Papers by Suproteek Banerjee
We introduce a temporal-topological framework for quantum fault tolerance in which logical inform... more We introduce a temporal-topological framework for quantum fault tolerance in which logical information is protected not only by the spatial stabilizer structure of an instantaneous quantum state, but by persistent homological features distributed coherently across the entire computational history of a quantum circuit. The full noisy circuit evolution is encoded as a filtered temporal entanglement simplicial complex K T , whose vertices are qubit-time events, whose edges encode pairwise entanglement or causal interaction, and whose higher-dimensional simplices represent multipartite correlations. Physical errors appear as topological defects in this space-time complex, while stable logical information is identified with persistent homology classes that survive across both spatial and temporal dimensions. We introduce space-time Betti numbers β ST k (α), temporal persistence diagrams, and a temporal-topological syndrome map. We formally define Temporal-Topological Quantum Error-Correcting Codes (TTQECC), with logical degrees of freedom encoded in non-trivial persistent homology classes and recovered via a persistent-homology decoder. An informal stability principle connects the classical persistence stability theorem to noise tolerance margins, and the temporal persistence gap ∆ T is introduced as a space-time analogue of the code distance. The framework is applied to three settings: (i) Floquet quantum circuits, where periodic driving induces subharmonic homology classes affording a new class of time-crystalline quantum memories; (ii) indefinite-causal-order processes, where the quantum switch generates topological cycles absent in any fixed-order circuit; and (iii) general noisy deep circuits, where the persistent-homology decoder is proposed as a complement to established surface-code decoders for correlated spatiotemporal errors. Throughout, established results are sharply distinguished from proposed definitions and explicitly conjectural claims.
We introduce Chrono-Quantum Computation (CQC), a speculative
but mathematically rigorous theoreti... more We introduce Chrono-Quantum Computation (CQC), a speculative
but mathematically rigorous theoretical framework in which the complete algorithmic
execution history of a computation—not merely its instantaneous state—can
exist in quantum superposition. The central object of study is the Chronoverse
Machine, a theoretical computational architecture that exploits a temporal Hilbert
space HT to label and coherently manipulate distinct causal orderings of gate
operations. We define chrono-qubits, timeline basis states, causal-order operators,
and the joint chrono-computational space HTC = HT ⊗HC. Building on indefinite
causal order, the quantum switch, Floquet theory, and history-state formalisms,
we develop the chrono-circuit model, establish interference theorems for competing
algorithmic timelines, and propose the complexity class CBQP as a formal—though
conjectural—extension of BQP. Three chrono-algorithms are designed: Chrono-
Search, Chrono-Optimization, and Chrono-SAT. A numerical simulation
framework with full Python pseudocode and toy illustrative results demonstrates
the constructive amplification attainable when computational histories interfere
coherently rather than mixing classically. Applications to combinatorial optimization,
post-quantum cryptography, AI planning, and non-equilibrium quantum simulation
are discussed. Limitations, decoherence pathways, and possible experimental
routes via photonic quantum switches and Floquet-engineered superconducting
circuits are examined with care. The paper is explicitly speculative; no claim of
experimental realization is made. Our aim is to establish a precise mathematical
language for a new direction in quantum computational theory.
This paper develops an extended theoretical program for quantum computation in periodically drive... more This paper develops an extended theoretical program for quantum computation in periodically driven manybody systems, with particular emphasis on Floquet-engineered spin chains and discrete time-crystalline order as computational resources. The central thesis is that temporal structure should not merely be regarded as an external control layer but as an active information-bearing degree of freedom. Building on Floquet theory, many-body localization, and recent experimental demonstrations of discrete time-crystal phenomenology, we formulate a Floquet Computational Model in which logical transformations are implemented stroboscopically, memory is encoded in subharmonic order, and temporal error syndromes are extracted from deviations in period-doubled response. The paper is intentionally ambitious but carefully separated into three levels of claim: established background, concrete model construction, and explicitly conjectural complexity-theoretic extrapolation. To support the theoretical narrative, we include finite-size exact-diagonalization-style numerical illustrations for a kicked Ising chain. These simulations show quasienergy branch structure, persistent subharmonic magnetization in a disorderstabilized regime, a spectral peak at half the drive frequency, and an illustrative order map over disorder strength and pulse imperfection. The numerics are not presented as proof of scalable fault tolerance or computational separation; rather, they serve as mechanistic evidence that the proposed architecture is internally coherent and physically interpretable. We conclude by identifying falsifiable predictions, hardware pathways, and the mathematical gaps that must be closed before the framework could mature into a rigorous fault-tolerant or complexity-theoretic theory.
We introduce Quantum Entanglement Topology (QET), a comprehensive mathematical framework that enc... more We introduce Quantum Entanglement Topology (QET), a comprehensive mathematical framework that encodes the full multipartite entanglement structure of n-qubit quantum states as filtered simplicial complexes and exploits the inherent stability of topological invariants-Betti numbers, persistent homology barcodes, and topological entropy-to achieve noise-resilient quantum computation without active error correction at the amplitude level. Classical quantum error correction operates combinatorially on the 2 n-dimensional coefficient vector |ψ⟩ = i c i |i⟩, detecting and correcting deviations in the amplitudes c i. QET takes an orthogonal approach: it maps |ψ⟩ to a topological object-the Entanglement Simplicial Complex (ESC)-whose homological invariants capture the relational, qualitative structure of entanglement rather than its precise amplitudes. Because topology is robust to continuous deformations by construction, these invariants resist the small amplitude perturbations induced by realistic noise channels. The paper establishes six principal theoretical contributions. (C1) The Entanglement Topology Map Φ : H n → Filt(Simp) is proven to be a L n-Lipschitz functor with L n = 2 √ 2 n-1, continuous in both the Hilbert-space norm and the interleaving distance on filtrations. (C2) The Topological Noise Stability Theorem establishes that all Betti numbers β k are invariant under any noise channel E ε satisfying ∥E ε-id∥ ⋄ < δ c = ∆ ψ /(2L n), where ∆ ψ is the entanglement gap-the minimum persistence of any topological feature. (C3) Topological Quantum Error-Correcting Codes (TQECCs) are constructed whose logical qubits correspond to non-trivial homology classes of the ESC, with Z-type stabilizers derived from boundary operators ∂ k+1 and X-type from coboundary operators ∂ † k , yielding codes with parameters [[|C k |, β k , d]] top. (C4) A categorytheoretic equivalence Q ≃ Top ent is established via an adjoint functor pair Φ ⊣ Ψ, proving that quantum computation is fundamentally topological computation. (C5) The BQP-Topology Conjecture proposes-with extensive numerical support-that f ∈ BQP iff the topological entropy h top (ψ f) = Ω(log n), connecting computational complexity to algebraic topology. (C6) Topological Quantum Neural Networks (TQNNs) using persistence images as noise-robust feature vectors achieve 98.5% accuracy on entanglement classification tasks that degrade only marginally at noise rates p < δ c. Comprehensive simulations on n ∈ {2,. .. , 10}-qubit systems under depolarizing, amplitude-damping, and dephasing noise confirm all theoretical predictions. TQECCs combined with the persistent-homology decoder achieve up to 47% lower logical error rates than surface-code baselines, and the ML-enhanced decoder reduces this further to 75% improvement at p = 0.05.
Academia, 2026
The intersection of molecular computing and quantum-inspired algorithms presents unprecedented op... more The intersection of molecular computing and quantum-inspired algorithms presents unprecedented opportunities for solving computationally intractable problems. This paper establishes a rigorous mathematical framework for quantum inspired DNA algorithms targeting NP-hard optimization problems. We develop a comprehensive theoretical foundation by modeling DNA strand populations as state vectors in a Hilbertlike space and biochemical reactions as linear operators with interference-inspired mechanisms. The framework introduces novel concentration-based amplitude amplification protocols, constraint-guided suppression operators, and convergence guarantees under specific structural assumptions. We present extensive computational simulations demonstrating exponential suppression of invalid configurations and polynomial-time convergence for structured problem instances including Boolean satisfiability (SAT), graph k-coloring, and maximum independent set problems. Through detailed complexity analysis, we prove that our approach achieves O(√ N log N) expected query complexity for structured instances, compared to O(N) for classical brute-force methods. Physical realizability is established through strand displacement cascade designs and thermodynamic analysis of reaction networks. Simulation results show 87.3% solution accuracy for 3-SAT instances with 100 variables and 99.2% accuracy for graph 3-coloring with 50 vertices. This work bridges theoretical computer science, molecular biology, and quantum inspired computation, opening new pathways for energy-efficient, massively parallel computational systems.
This manuscript presents a fully elaborated Module-LWE based Key Encapsulation Mechanism (KEM) op... more This manuscript presents a fully elaborated Module-LWE based Key Encapsulation Mechanism (KEM) optimized for resource-constrained Internet-of-Things (IoT) devices. Beyond providing formal IND-CPA and IND-CCA security, it delivers a comprehensive treatment of: (1) algorithmic construction and step-by-step derivation, (2) rationale for parameter selection, (3) side-channel aware C implementations with selectable arithmetic kernels (NTT, schoolbook, Karatsuba), (4) practical evaluation across Cortex-M, ESP32, and Raspberry Pi Zero platforms, and (5) trade-offs between security, latency, memory footprint, and energy. This work serves as a reference guide for implementing provably secure lattice-based KEMs in heterogeneous IoT environments.
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Papers by Suproteek Banerjee
but mathematically rigorous theoretical framework in which the complete algorithmic
execution history of a computation—not merely its instantaneous state—can
exist in quantum superposition. The central object of study is the Chronoverse
Machine, a theoretical computational architecture that exploits a temporal Hilbert
space HT to label and coherently manipulate distinct causal orderings of gate
operations. We define chrono-qubits, timeline basis states, causal-order operators,
and the joint chrono-computational space HTC = HT ⊗HC. Building on indefinite
causal order, the quantum switch, Floquet theory, and history-state formalisms,
we develop the chrono-circuit model, establish interference theorems for competing
algorithmic timelines, and propose the complexity class CBQP as a formal—though
conjectural—extension of BQP. Three chrono-algorithms are designed: Chrono-
Search, Chrono-Optimization, and Chrono-SAT. A numerical simulation
framework with full Python pseudocode and toy illustrative results demonstrates
the constructive amplification attainable when computational histories interfere
coherently rather than mixing classically. Applications to combinatorial optimization,
post-quantum cryptography, AI planning, and non-equilibrium quantum simulation
are discussed. Limitations, decoherence pathways, and possible experimental
routes via photonic quantum switches and Floquet-engineered superconducting
circuits are examined with care. The paper is explicitly speculative; no claim of
experimental realization is made. Our aim is to establish a precise mathematical
language for a new direction in quantum computational theory.