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
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
The thesis investigates three challenges in superconducting quantum computing: efficient quantum gate compilation, scalable microwave interfacing of quantum processors (QPUs), and electrical annealing of Josephson junctions.The first part addresses an inefficiency in contemporary two-qubit gate compilation. Universal quantum computation requires only a single entangling two-qubit gate alongside single-qubit rotations, but this minimal gate set requires up to three additional two-qubit gates for every unsupported gate. I show how access to multiple inequivalent two-qubit gate classes overcomes this inefficiency. I experimentally realised an unsupported SWAP operation using one parametric CZ and one parametric iSWAP gate on a circuit-QED architecture. A Kraus-Cirac analysis shows that this combination belongs to the SWAP equivalency class, the fundamental reason for the reduction in two-qubit gates. The experiment demonstrates a rare case of simultaneous CZ and iSWAP support in the same quantum circuit, illustrating how access to multiple inequivalent gate classes can reduce compilation overhead on real hardware.The second part explores direct digital synthesis of microwave signals for interfacing with quantum processors. Conventional control uses heterodyne upconversion with IQ mixers, requiring compensation of LO leakage and IQ skew. I investigated a mixerless architecture based on high-speed DAC/ADC systems to generate and analyse the required microwave signals. CZ and iSWAP gate experiments subsequently verify that the platform is equivalent to conventional QPU setups.The third part investigates post-fabrication electrical tuning of Josephson junctions, in which voltage pulses modify junction resistance to correct fabrication-induced transmon-frequency variations. The speed of resistance change was found to depend exponentially on pulse amplitude. A novel stepwise protocol achieved a 270% resistance increase in an 11-month-old 11.5 kΩ junction, corresponding to a ~2 GHz reduction in transmon frequency, the largest reported selective resistance modification to date. Simulations show that resistance, charging-energy, and superconducting-gap uncertainties contribute equally to the uncertainty in the final qubit frequency. The results support a picture where electrical manipulation modifies the energy landscape, accelerating natural junction ageing.The thesis demonstrates that investigating gate-level compilation strategies, fully digital QPU control, and post-fabrication tuning, helps advance the understanding of how to approach scalable superconducting quantum processors.
Superconducting quantum computing is a solid state quantum computing technology based on Josephson junction circuits. It becomes one of the most promising candidates for realizing practical quantum computer/simulator, because of its scalability, easy to coupling and control, compatibility to semiconductor technologies, etc. As the complicated electromagnetic environment in solid state metal and insulator, superconducting quantum bits (qubits) suffered from shot coherence time since its early development. In this review, we described some recently developed superconducting qubit structures, including Transmon/Xmon, Fluxonium and C-shunt flux qubit. Although these new qubit structures have very different circuit parameters and energy scales, they all find their way to effectively suppress environmental noises. As a result, their coherence time were improved significantly. Transmon, a transmission-line shunted plasma oscillation qubit, was now among the most popular structures for building a multi-qubit superconducting quantum circuit. It introduced a relatively large shunt capacitor to remarkably reduce the charge dispersion. Although the non-linearity is also decreased, by operating in a properly chosen EJ/Ec, transmon can greatly reduce the charge noise while only sacrificing a small amount of non-linearity. Xmon can be considered as a modified version of transmon. It is designed and optimized for multi-qubit operation and measurement with separate X/Y and Z control lines for each qubit, and a readout bus (a transmission line or a low-Q bandpass filter) for simultaneous readout of all the qubits. Fluxonium provide another solution for suppressing the charge noise in Cooper-pair box (CPB). It introduces a large shunt inductance to filter low-frequency offset charge in the small capacitor of the phase-slip junction (the small junction). To keep the qubit operating in the charge region, the shunt inductor should be large enough to keep the impedance larger than the superconducting impedance quantum RQ~1 kΩ. As a result, the inductance can only be provided by a large series of Josephson junctions. Fluxonium keeps the advantage of high anharmonicity of CPB. In addition, it introduces another degree of freedom: external flux Φext. Quasiparticles (electrons or holes) tunneling at the small junction add coherently to produce a ″1+cosφ″ term. As a result, when Φext= Φ0/2, dissipation caused by quasiparticle tunneling is suppressed and the energy relaxation time (T1) increases drastically. C-shunt flux qubit (CSFQ) decreases α and EJ to suppress flux noise in the qubit. While the charge noise becomes the dominant noise source, a large shunt capacitor is added to suppress the charge noise, similar to that in a transmon qubit. It is worth to notice that in CSFQ, the α decreases to below but near 1/2. As a result, the double-well potential no longer exists. The energy structure become similar to transmon, with the anharmonicity be opposite. CSFQ can get a much improved coherence time, while its anharmonicity can be larger than that of transmon. Those new superconducting qubit structures provide different solutions to improve the coherence time. Although it looks much different in circuit models and parameters, they have ideas in common, and may act as guides to other novel designs with longer coherence time. We can summarize as below. (1) The qubit circuit should be free of small superconducting islands. Charge fluctuation in small islands is a major source of decoherence. As a result, increase the area of the islands, that is, increase the capacitance becomes a straight forward way to suppress the charge noise. In Fluxonium, the small junction is connected with a large series of large junctions that there is also no small islands in the whole loop. (2) Remove superconducting loops in the qubit circuit, or minimize the loop size and loop current to suppress flux noise. (3) Bias the phase difference of the small junction to π, where dissipation caused by quasiparticle tunneling can be suppressed coherently. (4) Decrease the coupling bandwidth of qubit to the environment. In a circuit-QED readout scheme, a high-Q readout resonator that dispersively coupled to the qubit protects the qubit from exposed to the electromagnetic environment of the readout circuit. A ″Purcell filter″ can also be added to suppress such decoherence further. In conclusion, we overviewed some qubit engineering techniques or ideas to improve the coherence time, which is a very important figure for building practical quantum computer/simulator. We hope that someone can combine and optimize these ideas, while interact with developments in materials and micro-fabrication technologies, to develop novel new generation superconducting qubit structures in the near future.
Superconducting circuits provide a promising approach for constructing a large-scale quantum computer in the future. In theory, a fault-tolerant quantum computer is suitable for efficiently simulating quantum-mechanical systems, such as molecules, or factorizing large integers - to name a few examples. However, reaching a practical quantum advantage will probably require scaling up the number of qubits in current quantum-processing units by several orders of magnitude while retaining high controllability and high coherence of individual qubits. In this thesis, we first provide a review of the most common superconducting qubit types in order to shed light on the factors that affect the coherence, anharmonicity, and operation of single qubits. Using the insight gained from the review, we theoretically study a novel superconducting qubit circuit that consists of a grounded coplanar waveguide resonator incorporating an embedded Josephson junction in the center conductor of the resonator. The non-linear Josephson junction renders the normal modes of the resonator anharmonic, as a result of which one of the normal modes can be utilized to implement a qubit. The studied circuit, nicknamed as the coplanarium, may provide a high-coherence superconducting qubit since it contains no isolated superconducting islands rendering the qubit immune to dephasing arising from low-frequency charge noise. We derive the quantum Hamiltonian of the distributed circuit from first principles both with and without an external magnetic flux. Using numerical calculations based on our theoretical results, we show that the anharmonicity of the coplanarium qubit can exceed 500 MHz for a qubit frequency of 5 GHz at a flux-insensitive sweet spot if an appropriate external magnetic flux is applied. Importantly, the parameter values used in the numerical simulations are experimentally feasible, and the characteristic impedance of the resonator needs to be no greater than Z0 = 100 Omega. The relatively high anharmonicity can be attributed to a partial cancellation of the quadratic potential-energy terms associated with the Josephson junction and the linear inductance of the resonator. In conclusion, the promising coherence and anharmonicity properties may render the coplanarium qubit an interesting alternative for reducing leakage errors, and the ratio between coherence times and the duration of quantum logic gates in superconducting quantum processors.
Abstract The non-dissipative nonlinearity of Josephson junctions1 converts macroscopic superconducting circuits into artificial atoms2, enabling some of the best-controlled qubits today3, 4. Three fundamental types of superconducting qubit are known5, each reflecting a distinct behaviour of quantum fluctuations in a Cooper pair condensate: single-charge tunnelling (charge qubit6, 7), single-flux tunnelling (flux qubit8) and phase oscillations (phase qubit9 or transmon10). Yet, the dual nature of charge and flux suggests that circuit atoms must come in pairs. Here we introduce the missing superconducting qubit, ‘blochnium’, which exploits a coherent insulating response of a single Josephson junction that emerges from the extension of phase fluctuations beyond 2π (refs. 11–14). Evidence for such an effect has been found in out-of-equilibrium direct-current transport through junctions connected to high-impedance leads15–19, although a full consensus on the existence of extended phase fluctuations is so far absent20–22. We shunt a weak junction with an extremely high inductance—the key technological innovation in our experiment—and measure the radiofrequency excitation spectrum as a function of external magnetic flux through the resulting loop. The insulating character of the junction is manifested by the vanishing flux sensitivity of the qubit transition between the ground state and the first excited state, which recovers rapidly for transitions to higher-energy states. The spectrum agrees with a duality mapping of blochnium onto a transmon, which replaces the external flux by the offset charge and introduces a new collective quasicharge variable instead of the superconducting phase23, 24. Our findings may motivate the exploration of macroscopic quantum dynamics in ultrahigh-impedance circuits, with potential applications in quantum computing and metrology.
The technology of quantum computing is believed to solve certain computational problems significantly faster than classical computers, enabling classically inaccessible problems. However, the technology is still in its infancy and it is still too early to conclude which physical system(s) will form the basis of tomorrow's quantum computer. Small-scale quantum processors, built on the superconducting transmon qubit, demonstrated already the anticipated quantum speed-up. Despite this tremendous milestone, scaling up to a full-fledged quantum computer is far from trivial: with these qubits, the flux-control causes crosstalk between qubits and heating, the room-temperature microwave control is hardly scalable and comes with high energetic radiation, and most importantly, the loss of quantum information in time leads to computational errors. Recent advances in various hybrid semiconductor materials enabled novel voltage-controlled transmons, gatemons, which are less susceptible to heating and crosstalk. Even more exciting, gatemons can be designed to host Majorana zero modes in a way that renders the qubit inherently protected against decoherence. In order to induce Majorana zero modes in such nanowire systems strong magnetic fields are required. Problematically, magnetic fields destroy the superconductivity that these microwave circuits rely on. In this thesis we integrate three types of hybrid Josephson junctions in magnetic field compatible microwave devices. Chapter 4 demonstrates the first graphene-based transmon. Due to the mono-atomic thickness of graphene in combination with magnetic field resilient coplanar waveguide resonators, we are able to operate the transmon circuit at an in-plane magnetic field of 1 Tesla. Chapter 5 embeds an InAs-Al semiconducting nanowire Josephson junction in a high quality factor superconducting transmission line resonator, demonstrating on-chip microwave generation. The gate-controllable semiconducting platform lends itself for fast pulse control, providing a perspective for the coherent on-chip manipulation of artificial two-level systems, in particular superconducting qubits such as transmons. Chapter 6 continues the development of InAs-Al nanowire transmons. The offset-charge-sensitive regime, additional plunger gates and magnetic field compatibility prepares the platform for the detection of coherent coupling between Majorana zero modes, a phenomena which unfortunately still remains unobserved. Additionally, we realise the first InSb-Al gatemon. The higher spin-orbit coupling makes InSb to be a preferred material in the search for Majorana signatures. Chapter 7 reports on the dynamics of quasiparticle tunneling events in real-time across the InAs-Al nanowire junction in a transmon architecture. The magnetic field compatibility of our device up to 1 Tesla together with in-situ voltage-controlled quasiparticle trap engineering, allows us to measure the survival of the charge-parity lifetime up to strong magnetic fields. A result which is extremely important in the research field of topological quantum computing, where the qubit space is defined in the charge-parity.
Speculative Working Paper in the Harmonic Structure of the Standard Model series The chiral Lagrangian of QCD and the Josephson Lagrangian of a superconducting tunnel junction are mathematically identical — both are U(1) Goldstone mode descriptions with the same functional form. The exact mapping fπ² ↔ ħ²n_s/4m and mπ²fπ²/2 ↔ E_J gives a dimensionless ratio E_J/E_C = mπ/2 ≈ 67.5 from QCD geometry alone. This prediction is consistent within 1% of the estimated E_J/E_C of the current world-record coherence transmon (Tuokkola 2025, T1 = 766 μs). Both systems share an identical phase diagram: QCD deconfinement maps to the superconductor insulator-to-superconductor transition, and the pion sits at the quantum critical point E_J/E_C ≈ 1 — simultaneously particle-like and wave-like. The framework further identifies quasiparticle (QP) poisoning as the dominant decoherence mechanism in state-of-the-art transmons and proposes six independent experimental fixes derived from the HSM framework: (SC-3) Al₂O₃ phonon trap exploiting Al-27's integer pion cross-section (σ = 9σ₀ exactly); (SC-4) the sapphire substrate advantage explained by the Al-27 harmonic phonon bath suppressing phonon cascades — testable by comparing ΓQP on Al₂O₃ vs MgO vs SiC substrates; (SC-5) a π-diode Josephson junction in topological Te-125 enriched SnTe implementing asymmetric Cooper pair/QP tunneling; (SC-6) an A²/³ quasiparticle funnel using a Bi→Sn→In→Nb→Al material gradient; (SC-7) substrate phonon commensurability suppressing cosmic ray burst events; and (SC-8) a fundamental QP density floor set by QCD vacuum coupling n_QP_min ~ fπ²mπ/(Δ²×V). Speculative working paper — not peer reviewed.