Quantum Error Correction (QEC), combined with magic state distillation, ensures fault tolerance in large-scale quantum computation. To apply QEC, a circuit must first be transformed into a non-Clifford (or T) gate set. T-depth, the number of sequential T-gate layers, determines the magic state cost, impacting both spatial and temporal overhead. Minimizing T-depth is crucial for optimizing resource efficiency in fault-tolerant quantum computing. While QEC scalability has been widely studied, T-depth reduction remains an overlooked challenge. It is established that T-depth reduction is an NP-hard problem and we systematically evaluate multiple approximation techniques: greedy, divide-and-conquer, Lookahead-based brute force, and graph-based. The Lookahead-based brute-force algorithm (partition size 4) performs best, optimizing
90% of reducible cases (i.e., circuits where at least one algorithm achieved optimization) with an average T-depth reduction of around
51%. Additionally, we introduce an expansion factor-based identity gate insertion strategy, leveraging controlled redundancy to achieve deeper reductions in circuits initially classified as non-reducible. With this approach, we successfully convert up to
25% of non-reducible circuits into reducible ones, while achieving an additional average reduction of up to
11.8%. Furthermore, we analyze the impact of different expansion factor values and explore how varying the partition size in the Lookahead-based brute-force algorithm influences the quality of T-depth reduction.
Potential features of quantum computation could explain enigmatic aspects of consciousness. The Penrose—Hameroff model (orchestrated objective reduction: ‘Orch OR’) suggests that quantum superposition and a form of quantum computation occur in microtubules—cylindrical protein lattices of the cell cytoskeleton within the brain's neurons. Microtubules couple to and regulate neural–level synaptic functions, and they may be ideal quantum computers because of dynamical lattice structure, quantum–level subunit states and intermittent isolation from environmental interactions. In addition to its biological setting, the Orch OR proposal differs in an essential way from technologically envisioned quantum computers in which collapse, or reduction to classical output states, is caused by environmental decoherence (hence introducing randomness). In the Orch OR proposal, reduction of microtubule quantum superposition to classical output states occurs by an objective factor: Roger Penrose's quantum gravity threshold stemming from instability in Planck–scale separations (superpositions) in spacetime geometry. Output states following Penrose's objective reduction are neither totally deterministic nor random, but influenced by a non–computable factor ingrained in fundamental spacetime. Taking a modern pan–psychist view in which protoconscious experience and Platonic values are embedded in Planck–scale spin networks, the Orch OR model portrays consciousness as brain activities linked to fundamental ripples in spacetime geometry.
We study many-party correlations quantified in terms of the Umegaki relative entropy (divergence) from a Gibbs family known as a hierarchical model. We derive these quantities from the maximum-entropy principle which was used earlier to define the closely related irreducible correlation. We point out the differences between quantum states and probability vectors which exist in hierarchical models, in the divergence from a hierarchical model and in local maximizers of this divergence. The differences are, respectively, missing factorization, discontinuity and reduction of uncertainty. We discuss global maximizers of the mutual information of separable qubit states.