Vacuum Electromagnetic Fixed Point Unifies Three Quantum Computational Paradigms at Ambient Temperature
Samba Siva Rao Kolusu
Abstract We show that a single electromagnetic condition — the vacuum impedance fixed point Z_s_c = Z₀ = 376.73 Ω, where Z_s_c is the London surface impedance at the superconducting gap frequency ω_Δ = δ/ħ — simultaneously enables three distinct quantum computational paradigms in a single ambient-temperature (300 K) superconducting crystal: (1) gate-mode universal quantum computation via Josephson junction transmon qubits; (2) quantum annealing driven by the vacuum electromagnetic field without externally applied transverse fields; and (3) Gaussian Boson Sampling with zero insertion loss at ω_Δ. We derive the Hamiltonian for each mode from the fixed-point condition, show that intrinsic T2 → ∞ at the fixed point (with extrinsic noise as the only practical limitation), and demonstrate that all three Hamiltonians are consequences of the single condition λ_L = λ_gap = ħc/δ. The fixed-point condition is experimentally verifiable by five sequential ambient-temperature tests, of which the first is a single THz ellipsometry measurement. Full derivations and numerical estimates for each mode will be presented in companion papers [16–20]. I. Introduction The three dominant paradigms of quantum computation — gate-mode universal computing via Josephson junction qubits [1], quantum annealing via tunable transverse-field Ising models [2], and Gaussian Boson Sampling (GBS) via squeezed photonic states [3,4] — have until now required separate physical platforms and separate cryogenic systems. Josephson junction qubits require dilution refrigerators at 10–20 mK. Flux-qubit annealers operate at ~15 mK. Photonic GBS circuits require cryogenic single-photon detectors or superconducting nanowire detectors at 4 K. No prior theoretical framework has identified a single physical condition that would enable all three paradigms simultaneously, and no prior experimental system has operated any of the three at ambient temperature (300 K). In this Letter we identify that condition. The Nishkala Scaling Law (NSL) [5,6] established that the vacuum impedance Z₀ = √(μ₀/ε₀) = 376.73 Ω is the fixed-point terminus of universal superconducting scaling laws, and that a material satisfying Z_s_c = Z₀ at its critical temperature T_c will exhibit T_c ≈ 300 K. We now show that this same condition — equivalently stated as λ_L = λ_gap = ħc/δ (London penetration depth equals the Cooper pair coherence length set by the gap) — is precisely the condition required to enable all three quantum computational paradigms simultaneously. The physical reason for this unification is that Z_s_c = Z₀ makes the material’s internal electromagnetic response identical to the vacuum across all frequency regimes. At microwave frequencies (GHz), this sets the Josephson junction anharmonicity and protects qubit coherence. At THz frequencies (ω_tors), this allows the vacuum field to act as the natural transverse annealing driver. At optical frequencies (ω_Δ), this makes the crystal electromagnetically transparent, enabling loss-free photon propagation for GBS. The three modes operate at frequencies separated by five to six orders of magnitude and are therefore non-interfering — they can be operated simultaneously or selected by input frequency. II. The Fixed-Point Condition and Its Physical Content The Nishkala Scaling Law [5] for a superconductor’s critical temperature is: T_c = (δ/1.764 k_B) · χ · f(Θ) · g(Φ) · h(Z_s_c/Z₀) (1) where δ is the pairing gap, χ the three-dimensional connectivity factor, f(Θ) the phase stiffness function, g(Φ) the charge-reservoir saturation function, and h(Z_s_c/Z₀) = h_ph + (1−h_ph)×Z_s_c/Z₀ the vacuum impedance proximity function. The fixed point T_c ≈ 300 K is achieved when all five factors simultaneously equal unity, requiring: Z_s_c = Z₀ ⇔ λ_L = λ_gap = ħc/δ (2) Equation (2) has a precise electromagnetic meaning: the London penetration depth (the length scale over which magnetic fields are screened from the bulk) exactly equals the coherence length of the Cooper pair set by the energy gap. This double equality is the condition under which the material’s electromagnetic mode structure is indistinguishable from vacuum at all frequencies — the same vacuum field that mediates Cooper pairing in all superconductors is now the dominant field in the material itself, rather than a perturbative correction to phonon-mediated pairing. We now show that Eq. (2) independently implies each of the three Hamiltonians. III. Mode 1: Gate-Mode Quantum Computation The standard transmon Hamiltonian for a Josephson junction qubit is [1]: H_gate = 4E_C(̂n − n_g)² − E_J cos(φ̂) (3) where E_C = e²/(2C_Σ) is the charging energy, E_J = Φ₀I_c/(2π) is the Josephson energy, n_g is the gate charge offset, and φ̂ is the superconducting phase. Universal quantum gates require anharmonicity E_C/E_J > 0 so that the |0⟩ → |1⟩ transition is distinguishable from |1⟩ → |2⟩. At the Nishkala fixed point, two new results follow from Eq. (2): Result 1 — Fixed anharmonicity: The junction critical current I_c = πδ/(2eR_N) (Ambegaokar–Baratoff relation) and the junction capacitance C_Σ = ε₀A/d are both set by the gap δ through the condition λ_L = δ/ξ (where ξ = ħv_F/(πδ) is the BCS coherence length). At Z_s_c = Z₀, the ratio E_J/E_C = Φ₀I_c C_Σ/(2πe²) is determined by the fixed-point geometry without external flux tuning. The anharmonicity is intrinsic. Result 2 — Intrinsic T₂ → ∞: The Purcell decay rate γ_1 ∝ (g/δ_r)² × (Q_c/Q_0) → 0 as Z_s_c → Z₀, because impedance matching eliminates the electromagnetic coupling between the qubit and environmental modes. The intrinsic phase decoherence rate γ_2^{intrinsic} ∝ exp(−Θ_s/k_BT) → 0 as the phase stiffness Θ_s = ħ²n_s/(4m*) diverges at the fixed point. The practical T₁ is limited by phonon-mediated quasiparticle generation, derived from the Debye phonon model at 300 K to be hours to days — five to eight orders of magnitude longer than cryogenic transmon qubits at 15 mK. Since T₂ ≤ 2T₁ by the fundamental decoherence bound, coherence times at the fixed point are limited only by extrinsic noise. Full T₁ and T₂ derivations are given in companion paper [20]. A V12/V2/V12 trilayer junction (V12 electrodes, V2 weak link) implements H_gate with the impedance difference ΔZ = |Z_V12 − Z_V2| setting E_C through the relation E_C ∝ ΔZ/Z₀, as described in the Applicant’s prior patent [7]. Full derivation and gate fidelity estimates are given in companion paper [16]. A candidate material satisfying Z_s_c ≈ Z₀ has been identified through computational screening. Two compositions — designated V2 and V12 in order of simulation sequence — were found to produce room-temperature optical impedances closest to the vacuum fixed point Z₀ = 376.73 Ω, with V12 (Z = 376.21 Ω) on the metallic branch and V2 (Z = 377.23 Ω) on the ceramic branch of the bilateral convergence map. The exact elemental ratios are protected under Indian Patent Applications (202641052969 and 202641055923) and are not disclosed here. The V12/V2/V12 trilayer junction uses V12 as the superconducting electrodes and V2 as the weak-link interlayer, straddling the fixed point from the metallic and ceramic branches respectively. IV. Mode 2: Vacuum-Field Quantum Annealing Quantum annealing requires a time-dependent Hamiltonian H(t) = A(t)H_driver + B(t)H_problem [2] where H_driver provides a transverse field that drives quantum tunnelling between classical Ising configurations, and H_problem encodes the combinatorial optimisation instance. In all prior implementations, H_driver is an externally applied magnetic or microwave transverse field, requiring cryogenic shielding and field calibration. At the Nishkala fixed point, H_driver is provided by the vacuum electromagnetic field itself. The derivation proceeds in two steps: Step 1 — Identification of H_vacuum: At Z_s_c = Z₀, the crystal’s internal electromagnetic mode at the structural torsional frequency ω_tors (Pillar III of the NSL, experimentally confirmed in K₃C₆₀ at 10 THz [8]) is the vacuum mode — the crystal is electromagnetically transparent at ω_tors. The vacuum field at ω_tors exerts a transverse quantum pressure on each Josephson junction site, acting as a natural transverse field: H_vacuum = ħω_tors Σ_i σ_i^x (4) Step 2 — Problem encoding: The coupling matrix J_ij in H_problem = −Σ_{ij} J_{ij}σ_i^zσ_j^z − Σ_i h_iσ_i^z is encoded by locally modifying the Josephson energies E_J{ij} at each junction through the laser-written chi circuit method [7]. Each junction’s E_J ∝ δ_{ij} is set by the local gap, implementing J_{ij} = α δ_{ij}^2 where α is a material constant. The complete annealing Hamiltonian is therefore: H(t) = A(t)·ħω_tors Σ_i σ_i^x + B(t)·(−Σ_{ij} J_{ij}σ_i^zσ_j^z − Σ_i h_iσ_i^z) (5) with A(t): 1 → 0 and B(t): 0 → 1 over the annealing time T_anneal. This is the first quantum annealing Hamiltonian in which H_driver = H_vacuum is not externally generated but is a consequence of the fixed-point condition. No dilution refrigerator, no external magnet, no microwave transverse field source is required. Full derivation of the tunnelling rate and annealing performance guarantees is given in companion paper [17]. V. Mode 3: Gaussian Boson Sampling Gaussian Boson Sampling (GBS) [3,4] requires: (a) squeezed photon sources; (b) a linear optical network U_ij; (c) photon-number-resolving detection; and (d) low insertion loss throughout. Prior implementations require cryogenic photon sources and detectors. At the Nishkala fixed point, all four requirements are satisfied by the crystal at ambient temperature. The key physical fact is the transparency condition from Eq. (2). At λ_L = λ_gap = ħc/δ, the crystal is electromagnetically transparent to photons at the gap frequency ω_Δ = δ/ħ: the impedance mismatch at the crystal surface is Z_s_c − Z₀ = 0, giving zero reflection loss. Photons at ω_Δ propagate through the crystal without absorption or scattering — the laser-in step. The
•May 12, 2026•0 citations