Scalable architecture for measurement induced squeezed light interferometers

TL;DR

Problem: scaling multimode squeezed-light interferometers is hindered by losses that accumulate with circuit depth. Approach: a measurement-induced architecture shifts programmability to programmable homodyne measurements on time-domain graph states, yielding effective transformations in a shallow, low-loss platform. Contributions: a theoretical framework linking covariance, Williamson, and Bloch–Messiah decompositions to extract effective circuit parameters, simulations comparing measurement strategies and improved expressibility, and experimental demonstrations of 6- and 400-mode interferometers achieving high fidelity and near-Haar unitary statistics. Significance: establishes a scalable route for continuous-variable quantum technologies and a practical path toward NISQ-era quantum advantage.

Abstract

Scalable interferometers lie at the heart of photonic quantum technologies, but their expansion has been fundamentally limited by optical losses that grow with circuit depth. Here, we introduce and experimentally demonstrate a measurement-induced architecture for multimode squeezed-light interferometers that overcomes this barrier. By shifting complexity from deep optical networks to programmable homodyne measurements, we realize effective transformations within a shallow, low-loss platform. We validate the principle with a six-mode device and extend it to a 400-mode interferometer, marking a leap in scale beyond conventional designs. Crucially, this strategy not only enables scalable squeezed light interferometry but also provides a powerful route to the generation of large-scale entangled states - a key requirement for quantum computing, simulation, and communication. Our results establish measurement-induced circuits as a practical pathway toward noisy intermediate-scale quantum (NISQ) applications, and future demonstrations of quantum advantage.

Figures (4)

• Figure 1: Concept of measurement-induced squeezed light interferometers. a) Injecting $N$ single-mode squeezed states of light into a multimode interferometer with beam-splitters $\vec{T}$ and phase shifters $\vec{\phi}$, that implements an arbitrary linear transformation described by an $N\times N$ unitary matrix $V$, results in an entangled Gaussian state that can be described by a graph, b), where nodes and edges represent modes and correlations between them, respectively. c) A different way of obtaining the same graph state is to start from a larger graph state of $M$ modes and perform homodyne measurements on $M-N$ modes. The original correlations and the homodyne basis settings determine the resulting graph. d) The particular scheme we study in this paper consists of generating the initial graph state by injecting a sequence of squeezed states at time intervals $\tau$ into a two-mode, shallow-depth interferometer made up of unbalanced Mach-Zehnder interferometers with delay lengths of $\tau K_i$, for different integers $K_i$. This results in a multimode temporally encoded cluster state Yokoyama13cluster19, as illustrated by the graph in e). By partially measuring out this cluster state with variable homodyne basis settings $\vec{\theta}$, a reduced state corresponding to a graph as in b) is obtained. Note that the in-principle endless cluster state can be reduced to a finite size by $x$-basis measurements that remove correlations Menicucci2011. In our experiments, the input squeezing $\vec{r}_\text{in}$ is constant and $K_1=1$, $K_2=8$.
• Figure 2: Simulated relative deviation of measurement-induced unitaries from reference unitaries. Comparison between two different measurement strategies on an initial 1D cluster state, as illustrated at the top: a straight-forward "linear" measurement pattern (a), vs. a "Knight's distance" (KD) pattern (b). The panels show, for interferometers of sizes $N=8$, $16$ and $32$, the distributions (c-e) and the deviations (f-h) of a set of parametrized states from a random ensemble for different values of $t$ and the average photon number per mode in the output state, $\overline{n}_{pm}$. The inset provides a zoomed-in view of the datapoints corresponding to the KD strategy. Each dataset is generated by uniformly sampling the circuit parameters, with 1000 samples drawn per case, resulting in 1000 parametrized states and 1000 unitaries. The KD approach shows a clear advantage over the linear strategy, though this advantage gradually diminishes as $N$ increases.
• Figure 3: Measurement induced states and corresponding interferometers: five parametrized states and their induced unitaries generated as a result of varying measurement parameters on temporal mode 3 of spatial mode A on a 12 mode (6 temporal modes in A and 6 temporal modes in B) cluster state, demonstrating the ability of the method to induce parametrized interferometers. (a) The respective five different measurement settings applied to the 6 temporal modes. Note that the third temporal mode undergoes varying measurement bases, as highlighted in green. The covariance matrices of the parametrized states thus produced (b) are decomposed to form the unitary matrix whose amplitude (d) and phase elements (e) are shown indexed by the mode numbers of the output modes while the effective induced squeezing that enters the induced interferometers in also shown (c).
• Figure 4: Elements of the random matrix : (a) Amplitude and, (b) phase parts of the unitary that was induced through these random measurements. (c) The probability distribution of amplitude and, (d) phase elements obtained in the experiment with respect to a instance of a numerically generated Haar random matrix and the theoretical prediction are shown here. We report fidelities of 0.997 and 0.999 in the cases of amplitudes and phases obtained, respectively, with respect to samples drawn from the Haar measure which is an improvement over the previous efforts.