It is explained that the efficiently preparable states, device-generated distributions, variationally learned loading, and amortized preparation are required to get advantage from quantum machine learning and close with a checklist for evaluating input-dependent advantage claims.
Abstract
Quantum algorithms are conventionally presented with their input state supplied for free. When the input is classical data, this convention conceals a cost that is frequently larger than the algorithm it precedes. We review what the three standard encodings, such as basis encoding, amplitude encoding, and Grover--Rudolph distribution loading, actually cost once transpiled to a hardware gate set, and argue that the resulting $\Theta(N)$ bound is a counting theorem rather than an engineering limitation that improved hardware will remove. Measured gate counts for a representative loading task are reported: an optimal library implementation requires $247$ CNOT gates at $n=8$ qubits and doubles with each additional qubit, while the classical preprocessing that produces the rotation angles requires reading the entire input vector. We show how this cost eliminates the quadratic advantage of quantum amplitude estimation for Monte Carlo integration, and argue that the same accounting constrains quantum machine learning more broadly: the strong input models that make quantum algorithms fast on classical data also enable classical dequantization, and quantum kernel methods carry a $\Theta(M^2)$ state-preparation cost for the Gram matrix that does not amortize. We explain that the efficiently preparable states, device-generated distributions, variationally learned loading, and amortized preparation are required to get advantage from quantum machine learning and close with a checklist for evaluating input-dependent advantage claims. Executable notebooks reproducing every construction and measurement discussed here are available.
The unitary brick-wall is proposed: a $k-particle fermionic architecture for nearest-neighbor hardware, combining Reconfigurable Beam Splitter gates with interleaved single-qubit phase gates and a non-Gaussian magic-state encoding.
Quantum state preparation is the process of producing a target quantum state that will be used as the input to a quantum circuit. Many quantum algorithms require an input state where amplitudes, phases, or basis probabilities encode problem data, and the cost of preparing this state can be significant in gate count and circuit depth. This review summarizes common goals, assumptions, and methods for quantum state preparation, with emphasis on preparing states from classical vectors, probability distributions, and feature data used in quantum machine learning. We organize approaches by the information they load and by the resources they require, including gate count, circuit depth, qubit overhead, and classical preprocessing. It also compares exact and approximate preparation procedures, and discusses how precision targets affect cost. The review highlights links between families of methods, typical sources of resource estimates, and criteria that help match a preparation method to a task and hardware constraints.
Miguel A. Lisboa, Victor H. F. Brasil, João V. H. Duarte et al.· Anais do I Simpósio Brasilei...· 0 citations
Group Reservoir Computing is introduced, an efficient machine-learning paradigm for learning temporal dynamics whose training reduces to a single linear regression, to reduce the resources required.
F. Caravelli, Roberto Menta, Antonio Sannia· 0 citations
Distributed quantum computation needs to move logical qubits across lossy optical links, yet this transmission layer is usually designed separately from the computation it serves. We treat the two together by recognizing that a measurement-based quantum repeater is a two-dimensional code foliated along the transmission axis, so that the dominant channel loss is concentrated on the transmitted sector while the locally measured qubits are largely spared. Matching a code's distance to this structural asymmetry, we show that a rectangular Bacon-Shor subsystem code transmits a logical qubit markedly more efficiently than transmission-unaware encodings. Over continental distances, its cost-optimal repeater density is about an order of magnitude lower than that of a recent $[[48,6,8]]$ benchmark at comparable transmission rate, and roughly half that of a symmetric code of equal size. Moreover, we extend the framework to a central-to-client round trip in which a code-level, distance-preserving code switch joins the transmission legs to the client's computation, and joint decoding of the heterogeneous syndrome record at the central node lets distributed quantum computation proceed with a decoder-free client.
Wooyeong Song, Sungyeon Kook, Wonhyuk Lee et al.· 0 citations
A Clifford+T quantum circuit construction that approximately implements any classically specified unitary to within error $\epsilon$ and achieves a worst-case $T$-count with leading exponential scaling of $2^{5n/4}$ whenever $\log(1/\epsilon)=\operatorname{poly}(n)$.
We give a sampling problem that is solvable by shallow quantum circuits, hard for polynomial-time classical algorithms under lattice-based assumptions, and efficiently verifiable by a classical computer. The quantum sampler admits two implementations: one uses log-logarithmic-depth quantum circuits with one- and two-qubit gates, i.e., $\mathsf{QNC}^0[\log\log]$ circuits, while the other uses constant-depth quantum circuits with unbounded fan-in gates, i.e., $\mathsf{QAC}^0$ circuits. Our construction can be seen as compiling the Learning with Errors (LWE)-based single-round proof of quantumness of Arabadjieva et al. (2025) to very low depth. The price paid for this compilation is the reliance on less standard, though well-motivated, assumptions: in addition to the lattice knowledge assumption used by Arabadjieva et al. (2025), we require a strengthened variant of the adaptive-hardcore-bit property of LWE, for which we provide supporting evidence. Unlike previous low-depth proofs of quantumness, the quantum computation here requires no mid-circuit measurements or feed-forward: it consists only of running a shallow circuit and sampling from its output distribution. This shows that shallow quantum circuits have sufficient structure to solve certain classically hard tasks whose solutions can be verified efficiently.
Alexandru Gheorghiu· 0 citations
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