Continuous-variable Cluster States Research Articles

Gaussian tripartite entanglement in the simultaneous measurement of position and momentum

By utilizing the positive partial transpose criterion, we certify Gaussian tripartite entanglement in the dynamics of the simultaneous measurement process of position and momentum raised by Arthurs and Kelly, considering a measurement configuration where the system under examination is a squeezed coherent state. Hence, the system is classified as a fully inseparable. Moreover, using the residual tripartite Rényi-2 entanglement as a quantifier measure, we determine the amount and behavior of the entanglement in the three-mode system as in all its reduced and global mode bipartitions. Besides, we compare the entanglement structure of the Arthurs-Kelly dynamics with that of the set of linear three-mode continuous-variable cluster states. The certification and quantification of entanglement in the simultaneous measurements process of the canonical pair pave the way for integrating this scheme into quantum information processing tasks.

Equivalent noise properties of scalable continuous-variable cluster states

Equivalent noise properties of scalable continuous-variable cluster states

Qumode fusion for continuous-variable cluster states

Qumode fusion for continuous-variable cluster states

Frequency-domain engineering of bright squeezed vacuum for continuous-variable quantum information.

Multimode bright squeezed vacuum is a non-classical state of light hosting a macroscopic photon number while offering promising capacity for encoding quantum information in its spectral degree of freedom. Here, we employ an accurate model for parametric down-conversion in the high-gain regime and use nonlinear holography to design quantum correlations of bright squeezed vacuum in the frequency domain. We propose the design of quantum correlations over two-dimensional lattice geometries that are all-optically controlled, paving the way toward continuous-variable cluster state generation on an ultrafast timescale. Specifically, we investigate the generation of a square cluster state in the frequency domain and calculate its covariance matrix and the quantum nullifier uncertainties, that exhibit squeezing below the vacuum noise level.

Quantum Volume for Photonic Quantum Processors.

Defining metrics for near-term quantum computing processors has been an integral part of the quantum hardware research and development efforts. Such quantitative characteristics are not only useful for reporting the progress and comparing different quantum platforms but also essential for identifying the bottlenecks and designing a technology road map. Most metrics such as randomized benchmarking and quantum volume were originally introduced for circuit-based quantum computers and were not immediately applicable to measurement-based quantum computing (MBQC) processors such as in photonic devices. In this Letter, we close this long-standing gap by presenting a framework to map physical noises and imperfections in MBQC processes to logical errors in equivalent quantum circuits, whereby enabling the well-known metrics to characterize MBQC. To showcase our framework, we study a continuous-variable cluster state based on the Gottesman-Kitaev-Preskill (GKP) encoding as a near-term candidate for photonic quantum computing, and derive the effective logical gate error channels and calculate the quantum volume in terms of the GKP squeezing and photon transmission rate.

Generation of large-scale continuous-variable cluster states multiplexed both in time and frequency domains.

A large-scale continuous variable (CV) cluster state is necessary in quantum information processing based on measurement-based quantum computing (MBQC). Specially, generating a large-scale CV cluster state multiplexed in a time domain is easier to implement and has strong scalability in experiment. Here one-dimensional (1D) large-scale dual-rail CV cluster states multiplexed both in time and frequency domains are parallelly generated, which can be further extended to a three-dimensional (3D) CV cluster state by combining two time-delay nondegenerate optical parametric amplification systems with beam-splitters. It is shown that the number of parallel arrays depends on the corresponding frequency comb lines, the partite number of each array can be very large (million), and the scale of the 3D cluster state can be ultra-large. In addition, the concrete quantum computing schemes of applying the generated 1D and 3D cluster states are also demonstrated. Our schemes may pave the way for fault-tolerant and topologically protected MBQC in hybrid domains, by further combining with efficient coding and quantum error correction.

Spin-induced multipartite steady-state entanglement of motional modes in hexagonal boron nitride membranes

In this paper, we focus on a scheme in which three high-quality-factor mechanical modes of a hexagonal boron nitride (hBN) membrane monolayer are coupled to a common optically addressable spin defect present in the membrane via magnetic field interaction. We show that this coupling induces an effective phonon-phonon interaction in the dispersive regime and under appropriate magnetic field and microwave modulation. We derive the Langevin-Heisenberg equations of motion for vibrational modes to analyze optimal parameter regimes for reaching a physically stable system. We also investigate the effect of coupling strength on purity and entanglement. Our results demonstrate that bipartite and genuinely tripartite steady-state entanglement between different vibrational modes of hBN may be achieved in a broad spectrum of experimental parameters. This study has the potential to enable scalability to be implemented for the generation of two-dimensional continuous-variable cluster states for universal quantum computation.

Measurement-based generation and preservation of cat and grid states within a continuous-variable cluster state

We present an algorithm to reliably generate various quantum states critical to quantum error correction and universal continuous-variable (CV) quantum computing, such as Schrödinger cat states and Gottesman-Kitaev-Preskill (GKP) grid states, out of Gaussian CV cluster states. Our algorithm is based on the Photon-counting-Assisted Node-Teleportation Method (PhANTM), which uses standard Gaussian information processing on the cluster state with the only addition of local photon-number-resolving measurements. We show that PhANTM can apply polynomial gates and embed cat states within the cluster. This method stabilizes cat states against Gaussian noise and perpetuates non-Gaussianity within the cluster. We show that existing protocols for breeding cat states can be embedded into cluster state processing using PhANTM.

Generation of four-mode cluster states based on cascade four-wave mixing process

As a crucial quantum resource for quantum computing and quantum information processing, cluster state has attracted extensive attention due to its unique entanglement properties and rich structures. In this work, we theoretically propose a scheme for generating four-mode entangled states based on cascaded four-wave mixing (FWM) process. The internal entanglement characteristics are studied by using the positivity under partial transposition criterion and eigenmode decomposition. In addition, the output entangled states are reconstructed and optimized by adjusting the relative phase of balanced homodyne detection and postprocessing the signal noise, and finally three four-mode cluster states with different structures are generated. Such a method can effectively reduce the excess noise induced by finite squeezing. Our theoretical results provide a reliable way of generating scalable continuous variable cluster states based on FWM process in atomic ensemble.

Streamlined quantum computing with macronode cluster states

Continuous-variable cluster states allow for fault-tolerant measurement-based quantum computing when used in tandem with the Gottesman-Kitaev-Preskill (GKP) encoding of a qubit into a bosonic mode. For quad-rail-lattice macronode cluster states, whose construction is defined by a fixed, low-depth beam splitter network, we show that a Clifford gate and GKP error correction can be simultaneously implemented in a single teleportation step. We give explicit recipes to realize the Clifford generating set, and we calculate the logical gate-error rates given finite squeezing in the cluster-state and GKP resources. We find that logical error rates of $10^{-2}$-$10^{-3}$, compatible with the thresholds of topological codes, can be achieved with squeezing of 11.9-13.7 dB. The protocol presented eliminates noise present in prior schemes and puts the required squeezing for fault tolerance in the range of current state-of-the-art optical experiments. Finally, we show how to produce distillable GKP magic states directly within the cluster state.

Cluster States from Gaussian States: Essential Diagnostic Tools for Continuous-Variable One-Way Quantum Computing

Continuous-variable (CV) cluster states are a universal quantum computing platform that has experimentally out-scaled qubit platforms by orders of magnitude. Room-temperature implementation of CV cluster states has been achieved with quantum optics by using multimode squeezed Gaussian states. It has also been proven that fault tolerance thresholds for CV quantum computing can be reached at realistic squeezing levels. In this paper, we show that standard approaches to design and characterize CV cluster states can miss entanglement present in the system. Such hidden entanglement may be used to increase the power of a quantum computer but it can also, if undetected, hinder the successful implementation of a quantum algorithm. By a detailed analysis of the structure of Gaussian states, we derive an algorithm that reveals hidden entanglement in an arbitrary Gaussian state and optimizes its use for one-way quantum computing.

Hidden qubit cluster states

Continuous-variable cluster states (CVCSs) can be supplemented with Gottesman-Kitaev-Preskill (GKP) states to form a hybrid cluster state with the power to execute universal, fault-tolerant quantum computing in a measurement-based fashion. As the resource states that comprise a hybrid cluster state are of a very different nature, a natural question arises: Why do GKP states interface so well with CVCSs? To answer this question, we apply the recently introduced subsystem decomposition of a bosonic mode, which divides a mode into logical and gauge-mode subsystems, to three types of cluster state: CVCSs, GKP cluster states, and hybrid continuous-variable (CV)-GKP cluster states. We find that each of these contains a ``hidden'' qubit cluster state across their logical subsystems, which lies at the heart of their utility for measurement-based quantum computing. To complement the analytical approach, we introduce a simple graphical description of these CV-mode cluster states that depicts precisely how the hidden qubit cluster states are entangled with the gauge modes, and we outline how these results would extend to the case of finitely squeezed states. This work provides important insight that is both conceptually satisfying and helps to address important practical issues like when a simpler resource (such as a Gaussian state) can stand in for a more complex one (like a GKP state), leading to more efficient use of the resources available for CV quantum computing.

Subsystem analysis of continuous-variable resource states

Continuous-variable (CV) cluster states are a universal resource for fault-tolerant quantum computation when supplemented with the Gottesman-Kitaev-Preskill (GKP) bosonic code. We generalize the recently introduced subsystem decomposition of a bosonic code [Phys. Rev. Lett. 125, 040501 (2020)], and we use it to analyze CV cluster-state quantum computing with GKP states. Specifically, we decompose squeezed vacuum states and approximate GKP states to reveal their encoded logical information, and we decompose several gates crucial to CV cluster-state quantum computing. Then, we use the subsystem decomposition to quantify damage to the logical information in approximate GKP states teleported through noisy CV cluster states. Each of these studies uses the subsystem decomposition to circumvent complications arising from the full CV nature of the mode in order to focus on the encoded qubit information.

Modular Bosonic Subsystem Codes.

We introduce a framework to decompose a bosonic mode into two virtual subsystems-a logical qubit and a gauge mode. This framework allows the entire toolkit of qubit-based quantum information to be applied in the continuous-variable setting. We give a detailed example based on a modular decomposition of the position basis and apply it in two situations. First, we decompose Gottesman-Kitaev-Preskill grid states and find that the encoded logical state can be damaged due to entanglement with the gauge mode. Second, we identify and disentangle qubit cluster states hidden inside of Gaussian continuous-variable cluster states.

Near-Degenerate Quadrature-Squeezed Vacuum Generation on a Silicon-Nitride Chip.

Squeezed states are a primary resource for continuous-variable (CV) quantum information processing. To implement CV protocols in a scalable and robust way, it is desirable to generate and manipulate squeezed states using an integrated photonics platform. In this Letter, we demonstrate the generation of quadrature-phase squeezed states in the radio-frequency carrier sideband using a small-footprint silicon-nitride microresonator with a dual-pumped four-wave-mixing process. We record a squeezed noise level of 1.34dB (±0.16 dB) below the photocurrent shot noise, which corresponds to 3.09dB (±0.49 dB) of quadrature squeezing on chip. We also show that it is critical to account for the nonlinear behavior of the pump fields to properly predict the squeezing that can be generated in this system. This technology represents a significant step toward creating and manipulating large-scale CV cluster states that can be used for quantum information applications, including universal quantum computing.

Quantum computing with multidimensional continuous-variable cluster states in a scalable photonic platform

Quantum computing is a disruptive paradigm widely believed to be capable of solving classically intractable problems. However, the route toward full-scale quantum computers is obstructed by immense challenges associated with the scalability of the platform, the connectivity of qubits, and the required fidelity of various components. One-way quantum computing is an appealing approach that shifts the burden from high-fidelity quantum gates and quantum memories to the generation of high-quality entangled resource states and high fidelity measurements. Cluster states are an important ingredient for one-way quantum computing, and a compact, portable, and mass producible platform for large-scale cluster states will be essential for the widespread deployment of one-way quantum computing. Here, we bridge two distinct fields---Kerr microcombs and continuous-variable (CV) quantum information---to formulate a one-way quantum computing architecture based on programmable large-scale CV cluster states. The architecture can accommodate hundreds of simultaneously addressable entangled optical modes multiplexed in the frequency domain and an unlimited number of sequentially addressable entangled optical modes in time domain. One-dimensional, two-dimensional, and three-dimensional CV cluster states can be deterministically produced. We note cluster states of at least three dimensions are required for fault-tolerant one-way quantum computing with known error-correction strategies. This architecture can be readily implemented with silicon photonics, opening a promising avenue for quantum computing at a large scale.

Finding the optimal cluster state configuration. Cluster states classification by type of computations

In this paper, we study the transformations that are obtained in one-way quantum computation on continuous-variable cluster states of various configurations. Of all possible cluster configurations, we choose those that are suitable for universal Gaussian operations.

Josephson Array-Mode Parametric Amplifier

We introduce a novel near-quantum-limited amplifier with a large tunable bandwidth and high dynamic range - the Josephson Array Mode Parametric Amplifier (JAMPA). The signal and idler modes involved in the amplification process are realized by the array modes of a chain of 1000 flux tunable, Josephson-junction-based, nonlinear elements. The frequency spacing between array modes is comparable to the flux tunability of the modes, ensuring that any desired frequency can be occupied by a resonant mode, which can further be pumped to produce high gain. We experimentally demonstrate that the device can be operated as a nearly quantum-limited parametric amplifier with 20 dB of gain at almost any frequency within (4-12) GHz band. On average, it has a 3 dB bandwidth of 11 MHz and input 1 dB compression power of -108 dBm, which can go as high as -93 dBm. We envision the application of such a device to the time- and frequency-multiplexed readout of multiple qubits, as well as to the generation of continuous-variable cluster states.

Generation of time-domain-multiplexed two-dimensional cluster state.

Entanglement is the key resource for measurement-based quantum computing. It is stored in quantum states known as cluster states, which are prepared offline and enable quantum computing by means of purely local measurements. Universal quantum computing requires cluster states that are both large and possess (at least) a two-dimensional topology. Continuous-variable cluster states-based on bosonic modes rather than qubits-have previously been generated on a scale exceeding one million modes, but only in one dimension. Here, we report generation of a large-scale two-dimensional continuous-variable cluster state. Its structure consists of a 5- by 1240-site square lattice that was tailored to our highly scalable time-multiplexed experimental platform. It is compatible with Bosonic error-correcting codes that, with higher squeezing, enable fault-tolerant quantum computation.

Robust fault tolerance for continuous-variable cluster states with excess antisqueezing

The immense scalability of continuous-variable cluster states motivates their study as a platform for quantum computing, with fault tolerance possible given sufficient squeezing and appropriately encoded qubits [Menicucci, PRL 112, 120504 (2014)]. Here, we expand the scope of that result by showing that additional anti-squeezing has no effect on the fault-tolerance threshold, removing the purity requirement for experimental continuous-variable cluster-state quantum computing. We emphasize that the appropriate experimental target for fault-tolerant applications is to directly measure 15-17 dB of squeezing in the cluster state rather than the more conservative upper bound of 20.5 dB.