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High-Dimensional Photon Gates Operation First: L5 Addressing For A Four-State OAM Module

William J. Richardson

Published Feb 25, 2026• 0 citations
Publisher

Abstract

Based on the Source Contribution article: Quantum Computers Go High-Dimensional with a Four-State Photon Gate Foundational — This Important document, High-Dimensional Photon Gates Operation First: L5 Addressing For A Four-State OAM Module, converts a high-dimensional photonic gate headline into a runnable engineering module by treating the four-state OAM gate as an L5-addressable object whose placement is recorded as numeric geometry across independent address engines rather than as a fragile label, and by separating path content (mode basis and pad coordinate) from push content (control and stabilization schedule) so basis drift cannot be laundered into control authority. It upgrades heralding into a recognition stream that is frozen at the separation boundary before any tightening is allowed, preventing post-view retuning of selection rules from manufacturing a cleaner gate, and it keeps falsifiability minimal and strictly attached to the uplift by enforcing a frozen extractor and pad chart, refusing translator-created sign via lane separation and disable posture, and charging pad shrink with yield and SoZ so stability cannot be purchased by starvation. Net: it supplies reusable rule infrastructure for turning any high-dimensional “works in the lab” photonic result into a standards-ready, replayable contract object that can survive drift, disagreement among engines, and corridor tightening without narrative repair. Key Words: high-dimensional photonics; four-state qudit gate; orbital angular momentum; L5 addressing; pad placement; numeric geometry; path-versus-push separation; heralded gate recognition; tokens-only replay; SoZ-charged tightening.

DOI
10.5281/zenodo.18775594

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Prethermal Plateau Unification: Pad Geometry Plus MAP Translation

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This critical manuscript addresses a persistent failure mode in prethermal plateau and stability claims: the gap between demonstrating a long-lived dynamical regime and certifying that the regime is usable under fixed, replayable rules. Recent platform results show that structured random driving can suppress heating and extend prethermal lifetimes on many-qubit processors. While these results establish physical existence and controllable lifetime, they do not by themselves certify operational utility or guard against boundary narrative repair. This manuscript extends the earlier pad and triad-of-triads program by applying MAP as a unifying translation layer to prethermal plateau claims. Prior work established the signed-triad ledger, Strong-to-Weak downgrades, STLF refusal discipline, and tokens-only replay as independent enforcement tools. Here, those tools are bound together by MAP and explicitly externalized from the engine, allowing plateau lifetime claims to be evaluated as contract objects rather than as narrative curves. The result is a carry-forward certification spine that preserves earlier triad logic while adding a thermodynamic interpretation of acceptance leakage and a regime-transition marker (ZFlip) suitable for plateau-style datasets. The central contribution of this work is Mapping and Amplification Protocol (MAP), a pad-centered translation layer that externalizes certification logic from the engine and forces enforcement tools to act coherently under a shared coordinate meaning. MAP is not a new physical mechanism and not an optimizer. It is a deterministic translator from tokens to enforcement actions that binds Strong-to-Weak, STLF, Knob, and Sum-of-Zeros to the same declared pad and corridor. By doing so, MAP removes silent degrees of freedom that otherwise allow filtering, tightening, or drift to masquerade as stability. Under MAP, plateau behavior is no longer evaluated by a single flat curve or preferred projection. Instead, claims are promoted, downgraded, or refused through a triad-of-triads contract that separates signed state, windowed pattern fingerprints, and meta-promotion logic. Two independent redundancy cages (view square and ladder square) are enforced via double Four-Solves-Three auditing, blocking majority narratives and forcing disagreement to remain visible. Acceptance recovery is explicitly bounded: any recovered utility must be paid for through declared downgrades rather than repaired into Strong. Within this framework, the manuscript introduces a contract-level thermodynamic separation: what platform studies describe as “heating” is treated here as acceptance leakage in time under a fixed corridor. The quantity TzTzTz is operationalized as a burn-rate proxy that tracks how quickly tension is consumed as trajectories approach refusal, while ZFlipZFlipZFlip marks the first persistent regime transition where the effective plateau description fails. Plateau lifetime is therefore treated as necessary but not sufficient; the resource question is whether the plateau survives under fixed accounting until the flip. The intended outcome is a reusable, platform-independent certification object. MAP and the surrounding contract infrastructure are designed to carry forward across qubit, magnonic, photonic, and hybrid platforms, allowing future plateau datasets to be evaluated without modifying the rule spine. The result is not a critique of platform physics, but a durable method for turning plateau observations into bounded, replayable, and falsifiable objects of record.

•Jan 31, 2026•0 citations

Experimental engineering of OAM quantum states with photonics quantum walks (Conference Presentation)

Fabio Sciarrino

The preparation of high-dimensional quan- tum states is of great significance in quantum information sci- ence and technology. Compared to qubits, qudit states – de- scribing quantum systems in d-dimensional spaces – enable stronger foundational tests of quantum mechanics [1–3] and better-performing applications in secure quantum communi- cations [4–9], quantum emulation [10, 11], quantum error cor- rection [12–14], fault-tolerant quantum computation [15–19], and quantum machine learning [20–22]. Needless to say, protocols performed on systems living in Hilbert spaces of large dimension require an increasing degree of control, in light of the large number of parameters required to describe states and operations. Nonetheless, the endeav- our of preparing arbitrary qudit states has been successfully achieved in various physical platforms [11, 23–32]. However, most of these works rely on ad hoc strategies, whose specific dependence on the underpinning dynamics makes their trans- lation across different physical platforms very difficult. A very promising way to achieve the desired full inde- pendence of the physical platform, and thus a higher degree of universality, is the use of the rich dynamics offered by Quantum Walks (QWs) [33–35]. QWs, which can be thought of as the quantum counterparts of classical random walks, describe in their discrete version a high-dimensional qudit, named walker, embedded with an internal two-dimensional degree of freedom, conventionally dubbed coin. At every time step, the walker’s state moves coherently to the neighbouring sites in the lattice, conditionally to its coin state [36]. QWs have been successfully implemented [37] in systems as di- verse as trapped atoms [38] and ions [39, 40], photonic cir- cuits [41–50], and optical lattices [51]. Hence, an approach for state engineering based on their dynamics offers hope of being applicable effectively in a variety of different systems, independently of the details of the physical implementation. While the QW dynamics was previously shown to allow the engineering of specific walker’s states [52, 53], in Ref. [54] a scheme was proposed to use discrete-time QWs on a line to prepare arbitrary qudit states. This is achieved by enhanc- ing the degree of control over the walk’s dynamics through the arrangement of suitable step-dependent coin operations, which affect the coin-walker quantum correlations by de facto steering the state of the walker towards the desired final state, and finally projecting in the coin space. This last operation removes the correlations between walker and coin, thus pro- ducing a pure walker state with the desired features. In light of the large parameter space that characterizes the problem at hand, a systematic approach to the identification of the right set of coin operations and final projection is necessary. Such an analysis was presented in Ref. [54], in which a set of an- alytic conditions, together with suitable numerical optimiza- tions, was shown to guarantee the reaching of arbitrary target states with high probability. In this paper, we make use of the scheme of Ref. [54] to give the first demonstration of a state-engineering protocol based on the controlled dynamics generated by QWs. We use the orbital angular momentum (OAM) degree of freedom of single-photon states as a convenient embodiment of the walker [48, 55, 56]. OAM-based experiments offer the pos- sibility to cover Hilbert spaces of large dimensions in light of the favourable (linear) scaling of the number of optical ele- ments with the size of the walk. Moreover, the scheme al- lows for the full control of the coin operation that is key to the implementation of the walk. In order to demonstrate the ver- satility of our scheme, we focus on the interesting classes of cat-like states and spin-coherent states [57, 58]. Those classes play a critical role in the exploration of the boundaries be- tween quantum and classical physics and whose implementa- tion is, in general, still a challenging task. Furthermore, we show experimentally the capability of engineering arbitrary states. The quality of the states synthesized in our endeavours, and the relative simplicity of the experimental protocol that we have put in place, demonstrate the effectiveness of a hybrid platform for quantum state engineering. Such platform holds together a programmable quantum system, the photonic QW in the angular momentum, and classical optimization al- gorithms for finding the best evolution to reach a certain quantum target. [1] T. Ve ́rtesi, S. Pironio, and N. 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Wang, Physical Implementation of Quantum Walks (Springer Berlin Heidelberg, Berlin, Heidelberg, 2014). [38] R. Coˆte ́, A. Russell, E. E. Eyler, and P. L. Gould, New Journal of Physics 8, 156 (2006). [39] H. Schmitz, R. Matjeschk, C. Schneider, J. Glueckert, M. Enderlein, T. Huber, and T. Schaetz, Physical Review Letters 103, 090504 (2009). [40] F. Za ̈hringer, G. Kirchmair, R. Gerritsma, E. Solano, R. Blatt, and C. F. Roos, Physical Review Letters 104, 100503 (2010). [41] H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, Physical Review Letters 100, 170506 (2008). [42] A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wo ̈rhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, Science 329, 1500 (2010). [43] M. A. Broome, A. Fedrizzi, B. P. Lanyon, I. Kassal, A. Aspuru- Guzik, and A. G. White, Phys. Rev. Lett. 104, 153602 (2010). [44] A. Schreiber, K. N. Cassemiro, V. 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Complex Light and Optical Forces•Mar 8, 2019•0 citations

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William J. Richardson

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•Feb 14, 2026•0 citations

Parallelization of high-dimensional single-photon quantum gates

Jaroslav Kysela

Local quantum gates represent the basic building blocks of quantum computers. In the photonic domain, these gates act on individual photons and are usually implemented as single optical devices. In cases when the same gate is to be applied simultaneously to multiple photons, the corresponding physical implementation consists of a stack of identical devices. We present a systematic approach that allows one to replace this stack with a single device supplemented by pre- and post-processing stages. As a result, considerable savings in resources are obtained. We exemplify our scheme for the case of the orbital angular momentum (OAM) of single photons and demonstrate the scheme for high-dimensional Pauli gates and their arbitrary powers. As a byproduct, we also present a simple argument that explicitly shows how to construct an arbitrary quantum gate acting on OAM of single photons, where only conventional optical elements are utilized.

•Jun 21, 2021•0 citations

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William J. Richardson

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•Jul 17, 2026•0 citations
Based on the Source Contribution article: Quantum Computers Go High-Dimensional with a Four-State Photon Gate Foundational — This Important document, High-Dimensional Photon Gates Operation First: L5 Addressing For A Four-State OAM Module, converts a high-dimensional photonic gate headline into a runnable engineering module by treating the four-state OAM gate as an L5-addressable object whose placement is recorded as numeric geometry across independent address engines rather than as a fragile label, and by separating path content (mode basis and pad coordinate) from push content (control and stabilization schedule) so basis drift cannot be laundered into control authority. It upgrades heralding into a recognition stream that is frozen at the separation boundary before any tightening is allowed, preventing post-view retuning of selection rules from manufacturing a cleaner gate, and it keeps falsifiability minimal and strictly attached to the uplift by enforcing a frozen extractor and pad chart, refusing translator-created sign via lane separation and disable posture, and charging pad shrink with yield and SoZ so stability cannot be purchased by starvation. Net: it supplies reusable rule infrastructure for turning any high-dimensional “works in the lab” photonic result into a standards-ready, replayable contract object that can survive drift, disagreement among engines, and corridor tightening without narrative repair. Key Words: high-dimensional photonics; four-state qudit gate; orbital angular momentum; L5 addressing; pad placement; numeric geometry; path-versus-push separation; heralded gate recognition; tokens-only replay; SoZ-charged tightening.
This critical manuscript addresses a persistent failure mode in prethermal plateau and stability claims: the gap between demonstrating a long-lived dynamical regime and certifying that the regime is usable under fixed, replayable rules. Recent platform results show that structured random driving can suppress heating and extend prethermal lifetimes on many-qubit processors. While these results establish physical existence and controllable lifetime, they do not by themselves certify operational utility or guard against boundary narrative repair. This manuscript extends the earlier pad and triad-of-triads program by applying MAP as a unifying translation layer to prethermal plateau claims. Prior work established the signed-triad ledger, Strong-to-Weak downgrades, STLF refusal discipline, and tokens-only replay as independent enforcement tools. Here, those tools are bound together by MAP and explicitly externalized from the engine, allowing plateau lifetime claims to be evaluated as contract objects rather than as narrative curves. The result is a carry-forward certification spine that preserves earlier triad logic while adding a thermodynamic interpretation of acceptance leakage and a regime-transition marker (ZFlip) suitable for plateau-style datasets. The central contribution of this work is Mapping and Amplification Protocol (MAP), a pad-centered translation layer that externalizes certification logic from the engine and forces enforcement tools to act coherently under a shared coordinate meaning. MAP is not a new physical mechanism and not an optimizer. It is a deterministic translator from tokens to enforcement actions that binds Strong-to-Weak, STLF, Knob, and Sum-of-Zeros to the same declared pad and corridor. By doing so, MAP removes silent degrees of freedom that otherwise allow filtering, tightening, or drift to masquerade as stability. Under MAP, plateau behavior is no longer evaluated by a single flat curve or preferred projection. Instead, claims are promoted, downgraded, or refused through a triad-of-triads contract that separates signed state, windowed pattern fingerprints, and meta-promotion logic. Two independent redundancy cages (view square and ladder square) are enforced via double Four-Solves-Three auditing, blocking majority narratives and forcing disagreement to remain visible. Acceptance recovery is explicitly bounded: any recovered utility must be paid for through declared downgrades rather than repaired into Strong. Within this framework, the manuscript introduces a contract-level thermodynamic separation: what platform studies describe as “heating” is treated here as acceptance leakage in time under a fixed corridor. The quantity TzTzTz is operationalized as a burn-rate proxy that tracks how quickly tension is consumed as trajectories approach refusal, while ZFlipZFlipZFlip marks the first persistent regime transition where the effective plateau description fails. Plateau lifetime is therefore treated as necessary but not sufficient; the resource question is whether the plateau survives under fixed accounting until the flip. The intended outcome is a reusable, platform-independent certification object. MAP and the surrounding contract infrastructure are designed to carry forward across qubit, magnonic, photonic, and hybrid platforms, allowing future plateau datasets to be evaluated without modifying the rule spine. The result is not a critique of platform physics, but a durable method for turning plateau observations into bounded, replayable, and falsifiable objects of record.
The preparation of high-dimensional quan- tum states is of great significance in quantum information sci- ence and technology. Compared to qubits, qudit states – de- scribing quantum systems in d-dimensional spaces – enable stronger foundational tests of quantum mechanics [1–3] and better-performing applications in secure quantum communi- cations [4–9], quantum emulation [10, 11], quantum error cor- rection [12–14], fault-tolerant quantum computation [15–19], and quantum machine learning [20–22]. Needless to say, protocols performed on systems living in Hilbert spaces of large dimension require an increasing degree of control, in light of the large number of parameters required to describe states and operations. Nonetheless, the endeav- our of preparing arbitrary qudit states has been successfully achieved in various physical platforms [11, 23–32]. However, most of these works rely on ad hoc strategies, whose specific dependence on the underpinning dynamics makes their trans- lation across different physical platforms very difficult. A very promising way to achieve the desired full inde- pendence of the physical platform, and thus a higher degree of universality, is the use of the rich dynamics offered by Quantum Walks (QWs) [33–35]. QWs, which can be thought of as the quantum counterparts of classical random walks, describe in their discrete version a high-dimensional qudit, named walker, embedded with an internal two-dimensional degree of freedom, conventionally dubbed coin. At every time step, the walker’s state moves coherently to the neighbouring sites in the lattice, conditionally to its coin state [36]. QWs have been successfully implemented [37] in systems as di- verse as trapped atoms [38] and ions [39, 40], photonic cir- cuits [41–50], and optical lattices [51]. Hence, an approach for state engineering based on their dynamics offers hope of being applicable effectively in a variety of different systems, independently of the details of the physical implementation. While the QW dynamics was previously shown to allow the engineering of specific walker’s states [52, 53], in Ref. [54] a scheme was proposed to use discrete-time QWs on a line to prepare arbitrary qudit states. This is achieved by enhanc- ing the degree of control over the walk’s dynamics through the arrangement of suitable step-dependent coin operations, which affect the coin-walker quantum correlations by de facto steering the state of the walker towards the desired final state, and finally projecting in the coin space. This last operation removes the correlations between walker and coin, thus pro- ducing a pure walker state with the desired features. In light of the large parameter space that characterizes the problem at hand, a systematic approach to the identification of the right set of coin operations and final projection is necessary. Such an analysis was presented in Ref. [54], in which a set of an- alytic conditions, together with suitable numerical optimiza- tions, was shown to guarantee the reaching of arbitrary target states with high probability. In this paper, we make use of the scheme of Ref. [54] to give the first demonstration of a state-engineering protocol based on the controlled dynamics generated by QWs. We use the orbital angular momentum (OAM) degree of freedom of single-photon states as a convenient embodiment of the walker [48, 55, 56]. OAM-based experiments offer the pos- sibility to cover Hilbert spaces of large dimensions in light of the favourable (linear) scaling of the number of optical ele- ments with the size of the walk. 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Significant — This manuscript certifies a 91-qubit Floquet chaos verification claim under a fixed tensor corridor by converting dual-unitary admissibility, tensor-network baseline comparison, and mitigation workflows into declared corridor objects with tokens-only replay. The contract enforces MAP0–SEB–MAP1 separation so recognition cannot be repaired by enforcement, prohibits backflow authority, and treats mitigation as an explicit tightening ladder rather than as postprocessing convenience. A signed-triad record with zeros-stay-zeros discipline carries the primary sign record across tightening steps; flip-only audits and mitigation-disable (disable-L) falsifiers test anchor drift and translator dependence; strong-to-weak grading preserves value when survival fails without inflating the claim. Two ceilings bound what is certifiable (not what is physically chaotic): SoZ constrains yield/missingness under tightening, and an R≈1 containment ratio constrains instability growth versus declared budget. The output is a replayable branch-map decision record—promote, downgrade, refuse, or hold—with reason tokens, replay-kit fields, and falsifier-first logic suitable for bench transfer without moving thresholds.
Local quantum gates represent the basic building blocks of quantum computers. In the photonic domain, these gates act on individual photons and are usually implemented as single optical devices. In cases when the same gate is to be applied simultaneously to multiple photons, the corresponding physical implementation consists of a stack of identical devices. We present a systematic approach that allows one to replace this stack with a single device supplemented by pre- and post-processing stages. As a result, considerable savings in resources are obtained. We exemplify our scheme for the case of the orbital angular momentum (OAM) of single photons and demonstrate the scheme for high-dimensional Pauli gates and their arbitrary powers. As a byproduct, we also present a simple argument that explicitly shows how to construct an arbitrary quantum gate acting on OAM of single photons, where only conventional optical elements are utilized.
Foundational — The Importance of the PTT Engine: Measuring Strength, Sign, and Custody Across Six-Molecule Quantum Possibilities This article deserves a full reading because it demonstrates why identifying possible quantum transitions is only the beginning of a usable result. A six-molecule charge cluster creates a compact but highly complex test involving 64 binary placements, 20 fixed-three-charge arrangements, 8 inner-triad states, substrate-mediated movement, changing populations, directional reads, centered outcomes, typed zeros, and route burden. A simple gate table linked all 180 candidate transitions, yet the complete Pedigree--Transmission--Triad-of-Triads engine showed that those apparent passes carried sharply different levels of real authority. After population, placement, support, sign custody, D5 detour, directional return, and overlap were measured, only 108 routes transmitted: 81 graded Strong-to-Weak, 27 graded Weaker, and 72 retained as bounded refusal history. The article clearly explains how Pedigree preserves spherical placement and molecular identity, how Transmission converts placement into OAM sign, and how Triad-of-Triads certifies direction, strength, burden, and typed-zero custody. It also shows why Sign Net is essential for distinguishing full sign, 0Sforward0S_{\mathrm{forward}}0Sforward​, 0Stimeout0S_{\mathrm{timeout}}0Stimeout​, 0T0T0T, Strong-to-Weak, Weaker, and refusal. D3, D4, and D5 preserve the spatial scaffold, individual molecular cells, and substrate-mediated detour history, while STLF somethingness and nothingness measure which possibilities carry live support and which retain missing-support debt. Readers should also examine the coordinated tool stack because each tool removes a different source of uncertainty. SoZ preserves unpaid support, Flip 2.5 performs early gate-in and gate-out decisions, TWA+ recovers qualified borderline routes, P-Lane and L5 preserve center placement, Headwater and TzCenterTz_{\mathrm{Center}}TzCenter​ preserve directional history, SEB-MAP separates evidence recognition from enforcement, and the Overlap Filter consolidates final route authority. Together, these tools turn a crowded possibility field into a signed, strength-graded, replayable, and falsifiable component map. The article introduces an especially significant History Exclusion Gate that acts after completed history is written and before the next Pedigree intake. A certified failed route can establish a reusable boundary for weaker candidates in the same frozen monotonic family. In a 2,880-point bias sweep, this gate avoided 1,494 full PTT calculations, reducing the workload by 51.875 percent while preserving all committed engine fires and producing zero false exclusions against the complete validation sweep. This result shows that retained history can become an active computational asset: the engine uses previous certified failures to direct future calculation toward genuinely new boundaries and candidates with a measurable path to promotion. The broader importance of the article is that PTT measures possibilities rather than merely connecting them. It provides a reusable engine for deciding which apparent quantum routes possess real placement custody, lawful sign, directional continuity, measurable strength, recoverable burden, or valuable retained history. The six-molecule cluster supplies the stress test, while the PTT engine and its coordinated tools supply the general infrastructure.