Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0906.1811

Quantum algorithms know in advance 50% of the solution they will find in the future

Giuseppe Castagnoli
View original source ↗Read source document ↗Export metadata ↓

Abstract

Quantum algorithms require less operations than classical algorithms. The exact reason of this has not been pinpointed until now. Our explanation is that quantum algorithms know in advance 50% of the solution of the problem they will find in the future. In fact they can be represented as the sum of all the possible histories of a respective "advanced information classical algorithm". This algorithm, given the advanced information (50% of the bits encoding the problem solution), performs the operations (oracle's queries) still required to identify the solution. Each history corresponds to a possible way of getting the advanced information and a possible result of computing the missing information. This explanation of the quantum speed up has an immediate practical consequence: the speed up comes from comparing two classical algorithms, with and without advanced information, with no physics involved. This simplification could open the way to a systematic exploration of the possibilities of speed up.

Explore related subjects

quant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Giuseppe Castagnoli. 2009-07-29. Quantum algorithms know in advance 50% of the solution they will find in the future. https://doi.org/10.1007/s10773-009-0143-6

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Single-Ensemble Multiparameter Squeezing with Qudits

Conventional spin squeezing enhances a single sensing channel. Here, we show how internal qudit levels enable simultaneous multiparameter squeezing within one ensemble. In two-component magnetometry, a qutrit sensor provides two orthogonal and weakly compatible channels. A collective twisting interaction squeezes both responses while preserving joint attainability of the ultimate sensitivity. The sensing gain is quantified by using a matrix generalization of the Wineland sensitivity that retains both noise correlations and cross-channel response. An interaction-based echo amplifies the signal to overcome noise from a fixed local joint readout, yielding a simulated $13~\mathrm{dB}$ gain over the product-state standard quantum limit for $N=128$ qutrits. More generally, we use the single-site quantum Fisher information matrix to select reference states and channel quadratures for prescribed sensing tasks. The tangent geometry permits at most $d-1$ independent, weakly compatible channels around a common pure reference state for a $d$-level sensor. Our work provides a constructive task-to-protocol map for multiparameter squeezing in a single qudit ensemble.

quant-ph↗
arXiv2026

A Design Space Study of Density Matrix Parameterizations for Diffusion-Based Quantum State Tomography

Diffusion-based quantum state tomography (QST) has shown promising results, but all existing methods implicitly adopt a single parameterization (typically Cholesky) without systematic evaluation. We present the first design space study of density matrix parameterizations for diffusion QST, introducing a geometric framework based on the Jacobian Gram matrix $\mathbf{J}^\top\mathbf{J}$. Our calibration of seven parameterizations at 2- and 3-qubit scales, validated by end-to-end training, reveals that \emph{geometric conditioning alone does not predict end-to-end performance}: at 3-qubit scale, Hermitian direct ($κ= 2.0\times$) performs worse than Cholesky ($κ= 27\times$) at all shot levels---a $13.5\times$ isotropy advantage that translates into a fidelity \emph{disadvantage} of up to $+0.51$. The 2-qubit ranking (Hermitian $>$ Bloch) reverses at 3 qubits (Bloch 0.907 vs.\ Hermitian 0.394). We provide a geometric explanation: unbounded parameterizations suffer projection-induced information loss because the PSD constraint couples diagonal and off-diagonal coordinates in ways the unconstrained model cannot respect, whereas the Bloch representation places the maximally mixed state at the center of the valid region, minimizing projection loss.

quant-ph↗
arXiv2026

Entanglement free Metrology Exploiting Multimode Hong Ou Mandel Sensor Advantage

The Hong-Ou-Mandel (HOM) interference in the multimode frequency domain has been explored for precision metrology, with several experimental demonstrations exploiting its robustness against dispersion and phase noise, as well as its large dynamic range and compatibility with fragile samples. Conventional multimode HOM metrology exploits frequency-entangled states, which naturally satisfy bosonic exchange symmetry under any centered symmetric joint spectral distribution, to provide these advantages. However, these entangled states are typically generated via spontaneous parametric down-conversion (SPDC), requiring strong pump lasers that hinder practical implementation. In this paper, we employ frequency product states, which do not possess entanglement or path-mode exchange symmetry, as the probe state and post-select measurement outcomes exhibiting frequency anti-correlation. Our results demonstrate that these advantages,peak narrowing, dispersion cancellation, phase-noise immunity, a large dynamic range, and compatibility with fragile samples, arise neither from entanglement nor from bosonic exchange symmetry, but rather from spectral anti-correlation. We further show that entanglement is not the source of the measurement precision: the entanglement-free approach attains the same quantum Fisher information as the entangled-state scheme, indicating that the fundamental precision limit does not originate from entanglement.

quant-ph↗