Numerical simulation of continuous variable quantum state preparation is a necessary tool for optimization of existing quantum information processing protocols. A powerful instrument for such simulation is the numerical computation in the Fock state representation. It unavoidably uses an approximation of the infinite-dimensional Fock space by finite complex vector spaces implementable with classical digital computers. In this approximation we analyze the accuracy of several currently available methods for computation of the truncated coherent displacement operator. To overcome their limitations we propose an alternative with improved accuracy based on the standard matrix exponential. We then employ the method in analysis of non-Gaussian state preparation scheme based on coherent displacement of a two mode squeezed vacuum with subsequent photon counting measurement. We compare different detection mechanisms, including avalanche photodiodes, their cascades, and photon number resolving detectors in the context of engineering non-linearly squeezed cubic states and construction of qubit-like superpositions between vacuum and single photon states.
Numerical simulation of continuous variable quantum state preparation is a necessary tool for optimization of existing quantum information processing protocols. A powerful instrument for such simulation is the numerical computation in the Fock state representation. It unavoidably uses an approximation of the infinite-dimensional Fock space by finite complex vector spaces implementable with classical digital computers. In this approximation we analyze the accuracy of several currently available methods for computation of the truncated coherent displacement operator. To overcome their limitations we propose an alternative with improved accuracy based on the standard matrix exponential. We then employ the method in analysis of non-Gaussian state preparation scheme based on coherent displacement of a two mode squeezed vacuum with subsequent photon counting measurement. We compare different detection mechanisms, including avalanche photodiodes, their cascades, and photon number resolving detectors in the context of engineering non-linearly squeezed cubic states and construction of qubit-like superpositions between vacuum and single photon states.
Continuous-variable (CV) quantum computing is a promising candidate for quantum computation because it can, even with one mode, utilize infinite-dimensional Hilbert spaces and can efficiently handle continuous values. Although photonic platforms have been considered as a leading platform for CV computation, hybrid systems that use both qubits and bosonic modes, e.g., superconducting hardware, have shown significant advances because they can prepare non-Gaussian states by utilizing the nonlinear interaction between the qubits and the bosonic modes. However, the size of hybrid hardware is currently restricted. Moreover, the fidelity of the non-Gaussian state is also restricted. This work extends the projective squeezing method to establish a formalism for projecting quantum states onto the states that are unitary-transformed from the squeezed vacuum at the expense of the sampling cost. Based on this formalism, we propose methods for simulating larger quantum devices and projecting states onto the cubic phase state, a typical non-Gaussian state, with a higher squeezing level and higher nonlinearity. To make implementation practical, we can, by leveraging the interactions in hybrid systems of qubits and bosonic modes, apply the smeared projector by using either the linear-combination-of-unitaries or virtual quantum error detection algorithms. We numerically verify the performance of our methods and show that projection can suppress the effect of photon-loss errors.
Abstract Quantum photonic simulators are pivotal for designing and analyzing quantum photonic circuits that utilize both continuous-variable (CV) and discrete-variable (DV) encodings. This review critically examines the transition from Gaussian to non-Gaussian photonic models and the computational overhead that emerges from simulating systems with more than 20 modes or photon numbers exceeding 10 per mode. Gaussian states; such as coherent and squeezed states, are modeled efficiently using first-moment vectors and covariance matrices of dimension 2n×2n 2 n × 2 n , where n is the number of modes. Non-Gaussian elements like the cubic phase gate U=exp(iγx^3) U = exp ( i γ x ˆ 3 ) and photon-subtracted states demand full Fock space representations and scale exponentially with photon number d2 d 2 , where d is the Hilbert space dimension. We analyze simulators including , , and , benchmarking their support for tensor networks (bond dimension D >100), GPU acceleration, thus NVIDIA A100 with 1555 GB/s bandwidth, and SoC implementations such as Edge TPU with 8 TFLOPS. Special focus is given to noise models such as photon loss with transmissivity η , thermal noise modeled with nˉ=1.5 n ¯ = 1.5 , and dark count Poisson distributions ( λ=0.1 λ = 0.1 ). The review underscores scalable techniques and hybrid quantum-classical workflows vital for near-term photonic quantum computing.
Continuous-variable quantum-computing (CVQC) is the most scalable implementation of QC to date but requires non-Gaussian resources to allow exponential speedup and quantum correction, using error encoding such as Gottesman-Kitaev-Preskill (GKP) states. However, GKP state generation is still an experimental challenge. We show theoretically that photon catalysis, the interference of coherent states with single-photon states followed by photon-number-resolved detection, is a powerful enabler for non-Gaussian quantum state engineering such as exactly displaced single-photon states and M-symmetric superpositions of squeezed vacuum (SSV), including squeezed cat states (M=2). By including photon-counting based state breeding, we demonstrate the potential to enlarge SSV states and produce GKP states.
Abstract Conditional measurement schemes, which employ linear optical elements and photon detectors, have recently become powerful tools for generating and enriching nonclassical states in single- and multi-mode scenarios. Here, the nonclassical resourcefulness of a simple single-mode conditional measurement (CM) setup, with a coherent state as one input state, is examined. Studying the output of this setup in the form of displaced qudits (DQ) simplifies the complete characterization of nonclassical resources. The figures of merit of the prepared states are evaluated through quadrature squeezing and some of the non-Gaussian measures such as the Hilbert–Schmidt distance, the quantum relative entropy and the Wigner negativity to identify the squeezing and non-Gaussianity of the states, respectively. The squeezing capacity of the DQ output is compared with the achievable squeezing in finite superposed Fock states, since DQ also constitute a finite-dimensional representation. This optimal squeezing is attained when the detector detects the single photons in the CM setup. All the studied non-Gaussian measures confirm the qualitative agreement that the non-Gaussianity of the setup is limited and does not exceed that of the input number state. The interplay of nonclassical resources between non-Gaussianity and squeezing is exemplified, showing that states exhibiting non-Gaussianity do not exhibit squeezing, and vice versa. In addition, experimental imperfections, such as photon-source impurities and detector inefficiencies, are accommodated to analyze the realistic preparation of DQ. The calculated success probabilities are around 15 % to create the maximally squeezed states under experimental conditions. It demonstrates the potential of nonclassical state generation with minimal nonclassical inputs through the CM scheme.
We introduce a framework for simulating hybrid oscillator-qubit quantum processors on qubit-only systems through position encoding. By encoding continuous-variable position and momentum wave functions into qubit amplitudes, our method efficiently simulates all Gaussian and conditional Gaussian operations -- encompassing the phase-space instruction set (beam splitter, single-qubit rotation, conditional displacement) and extending to squeezing, conditional squeezing, conditional rotation, and conditional beam splitter -- using O(log2(Γ+log(1/ε))) qubit gates per hybrid gate, where Γ is the Fock-level bound and ε is the target precision. This polylogarithmic per-gate complexity represents an exponential improvement over Fock basis encoding approaches, which require exponential quantum or classical resources in the number of qubits per mode. We provide rigorous numerical characterization of quantum Fourier transform errors for Fock-bounded states, enabling precise resource estimation for practical implementations. This work establishes that hybrid oscillator-qubit algorithms can be implemented on qubit processors with polynomial overhead, providing new insights into the computational power trade-offs between discrete-variable and hybrid continuous-discrete-variable quantum computing.
Abstract Continuous-variable quantum-computing is the most scalable implementation of QC to date but requires non-Gaussian resources to allow exponential speedup and quantum correction, using error encoding such as Gottesman–Kitaev–Preskill (GKP) states. However, GKP state generation is still an experimental challenge. We show theoretically that photon catalysis, the interference of coherent states with single-photon states followed by photon-number-resolved detection, is a powerful enabler for non-Gaussian quantum state engineering such as exactly displaced single-photon states and M -symmetric superpositions of squeezed vacuum (SSV), including squeezed cat states ( M = 2). By including photon-counting based state breeding, we demonstrate the potential to enlarge SSV states and produce GKP states.