Title Redefining Quantum Computing with Quantized Time

One-liner

Treat time as a quantized computational resource—not a passive parameter—so algorithms engineer interfering histories on a time lattice.

Short abstract (≈110 words)

Conventional quantum computing treats time as a continuous, external parameter. We propose a time-quantized formulation where computation unfolds on a discrete time lattice (t_k=k,\Delta t). The primary object is a history ensemble over these slices, with dynamics given by CPTP maps (unitaries + noise) per slice and optional mid-circuit measurement/feedback. Probabilities at a “moment” become projections of an underlying history amplitude rather than fundamentals. This shift aligns theory with hardware realities (finite coherence, scheduling, control granularity) and enables new objectives: optimize interference across time-quantized trajectories under resource budgets. Practically, compilers target slice-wise controls, process tensors, and temporal logic constraints, yielding programs that are more robust to non-Markovian noise and explicitly co-design space × time.

Bullet brief

• Claim: Time is quantized ((t_k=k\Delta t)) and first-class in the model.
• Object: Computation = interfering history ensemble on a time lattice.
• Math: Slice maps (\mathcal{E}k(\rho)=\sum_j K{j}^{(k)}\rho K_{j}^{(k)\dagger}); process tensor (\Upsilon_{0:T}) for temporal correlations.
• Design shift: Compile to trajectories (with mid-circuit meas./feedback), not only terminal states.
• Why it matters: Matches control clocks, gate windows, and coherence budgets; exposes temporal trade-offs as native resources.
• Outcomes: Better scheduling, non-Markovian resilience, verifiable temporal specs for quantum programs.

Keyboard-friendly notation (copy/paste)

Time lattice: t_k = k*Δt
History amplitude: Phi[γ] = exp(i*S[γ]/ħ)
Slice channel: E_k(rho) = Σ_j K_j^(k) rho K_j^(k)†
Process tensor: Upsilon_{0:T}
Target: maximize | Σ_{γ∈Target} Phi[γ] |^2  subject to coherence/time budgets

Mini Gantree (concept spec)

TimeQuant_QC // Redefinition (proposal)
    TimeLattice // discrete t0..tT, step Δt
    HistoryEnsemble // trajectories across slices
    Dynamics // {E_k}: unitaries+noise (CPTP)
    TemporalControl // mid-circuit meas/feedback
    Objective // trajectory interference under budgets
    Verification // temporal logic + process tensor checks
    CompilerOut // slice schedules + circuit IR

Want this converted to a longer white-paper abstract or a PPR-DSL/SynQ spec? Say “고”.