Abstract
We provide a recipe for the digitalization of linear and nonlinear quantum optics in networks of superconducting qubits. By combining digital techniques with boson-qubit mappings, we address relevant problems that are typically considered in analog simulators, such as the dynamical Casimir effect or molecular force fields, including nonlinearities. In this way, the benefits of digitalization are extended in principle to a new realm of physical problems. We present preliminary examples launched in IBM Q 5 Tenerife.
Highlights
Afterdecades of both theoretical and experimental efforts, a new generation of technologies is on the brink of delivering the heralded quantum revolution
An example of the richness offered by the physics of the electromagnetic field is boson sampling [4], namely a computation of the number statistics of the output photons of a linear optics network, which can in principle be implemented in a quantum optical setup, but is widely believed to be intractable by classical means
While the digital quantum simulation of a post-classical boson sampler seems completely out of reach, we discuss the digitalization of all the necessary ingredients for boson sampling, which would enable the digitalization of a few-mode setup
Summary
As shown in [16,17], it is possible to map N bosonic modes containing a maximum number of Np excitations each to N(Np + 1) qubits. We are able to associate an (NP + 1)-qubit quantum state to each Fock state. |NP j ↔ |101112 · · · 0NP j where |n j denotes a quantum state with n bosons in the jth mode. Notice that the state |n j is simulated by a state where out of the NP + 1 qubits that are associated with the jth mode, the only one that is in the state |0 is the nth qubit. N=0 where a pair (n, j) refers to the nth qubit in the chain of qubits representing the jth bosonic mode. Once we have encoded the bosonic Hamiltonian into a suitable qubit-network Hamiltonian and before we enter into the details of examples and applications, let us recall the basic notion of digital quantum simulations, namely the Suzuki–Trotter approximation
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