Accounting for resources is the central issue in computational efficiency. We point out physical constraints implicit in information readout that have been overlooked in classical computing. The basic particle-counting mode of read-out sets a lower bound on the resources needed to implement a quantum computer. As a consequence, computers based on classical waves are as efficient as those based on single quantum particles.
Accounting for resources is the central issue in computational efficiency. We point out physical constraints implicit in information readout that have been overlooked in classical computing. The basic particle-counting mode of read-out sets a lower bound on the resources needed to implement a quantum computer. As a consequence, computers based on classical waves are as efficient as those based on single quantum particles.
The primary resource for quantum computation is the Hilbert-space dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources. Avoiding a demand for an exponential amount of these resources places a fundamental constraint on the systems that are suitable for scalable quantum computation. To be scalable, the number of degrees of freedom in the computer must grow nearly linearly with the number of qubits in an equivalent qubit-based quantum computer. These considerations rule out quantum computers based on a single particle, a single atom, or a single molecule consisting of a fixed number of atoms or on classical waves manipulated using the transformations of linear optics.
Constraint Physical Computing (CPC) asks whether engineered physical dynamics can perform useful computation directly from declarative constraint specifications. This white paper develops a feasibility, native-advantage, and validation roadmap for CPC on superconducting bosonic hardware, including cat-qubit, GKP, and multimode architectures. The central physical proposal combines stabilization dynamics protecting an admissible bosonic manifold with answer-independent, problem-dependent open-system dynamics intended to produce a declared semantic terminal sector. Rather than assuming that such a construction is computationally advantageous, the paper defines the physical, semantic, and resource-accounting conditions required to test it experimentally. These include bounded leakage, measurable convergence, control precision, robust referenced readout, fixed decoding, answer independence, provenance, and independent semantic validation. A Levinthal-Class Benchmark is introduced to distinguish large configuration-space avoidance from genuine computational advantage. Complete matched-confidence time-to-solution is compared against preregistered classical, quantum, physics-inspired, and structure-specific reference methods while accounting for compilation, physical synthesis, calibration, preparation, control, convergence, reset, readout, decoding, and validation. Four experimental outcomes are distinguished: backend conformance, physical semantic compatibility, competitive physical execution, and native CPC scaling advantage. The strongest outcome requires evidence of a growing advantage inconsistent with a constant implementation factor over the tested range. The proposal therefore treats native CPC advantage as a falsifiable experimental question rather than an assumed consequence of physical representation or engineered dissipation.
Quantum signal processing (QSP) realizes operator functions through polynomial transformations of a finite degree. In addition to function approximation errors, realistic implementations incur algorithmic errors also when encoding the input operator and in synthesizing gates into a discrete fault-tolerant gate set. We provide an end-to-end analysis of these errors and show that the input error propagation is governed by the operator-Lipschitz constant L⋆ of the implemented function. We then derive an efficient classical algorithm to compute tight lower and upper bounds on L⋆, and we show that these bounds induce in turn lower and upper bounds on the total quantum-resource cost (for instance, T-gate count) needed for QSP implementations compatible with a target total error. We further devise a procedure to search for a polynomial with minimum cost based solely on its coefficients, yielding a resource-aware polynomial-design procedure for QSP. We illustrate the resulting method for ground state energy estimation via eigenvalue thresholding for the H6 molecular Hamiltonian. In the tested hardware profiles, the resource-aware family improves the total-error budget and reduces the modeled T-gate count by 51.9%--56.7% relative to the standard analytical polynomial obtained from an error-function approximation.
Quantum circuit complexity quantifies the minimal number of gates needed to realize a unitary transformation and plays a central role in quantum computation. In this work, we investigate the complexity of quantum circuits through coherence and imaginarity resources. We establish a lower bound on the circuit cost by the Tsallis relative α entropy of cohering power, which is shown to be tighter than the one presented by Bu et al.[\textit{Communications in Mathematical Physics} 405, no. 7 (2024):161] under restrictive conditions. As a consequence, we obtain the relationships between the circuit cost and the coherence generating power via probabilistic average in terms of skew information/relative entropy, and present explicit bounds of the circuit cost for typical quantum gates. Moreover, we derive lower bounds on the circuit cost via the imaginaring power of the circuit, induced by the Tsallis relative α entropy and relative entropy. We demonstrate that imaginarity can yield nontrivial constraints on the circuit cost even when coherence-based lower bounds are zero (e.g., for the T gate), which implies that imaginarity may provide advantages under certain circumstances compared with coherence. Our results may help better understand the connections between quantum resources and circuit complexity.
Most of the architectural research on photonic implementations of measurement-based quantum computing (MBQC) has focused on the quantum resources involved in the problem with the implicit assumption that these will provide the main constraints on system scaling. However, the ‘flying-qubit’ architecture of photonic MBQC requires specific timing constraints that need to be met by the classical control system. This classical control includes, for example: the amplification of the signals from single-photon detectors to voltage levels compatible with digital systems; the implementation of a control system which converts measurement outcomes into basis settings for measuring subsequent cluster qubits, in accordance with the quantum algorithm being implemented; and the digital-to-analog converter (DAC) and amplifier systems required to set these measurement bases using a fast phase modulator. In this paper, we analyze the digital system needed to implement arbitrary one-qubit rotations and controlled-NOT (CNOT) gates in discrete-variable photonic MBQC, in the presence of an ideal cluster state generator, with the main aim of understanding the timing constraints imposed by the digital logic on the analog system and quantum hardware. We have verified that the design works using functional simulations, and have used static timing analysis of a Xilinx FPGA (7 series) to provide a practical upper bound on the speed at which the adaptive measurement processing can be performed, in turn constraining the photonic clock rate of the system. The design and testing system is freely available, for use as the basis of analysis of more complex designs, incorporating more recent proposals for photonic quantum computing.} Our work points to the importance of co-designing the classical control system in tandem with the quantum system in order to meet the challenging specifications of a photonic quantum computer.