A recently developed representation-theoretic framework for moments of random passive linear-optical circuits provides a systematic route for searching for regimes that unambiguously combine the absence of exponential concentration and lies beyond known efficient classical simulation methods.
Abstract
Passive linear optics is a restricted model of quantum computation, with complexity-theoretic evidence of quantum advantage for sampling tasks and low losses that make it attractive for near-term algorithms. In qubit architectures, a body of work has revealed a close connection between barren plateaus and classical simulability. Whether an analogous tradeoff exists for bosonic systems remains largely unexplored. Building on a recently developed representation-theoretic framework for moments of random passive linear-optical circuits, we characterize the concentration of expectation values for relevant families of particle-number-preserving observables by evaluating their projections into irreducible representations of the unitary group and analyzing their asymptotic scaling. We show that concentration is governed by the misalignment of the projections into irreducible representations of the input state and the observable, giving a unified representation-theoretic interpretation of generalized entanglement and locality in the bosonic setting. We further relate these concentration properties to existing classical simulation techniques, identifying broad classes of trainable observables that admit efficient classical simulation. Conversely, we identify Fock-state inputs and observables that appear to evade exponential concentration while retaining a polynomially large signal component not accessible to known efficient classical simulation methods. The separation is only partial: most of the signal remains classically tractable, and the residual part, while not exponentially suppressed, is small enough that a truncation serves as a classical surrogate with polynomially small error. Our framework nonetheless provides a systematic route for searching for regimes that unambiguously combine the absence of exponential concentration and lies beyond known efficient classical simulation methods.
Variational quantum algorithms are a leading approach to near-term quantum computing, but their scalability can be limited by barren plateaus and the sampling cost of resolving small changes in the loss landscape. Here, we study the trainability of passive linear-optical quantum circuits and introduce a framework based on the ratio of sample variance to circuit variance. This ratio determines the number of circuit samples required to resolve local loss differences and gradients to proportional accuracy. We apply this framework to photon-number observables and identify both trainable and non-trainable regimes. Supported by analytic results and a numerically observed polynomial decay of the circuit variance, we find that fixed-order photon-number polynomials require only polynomially many samples as the system size grows, whereas high-order polynomials and observables based on output probabilities generally require exponentially many samples. Within the trainable regime, we further identify classes of observables in which quantum estimation achieves a polynomial speed-up over multiple classical methods. Within this family, neural network observables provide one practical construction that allow measurement outcomes to be efficiently processed into the desired polynomial. These results establish photonic variational quantum computing as a promising platform for near-term applications.
Alexander Makarovskiy, Adam J. Taylor, Zhenghao Li et al.· 1 citation
Virtual distillation is a promising error-mitigation technique that exploits multiple copies of a noisy quantum state to estimate observables as if measured on a purified state. Although originally introduced in the context of bosonic many-body systems under the name of virtual cooling, its development and applications have largely focused on qubit-based quantum computation. Here, we establish a framework for virtual distillation in bosonic quantum information processing and continuous-variable quantum computing. Building on a diagonalization of cyclic shift operators implemented with passive linear-optical interferometers, we derive experimentally accessible protocols for estimating virtually distilled expectation values of observables relevant to bosonic architectures. In particular, we show how to recover noise-mitigated expectation values of number operators, phase-shift operators, and arbitrary quadratures from multi-copy measurements. For number operators, we further demonstrate the estimation of virtually distilled correlators of arbitrary order through the characteristic function of the photon-number distribution. We apply the framework to states affected by photon loss and dephasing, two of the dominant noise mechanisms in bosonic quantum computation, and quantify the resulting suppression of noise contributions. Our results extend virtual distillation beyond its original setting and provide a practical route toward error-mitigated measurements in bosonic quantum processors using experimentally available linear-optical resources.
Leonardo Finocchiaro, M. Robbio, Diogo Gomes et al.· 0 citations
Quantum processors encode an N-point field in log_2(N) qubits, which renders nonlinear wave equations an important application for quantum simulation. Nonlinear evolution, however, requires the field values themselves, and these are not directly accessible without quantum measurement. Existing algorithms circumvent this measurement through linear embeddings and state copies, thereby obscuring its cost within the truncation order, the auxiliary dimensions, and the state preparation. In order to expose this cost, a hybrid split-step solver is proposed in which the field is measured, updated classically, and reloaded at every step, with all shots and gates accounted for in a single cost-and-error model. Since the entire field is available at every step, a property unavailable to linear approximations in strongly nonlinear regimes, the design of the solver reduces to a budgeting problem over the timestep, the polynomial degree, and the shot count. The coherent kernels of the solver are validated on superconducting hardware. An identical structure and bottleneck govern the viscous Burgers'equation in one and two dimensions. Because every step reads the full field, the quantum cost per step, measured as circuit depth multiplied by measurement shots, exceeds the classical cost with increasing grid size. The framework consequently identifies a coherent, measurement-free nonlinear update as the quantitative target that any end-to-end advantage must meet.
Ziqing Guo, Viraj Dsouza, Alex Khan et al.· 0 citations
Nanomechanical structures have been investigated as a method of achieving long-lived quantum excitations at radio frequencies. Their high quality factors are especially intriguing as a medium for bosonic encoding of quantum information. However, to leading order, mechanical modes typically lack the nonlinearities necessary to achieve interaction between bosonic channels and thus are limited in their ability to scale to the many-qubit regime necessary for practical quantum computing. In this work, we propose and describe an approach for bosonic quantum information processing that uses strain-sensitive solid-state spins as nonlinear elements to produce the relevant nonclassical mechanical states. We outline the architecture required to achieve nearest-neighbor connectivity between mechanical cat-state qubits on-chip, as well as the control and readout architecture required for universal quantum computation. In addition, we show that this architecture can allow for a high spatial density of logical qubits by leveraging both the efficiency of bosonic error correction schemes and the small sizes of the constituent nanomechanical resonators and spin qubits. Finally, we identify the necessary performance metrics that will enable error-correction thresholds at high qubit densities, illuminating a path towards scalable quantum information processing.
H. Raniwala, E. Arnault, Dirk R. Englund et al.· 0 citations
A protocol for approximating the measurement distributions of quantum states, extending beyond standard observable estimation is introduced, and tightened gate complexity bounds for practically relevant systems, including those with k-local interactions, long-tailed matrix ensembles, and conserved quantities are provided.
A. Mazumder, James D. Watson, Samson Wang· 0 citations
Boson sampling demonstrates quantum advantage through the interference of indistinguishable particles, with output probabilities governed by matrix permanents. Realizing it on deterministic, matter-based platforms requires encoding the bosonic modes in finite-dimensional local Hilbert spaces, which introduces a leakage channel absent in linear optics: multi-particle bunching beyond the local truncation $d$. We develop a unified framework for non-interacting sampling on the irreducible representations of compact Lie groups, in which the transition amplitude is the immanant of a submatrix of the single-particle transition matrix, recovering the permanent in the bosonic case. Within this framework we bound the bunching leakage through a Dyson-series analysis: decomposing the correlated many-body leakage operator into independent random matrices and applying non-commutative concentration inequalities, we prove, in a Gaussian model of the transition matrix, that its spectral norm concentrates at $\tilde{O}(\sqrt{n})$ rather than the $O(n)$ worst-case of prior spin-based emulations; the passage to the physical Haar ensemble is reduced to a single submatrix-comparison input, verified at leading order. Exact numerics across local dimensions $d=2$--$5$ indicate that the bound is tight, the Haar-ensemble norm matching the closed form $\sqrt{d(n-d+1)}$ to sub-percent accuracy. This tightens the required mode number from $m=\Omega(n^4)$ to the near-optimal $m=\tilde{\Omega}(n^{1+2/(d-1)})$; for a spin-1 representation ($d=3$) the overhead falls to $m=\tilde{\Omega}(n^2)$, matching the collision-free threshold. The result is independent of particle statistics and applies across finite-dimensional Lie-symmetric architectures, quantifying the spatial resources needed to preserve sampling hardness.
