not always sufficient – in that case, it is required that λn,1 = (−1)n+1 λn|ψT when the eigenvectors are ordered by decreasing eigenvalue
Many different cases of fractional revivals can be reengineered from a perfect state transfer chain, meaning that a single excitation can be input at one end of a chain, and the natural dynamics evolve it into the desired superposition of that single excitation across a small number of sites, usually localised at either end of the chain
Summary
The task of quantum state synthesis lies at the heart of quantum technologies – before any quantum protocol can be run, be it a Bell test [1], quantum key distribution [2], quantum cloning [3,4,5], random number generation [6] or quantum computation [7], a non-trivial quantum resource, such as a Bell state, W -state or GHZ state must be prepared. We take the existing constructions for perfect state transfer and re-engineer them to produce arbitrary (one-excitation) quantum states, concentrating on the particular case of so-called fractional revivals wherein the amplitude of the final state is spread over a small number of sites on the chain. These admit the possibility of analysis (Sections 2 and 3), while we provide a widely applicable numerical scheme (Section 5), permitting the creation of W -states and similar, along with a starting point that appears to work well for systems of up to about 50 qubits.
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