Realising and Compressing Quantum Circuits With Quantum Reservoir Computing

Abstract

Quantum computers require precise control over parameters and careful engineering of the underlying physical system. In contrast, neural networks have evolved to tolerate imprecision and inhomogeneity. Here, using a reservoir computing architecture we show how a random network of quantum nodes can be used as a robust hardware for quantum computing. It induces quantum operations by optimising only a single layer of quantum nodes, a key advantage over the traditional neural networks where many layers of neurons have to be optimised. We demonstrate how a single network can induce different quantum gates, including a universal gate set. Moreover, we show that sequences of multiple quantum gates in quantum circuits can be compressed with a single operation, greatly reducing the operation time and complexity. As the key resource is a random network of nodes, with no specific topology or structure, this architecture is a hardware friendly alternative paradigm for quantum computation.

Opportunities in Quantum Reservoir Computing and Extreme Learning Machines

“…As shown in ref. [62], a quantum substrate can also provide a general framework for quantum computing, achieving a universal set of quantum gates and also non‐unitary operations, of interest to simulate open quantum systems. Although this is a prominent quantum task (QQQ) inspired by extreme learning techniques, the model of ref.…”

“…Although this is a prominent quantum task (QQQ) inspired by extreme learning techniques, the model of ref. [62] escapes the basic three‐layer scheme of Figure 1 with random or arbitrarily chosen input mappings. Indeed, in ref.…”

“…Indeed, in ref. [62], the weight optimization involves both the input‐reservoir coupling and the reservoir‐output links, given that the physical input nodes coincide with the output ones. While this kind of mirror architecture is specific of the cited work, we notice that any task whose target is represented by a time series of density matrices would require some tuning of (part of) the Hamiltonian parameters.…”

“…Two suitable candidates to implement spin‐network models [ 33–37,40,52 ] are a) nuclear magnetic resonance in molecules, [ 51 ] and b) trapped ions. [ 75 ] c) State‐of‐the‐art ultracold atomic setups in optical lattices with bosonic and fermionic species are well‐suited for Bose–Hubbard and Fermi–Hubbard discrete models, [ 46,48–50,62 ] respectively. Additionally, other physical implementations are possible, for example, in arrays of quantum dots in semiconductor devices, and in d) coupled superconducting qubits.…”

“…Going beyond classical tasks, discrete‐variable models of fermions, as depicted in Figure 2c, have been introduced to solve non‐temporal quantum tasks. [ 46,50,62 ] The authors of ref. [46] proposed a 2D Fermi‐Hubbard model with nearest‐neighbor couplings as a substrate, where each lattice site is pumped by incoherent excitations, while the input is written in two bosonic modes that are coupled to the reservoir via the dissipative “cascaded formalism.” The whole system is modeled by a Lindblad master equation and the output is built as a function of the fermionic occupation numbers.…”