In situ characterization of linear-optical networks in randomized boson sampling

Abstract

We introduce a method for efficient, in situ characterization of linear-optical networks (LONs) in randomized boson-sampling (RBS) experiments. We formulate RBS as a distributed task between two parties, Alice and Bob, who share two-mode squeezed-vacuum states. In this protocol, Alice performs local measurements on her modes, either photon counting or heterodyne. Bob implements and applies to his modes the LON requested by Alice; at the output of the LON, Bob performs photon counting, the results of which he sends to Alice via classical channels. In the ideal situation, when Alice does photon counting, she obtains from Bob samples from the probability distribution of the RBS problem, a task that is believed to be classically hard to simulate. When Alice performs heterodyne measurements, she converts the experiment to a problem that is classically efficiently simulable, but more importantly, enables her to characterize a lossy LON on the fly, without Bob's knowing. We introduce and calculate the fidelity between the joint states shared by Alice and Bob after the ideal and lossy LONs as a measure of distance between the two LONs. Using this measure, we obtain an upper bound on the total variation distance between the ideal probability distribution for the RBS problem and the probability distribution achieved by a lossy LON. Our method displays the power of the entanglement of the two-mode squeezed-vacuum states: the entanglement allows Alice to choose for each run of the experiment between RBS and a simple characterization protocol based on first-order coherence. Alice Classical channel Bob SPDC Classical channel SPDC SPDC LON Alice Bob C Q C Q C Q Q Q Q FIG. 1: M two-mode squeezed-vacuum states with the same squeezing parameter are generated by SPDC sources and shared between Alice and Bob. Bob inputs his modes to the LON, makes photon-counting measurements at the output of the LON, and sends the outcomes to Alice via a classical channel. Alice uses photon-counting measurements, denoted by Q, for the sampling runs of the RBS problem and makes heterodyne measurements, denoted by C, for characterizing Bob's LON. Because of the entanglement shared between the two parties, Alice can switch from a problem, based on photon counting, that is classically hard and not useful for characterization to a problem, based on heterodyne measurements, that is classically efficiently simulable and can be used for characterization.

Characterization of multimode linear optical networks

“…further refinement for reconstructing the U matrix in the presence of internal unbalanced losses. 41 The other method proposed in Ref. 30, based on classical intensity measurements, requires phase stability within the measurement time to estimate matrix phases, since these values are extracted from first-order correlation functions.…”

“…One of the main constraints of such an approach is the requirement of measurement with quantum light. Recently, a further method that exploits quantum light probes, such as two-mode squeezed states, and single-photon counting combined with heterodyne measurements, provided further refinement for reconstructing the U matrix in the presence of internal unbalanced losses 41 …”

Reframing SU(1,1) Interferometry

“…Though the example is drawn from my own work, I emphasize that none of the material is original to this paper. The example deals with in situ characterization of a passive linear optical network used for randomized boson sampling and is work done with Saleh Rahimi-Keshari and Sima Baghbanzadeh and reported fully in [46], which the reader should consult for a complete exposition. Fig.…”

“…IV, the goal is not high sensitivity in a single shot, but rather reliable detection or characterization of a persistent disturbance over many trials by taking advantage of the modal entanglement within an SU (1,1) interferometer. This scenario is illustrated by an example from my own recent work, a protocol [46] for characterizing a lossy, passive linear optical network in randomized boson sampling [47].…”

Validation tests for GBS quantum computers using grouped count probabilities

“…An analysis of sampling errors generated from increased photon-number-resolving correlation order is given, as normally-ordered positive-P phase-space representations have no vacuum noise, and are often most efficient in simulating photo-detection. Due to its greatly reduced sampling errors, meaning that exponentially fewer samples are needed, we show that the positive-P method [37] is applicable to existing large-scale datasets, and is exponentially faster than proposed non-normally ordered methods [36,38]. These, however, are very useful for analyzing multipartite entanglement, in which case the primary data generally comes from quadrature measurements [22].…”