Programmable Continuous-Variable Photonic Quantum Computing in the Time Domain

Quantum computing has been pursued with various hardware platforms and an optical system is one of the most reasonable choices for large-scale computation. In the optical continuous-variable computation scheme, the incorporation of Gaussian gates and a highly nonclassical non-Gaussian state enables universal quantum computation. Although basic technologies for Gaussian gates and non-Gaussian state generation have long been developed, these building blocks have not yet been integrated in a scalable fashion. Here, we integrate them to develop a scalable and programmable optical quantum computing platform that can sequentially perform an essential Gaussian gate, the squeezing gate, on a non-Gaussian input state. The key enablers are a loop-based optical circuit with dynamical and programmable controllability and its time synchronization with the probabilistic non-Gaussian state generation. We verify the deterministic, programmable, and repeatable quantum gates on a typical non-Gaussian state by implementing up to three-step gates. The gates implemented are of such high quality that strong evidence of the nonclassicalities of the states, the negativities of the Wigner functions, are preserved even after multistep gates. This platform is compatible with other non-Gaussian states and can in principle realize large-scale universal quantum computing by incorporating other existing processing technologies. Published by the American Physical Society 2025

Continuous-variable measurement-based quantum computation, which requires deterministically generated large-scale cluster states, is a promising candidate for practical, scalable, universal, and fault-tolerant quantum computation. In this work, based on our compact and scalable scheme of generating a two-dimensional spatiotemporal cluster state, a complete architecture including cluster state preparation, gate implementations, and error correction, is proposed. First, a scheme for generating two-dimensional large-scale continuous-variable cluster state by multiplexing both the temporal and spatial domains is proposed. Then, the corresponding gate implementations by gate teleportation are discussed and the actual gate noise from the generated cluster state is considered. After that, the quantum error correction can be further achieved by utilizing the square-lattice Gottesman-Kitaev-Preskill (GKP) code. Finally, a fault-tolerant quantum computation can be realized by introducing bias into the square-lattice GKP code (to protect against phase-flip errors) and concatenating a repetition code (to handle the residual bit-flip errors), with a squeezing threshold of 12.3 dB. Our work provides a possible option for a complete fault-tolerant quantum computation architecture in the future.

Now that it is possible to achieve measurement and control fidelities for individual quantum bits (qubits) above the threshold for fault tolerance, attention is moving towards the difficult task of scaling up the number of physical qubits to the large numbers that are needed for fault-tolerant quantum computing. In this context, quantum-dot-based spin qubits could have substantial advantages over other types of qubit owing to their potential for all-electrical operation and ability to be integrated at high density onto an industrial platform. Initialization, readout and single- and two-qubit gates have been demonstrated in various quantum-dot-based qubit representations. However, as seen with small-scale demonstrations of quantum computers using other types of qubit, combining these elements leads to challenges related to qubit crosstalk, state leakage, calibration and control hardware. Here we overcome these challenges by using carefully designed control techniques to demonstrate a programmable two-qubit quantum processor in a silicon device that can perform the Deutsch-Josza algorithm and the Grover search algorithm-canonical examples of quantum algorithms that outperform their classical analogues. We characterize the entanglement in our processor by using quantum-state tomography of Bell states, measuring state fidelities of 85-89 per cent and concurrences of 73-82 per cent. These results pave the way for larger-scale quantum computers that use spins confined to quantum dots.

Quantum information and quantum computing offer a new range of possibilities in terms ofnew computing algorithms, the ability to perform new types of operations and make statementsabout information in terms of what it is physically possible to know about a system.Experiments in quantum information and quantum computing have been advancing significantly,especially over the last decade. In optical quantum computing there are two maintypes of experiments that are performed today. They are experiments involving single photonswith information encoded on the polarisation of the photon and experiments involvingstates with Gaussian noise profiles in their quadratures. There appears to be no way toperform the required operations for universal quantum computing using operations whichtake Gaussian states to Gaussian states. Universal quantum computing using single photonsis possible but uses either enormously large non-linearities or a large number of resources.Also, operations which take Gaussian states to non-Gaussian states are not well understoodin general and can often be very difficult to implement.This thesis presents three sources of optical non-Gaussian states which demonstrate someof the interesting properties of these states. First, a scheme for universal quantum computingusing superpositions of coherent states is presented. Error correction and the fault toleranceproperties of this scheme is also explored and compared with current single photon architectures.These gates require superpositions of coherent states as resources and a relativelysimple scheme is shown for how these states may be generated. Next a scheme for distillingnear ideal Gaussian entanglement using non-Gaussian operations is presented. The loss andnoise conditions under which ideal distillation can be achieved are presented. Finally, a verysimple way of generating mixed non-Gaussian states from two Gaussian states is presented.These states are shown to give rise to counter-intuitive results when measuring their entanglementand when analysing their operational ability in terms of teleportation and quantumkey distribution.

Quantum computing is a multidisciplinary field at the intersectionof quantum physics, computer science, and mathematics, aiming to har-ness quantum mechanical phenomena for computational advantage. Thisarticle provides a comprehensive review of both the foundational princi-ples and advanced theoretical models of quantum computing. We beginwith the basic framework of quantum computation, introducing the con-cept of qubits as two-level quantum systems, the linear algebra of Hilbertspaces, Dirac’s bra–ket notation, and the postulates of quantum mechan-ics (state superposition, unitary evolution, and projective measurement).We then discuss quantum logic gates and circuits, highlighting how clas-sical reversible computation principles extend to universal quantum gatesets. Next, we survey key quantum algorithms (from Shor’s factoring toGrover’s searching and beyond) and the complexity-theoretic implicationsof quantum computers, contrasting the class BQP with classical complex-ity classes. We cover the theoretical foundations of quantum error cor-rection and fault tolerance, explaining how quantum information can beprotected from decoherence using redundancy and how fault-tolerant pro-tocols can, in principle, allow scalable quantum computation despite noisyhardware. We then explore advanced models and paradigms of quantumcomputation, including measurement-based quantum computing (one-wayquantum computing), topological quantum computation with anyons, adi-abatic quantum computing and quantum annealing, continuous-variablequantum computing, and related approaches. We also provide an overviewof quantum information theory as it relates to computation, discussingentanglement, quantum entropy, and information-theoretic limits like theHolevo bound. Finally, we review the leading physical implementations(quantum hardware models) of quantum computers—trapped ions, super-conducting circuits, photonic systems, solid-state spin qubits, and oth-ers—outlining the challenges and achievements of each approach.

We present a general, systematic, and efficient method for decomposing any given exponential operator of bosonic mode operators, describing an arbitrary multimode Hamiltonian evolution, into a set of universal unitary gates. Although our approach is mainly oriented towards continuous-variable quantum computation, it may be used more generally whenever quantum states are to be transformed deterministically, e.g., in quantum control, discrete-variable quantum computation, or Hamiltonian simulation. We illustrate our scheme by presenting decompositions for various nonlinear Hamiltonians including quartic Kerr interactions. Finally, we conclude with two potential experiments utilizing offline-prepared optical cubic states and homodyne detections, in which quantum information is processed optically or in an atomic memory using quadratic light-atom interactions.

It has been proven that universal quantum computers based on qubits and classical analog networks both have superTuring capabilities. It is a grand challenge to computer science to prove that the combination of the two, in analog (continuous variable) quantum computing, offers supersuperTuring capability, the best we can achieve. Computing with continuous spins is now the most promising path AQC. Two papers at SPIE2014 described unbreakable quantum codes using continuous spins beyond what traditional qubits allow. To make this real, we must first develop a realistic ability to model and predict the behavior of networks of spin gates which act in part as polarizers. Last year I proposed a triphoton experiment, where three entangled photons go to linear polarizers set to angles θ_a, θ_b and θ_c. Assuming a “collapse of the wave function” yields predictions for the coincidence detection rate, R₃/R₀(θ_a, θ_b, θ_c) significantly different from the prediction of a new family of models based on classical Markov Random Fields (MRF) across space time, even though both yield the same correct prediction in the two-photon case. We cannot expect to predict systems of 100 entangled photons correctly if we cannot even predict three yet. Yanhua Shih is currently performing this experiment, as a first step to demonstrating a new technology to produce 100 entangled photons (collaborating with Scully) and understanding larger systems. I have also developed continuous-time versions of the MRF models and of “collapse of the wave function”, so as to eliminate the need to assume metaphysical observers in general.

Although qubits are the leading candidate for the basic elements in a quantum computer, there are also a range of reasons to consider using higher dimensional qudits or quantum continuous variables (QCVs). In this paper we use a general `quantum variable' formalism to propose a method of quantum computation in which ancillas are used to mediate gates on a well-isolated `quantum memory' register and which may be applied to the setting of qubits, qudits (for $d>2$) or QCVs. More specifically, we present a model in which universal quantum computation may be implemented on a register using only: repeated applications of a single fixed two-body ancilla-register interaction gate, ancillas prepared in a single state, and local measurements of these ancillas. In order to maintain determinism in the computation, adaptive measurements via a classical-feedforward of measurement outcomes are used, with the method similar to that in measurement-based quantum computation (MBQC). We show that our model has the same hybrid quantum-classical processing advantages as MBQC, including the power to implement any Clifford circuit in essentially one layer of quantum computation. In some physical settings, high-quality measurements of the ancillas may be highly challenging or not possible, and hence we also present a globally unitary model which replaces the need for measurements of the ancillas with the requirement for ancillas to be prepared in states from a fixed orthonormal basis. Finally, we discuss settings in which these models may be of practical interest.

Genetically encoded voltage indicators (GEVIs) can measure millisecond-scale subthreshold neural responses with cell type specificity. Here, we successfully expressed, for the first time, a GEVI in excitatory V1 neurons in macaque monkeys. We then used widefield fluorescent imaging to measure V1 dynamics in response to visual stimuli with diverse temporal waveforms and contrasts, and compared these responses to signals measured using a genetically encoded calcium indicator (GECI) and a synthetic voltage-sensitive dye (VSD). When compared to GECI, GEVI captures faster response dynamics, tracks higher temporal frequencies, and responds to lower contrasts. To quantitatively characterize these three signals, we developed a simple nonlinear model that predicts the response dynamics to stimuli with arbitrary temporal waveforms and contrasts. Our results are consistent with the hypothesis that GEVI signals reflect the dynamics of locally summed membrane potentials, thus opening the door for a new class of experiments in behaving primates.

A temporal femtosecond pulse shaping device, based on all-diffractive method, is designed for arbitrary waveform generation. The key components of the device are micro-gratings arranged in line. By changing the period and phase pattern of each grating, the diffraction angle, phase and amplitude of the first order diffraction light can be modulated. Experimental results are consistent well with simulation results, which indicate that arbitrary temporal waveforms can be gained by using micro-gratings array. Additionally, the configuration of the device allows for multiple outputs and can operate over a large wavelength range from ultraviolet to infrared pulse.

One of the biggest challenges to a viable quantum computer with real-world impact is scaling it up to handle large computations. Continuous-variable (CV) cluster states, which are resource states for measurement-based quantum computation, can be made on a vast scale with minimal experimental resources. I will present recent experimental breakthroughs in producing large-scale CV cluster states, and I will illustrate how to use these states for fault-tolerant quantum computation.

We designed, fabricated, and characterized a programmable qudit-based quantum processor on silicon. We implemented several quantum algorithms with qudits, showing the logarithmic speed-up, photon detection rate enhancement and accuracy improvement in the qudit-based quantum information processing.

We designed, fabricated, and characterized a programmable qudit-based quantum processor on silicon and several quantum algorithms were implemented using qudits which shows the logarithmic speed-up, counting rate acceleration and accuracy improvement of the qudit processor.

We introduce a family of Hamiltonian systems for measurement-based quantum computation with continuous variables. The Hamiltonians (i) are quadratic, and therefore two body, (ii) are of short range, (iii) are frustration-free, and (iv) possess a constant energy gap proportional to the squared inverse of the squeezing. Their ground states are the celebrated Gaussian graph states, which are universal resources for quantum computation in the limit of infinite squeezing. These Hamiltonians constitute the basic ingredient for the adiabatic preparation of graph states and thus open new venues for the physical realization of continuous-variable quantum computing beyond the standard optical approaches. We characterize the correlations in these systems at thermal equilibrium. In particular, we prove that the correlations across any multipartition are contained exactly in its boundary, automatically yielding a correlation area law.

A qubus quantum computer can perform a quantum Fourier transform with a linear number of operations. This implies continuous-variable ancilla-driven quantum computation is equivalent to the quantum circuit model plus unbounded fan-out.