arXiv subjects

Jianshuo Gao

Publications and source records attributed to Jianshuo Gao.

5 recordsLinked to original sources

arXiv2026

Extremely Low-Cost Magic State Preparation toward Fault-Tolerant Quantum Computing

Fault-tolerant preparation of non-Clifford resource states is a major contributor to the overhead of quantum computation, motivating protocols that achieve high output fidelity with minimal qubit and circuit costs. We introduce a low-cost magic-state preparation protocol in which the choice of stabilizer generators is co-designed with the flag gadgets, allowing the syndrome-extraction circuit itself to filter correlated faults across a non-Clifford layer. The protocol prepares a logical plus state in the 15-qubit quantum Reed-Muller code, applies a transversal T gate, and gauge-fixes the same register into the seven-qubit Steane code. By reorganizing equivalent Z-type stabilizer generators into jointly flagged measurement groups, the protocol eliminates all accepted logical-error contributions arising from one or two circuit faults under destructive error detection. Under a uniform circuit-level depolarizing noise model, the postselected infidelity is $210.2p^3+O(p^4)$. At $p=10^{-3}$, exact low-order enumeration combined with stratified sampling bounds the infidelity by $2.2\times10^{-7}$ at 99.9% joint confidence, while retaining an acceptance probability of 86.9%. The complete circuit requires only 19 qubits and 82 CNOT gates. These results demonstrate that stabilizer-generator design can substantially reduce the cost of postselected magic-state preparation, although corrected operation and the fidelity of an unmeasured output block require separate analysis.

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arXiv2026

A Resource Comparison of Logical T-State Preparation

Logical T state preparation is a major overhead source in fault tolerant architectures built from stabilizer operations. Existing protocols, however, are reported under different code families, noise models, postselection rules, and cost conventions, making direct comparison difficult. We compare three representative preparation routes: magic state distillation, magic state cultivation, and code switching, using currently available results. Rather than reducing heterogeneous data to a single cost metric, we retain source native cost units and record output error, single attempt cost, expected cost per accepted output, footprint, latency, and reporting completeness for each configuration. Within the current dataset, distillation reaches the lowest output error regime; code switching achieves the lowest reported single attempt cost and the smallest explicit footprint among the compatible rows; and recent RP2 cultivation results add low cost cultivation points with output errors between 1e-6 and 1e-9. As a simple algorithm level case study, we also examine the reported preparation routes under an error budget motivated by Shor factoring algorithm, in order to relate single state preparation costs to full workload requirements. The resulting comparison clarifies the trade offs currently supported across the literature, while remaining bounded by the conventions and coverage of the underlying papers.

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arXiv2026

Complexity-Aware Theory Testing from Bell Witnesses

Bell statistical-strength analyses and complexity-based model selection are usually treated separately. Here we relate them by showing that a witness obtained from a coarse-graining of full Bell trials yields, through data processing, a lower bound on the Kullback-Leibler (KL) distance to a competitor class in terms of the induced witness distribution. For binary Bell-game witnesses this reduces to a Bernoulli bound, and in the CHSH scenario the local image collapses to a single threshold, giving the closed-form expression D_KL(Bern(omega) || Bern(3/4)) under uniform inputs, with a corresponding extension to known nonuniform designs. A finite-sample Hoeffding argument gives a lower confidence bound under independent trials. We also include a non-CHSH example based on the three-party Mermin-GHZ game. Because the bound is measured in bits per trial, it can be compared directly with an MDL/BIC-type complexity penalty and thereby yields a conservative crossover criterion for when a more expressive competitor becomes worthwhile. For the reproducible four-photon data of Wang et al., the witness certifies a positive information gap against locality, while a full-table comparison across local, no-signaling, saturated, and two compact nonlocal families favors low-dimensional nonlocal descriptions once complexity is charged. A four-parameter unbiased-correlator control shows that the data support compact nonlocality over locality, while only weakly distinguishing the specific cosine structure of the two-parameter model; an AIC comparison instead favors broader nonlocal controls. We also report witness-based benchmarks from additional published CHSH experiments and discuss the interpretational scope of BIC for constrained or non-regular model classes.

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arXiv2026

Galilean One-Particle Kinematics from a Smooth Family of Reference States

Giannelli and Chiribella derived an observable-generator duality for energy from a collision model of informational nonequilibrium. We study a continuous-variable version aimed at the Galilean one-particle sector. A smooth family of reference states around an isotropic equilibrium supplies time, translation, rotation, and boost directions. The local observable-generator correspondence is obtained by differentiating a smooth extension of the single-state duality map, and the norm-one property of localization is obtained from a fiducial focusing assumption together with covariance. Combined with the standard smearing form of covariant localization observables, this yields sharp localization. With local inertial composition, the spin-cover action of rotations, and a central boost-translation holonomy, every irreducible sector is unitarily equivalent to the Hilbert space L2(R3) tensored with a (2s+1)-dimensional spin space. In that representation translations are generated by the canonical momentum, the holonomy is a scalar mass m > 0, boosts at t = 0 are generated by m times the position observable, the Hamiltonian is the free-particle kinetic term plus a constant E0, and the total angular momentum is orbital plus spin.

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arXiv2026

A Review of Variational Quantum Algorithms: Insights into Fault-Tolerant Quantum Computing

Variational quantum algorithms (VQAs) have established themselves as a central computational paradigm in the Noisy Intermediate-Scale Quantum (NISQ) era. By coupling parameterized quantum circuits (PQCs) with classical optimization, they operate effectively under strict hardware limitations. However, as quantum architectures transition toward early fault-tolerant (EFT) and ultimate fault-tolerant (FT) regimes, the foundational principles and long-term viability of VQAs require systematic reassessment. This review offers an insightful analysis of VQAs and their progression toward the fault-tolerant regime. We deconstruct the core algorithmic framework by examining ansatz design and classical optimization strategies, including cost function formulation, gradient computation, and optimizer selection. Concurrently, we evaluate critical training bottlenecks, notably barren plateaus (BPs), alongside established mitigation strategies. The discussion then explores the EFT phase, detailing how the integration of quantum error mitigation and partial error correction can sustain algorithmic performance. Addressing the FT phase, we analyze the inherent challenges confronting current hybrid VQA models. Furthermore, we synthesize recent VQA applications across diverse domains, including many-body physics, quantum chemistry, machine learning, and mathematical optimization. Ultimately, this review outlines a theoretical roadmap for adapting quantum algorithms to future hardware generations, elucidating how variational principles can be systematically refined to maintain their relevance and efficiency within an error-corrected computational environment.

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