Machine learning method for state preparation and gate synthesis on photonic quantum computers

Abstract

We show how techniques from machine learning and optimization can be used to find circuits of photonic quantum computers that perform a desired transformation between input and output states. In the simplest case of a single input state, our method discovers circuits for preparing a desired quantum state. In the more general case of several input and output relations, our method obtains circuits that reproduce the action of a target unitary transformation. We use a continuous-variable quantum neural network as the circuit architecture. The network is composed of several layers of optical gates with variable parameters that are optimized by applying automatic differentiation using the TensorFlow backend of the Strawberry Fields photonic quantum computer simulator. We demonstrate the power and versatility of our methods by learning how to use shortdepth circuits to synthesize single photons, Gottesman-Kitaev-Preskill states, NOON states, cubic phase gates, random unitaries, cross-Kerr interactions, as well as several other states and gates. We routinely obtain high fidelities above 99% using short-depth circuits, typically consisting of a few hundred gates. The circuits are obtained automatically by simply specifying the target state or gate and running the optimization algorithm.

Using states with a large photon number variance to increase quantum Fisher information in single-mode phase estimation

“…For the case that the photon number distribution is unbounded, on the other hand, we have discussed several particular photon number statistics which show Heisenberg scaling and sub-Heisenberg scaling without requiring nonlinear effects. The states discussed in this work have rarely been experimentally realized [39], but state-of-the-art quantum state engineering technique would enable the generation of an arbitrary photon number superposition via quantum circuit optimization [42][43][44]. In the scenario when a priori probability distribution of the parameter is unknown and the number of measurements is limited, those states may not be useful since they are still Heisenberg-scaling limited with n = N N tot , the total average number of photons being used.…”

“…Therefore, the 0&M state is the optimal state and H 0&M is the upper bound for the QFI within the class of the states having a bounded photon number distribution. The 0&M state has been considered as the so-called ON states in the context of quantum computation [55] and a few schemes for its experimental generation have been proposed [43,56]. The 0&M state has already been discussed as the state showing an arbitrarily large QFI in single-mode phase estimation [31,57], but here we prove, by using the Bhatia-Davis inequality of equation (10), that the 0&M state is the theoretical optimal state exhibiting the maximum photon number variance among the states with bounded photon number distributions.…”

“…Note that H 0&M in the order of 10 5 can be theoretically attained by increasing M even when N is fixed. The 0&M state has been realized up to = M 18 in the harmonic motion of a single trapped ion [39], and the states with higher M can also be realized in quantum optical circuits with current technology [42][43][44].…”

“…It would require the development of quantum technology geared towards engineering states with photon number statistics on demand. Recently, an arbitrary photon number statistics has been shown to be producible with current technology through quantum optical circuits being optimized for a target photon number statistics [40][41][42][43]. Having the ability to prepare such quantum states unlocks their use for various purposes in quantum applications [44].…”

Universal programmable photonic architecture for quantum information processing

“…In the previous section we discussed preparation of arbitrary quantum states or operators by obtaining appropriate phase shifter values to implement an exact decomposition of the desired operation using only singlequbit and nearest-neighbor cσ z gates. In this section, we demonstrate a method, building on our previous work for classical MZI networks [13,14] and on work for continuous-variable quantum neural networks [51], of automatically discovering high-fidelity approximate decompositions of a target operator using a gradient-based optimization approach. As shown in Section IV A 4, these "learned" implementations of quantum operators are often far more compact than an explicit decomposition, allowing for lattices with a fraction of the physical depth.…”