We show that encoding superconducting qubits as dual-rail or spin-locked transmons lets a metamaterial waveguide couple them all-to-all while suppressing the spurious entanglement that burdens shared-mode architectures, a step toward the non-local connectivity that quantum low-density parity-check codes require. In a bare-transmon architecture, the dispersive coupling between each populated mode and every idle qubit attached to it entangles spectators with the gate, and cancelling it by dynamical decoupling lengthens every gate. The encoding suppresses this coupling at the hardware level, from second to fourth order in the inverse qubit--mode detuning. A two-tone cross-resonance drive then generates a Mølmer-Sørensen interaction between encoded qubits, which we use for an entangling gate and a joint parity measurement, both selective and parallelizable through different modes. Simulating two dual-rail transmons sharing three resonators with a mode lifetime of $30\,μ$s, we find that heralding transmon relaxation as erasure leaves a gate infidelity of $1.4\times10^{-3}$ at $152$~ns, dominated by photon loss. Photon loss and mode crowding together bound the array size. The gate duration must exceed the inverse mode spacing, which shrinks as the array lengthens, while photon loss grows with gate duration. This bound grows linearly with the mode lifetime and with the inter-resonator coupling; at a lifetime of $150\,μ$s, five times the simulated value, and a coupling of $80$~MHz, a $10^{-3}$ error budget admits $13$ qubits on $25$ resonators.
AI Summary
Shared-mode superconducting architectures offer nonlocal interactions, but populated bus modes dispersively entangle idle spectator qubits. This paper proposes coupling dual-rail or spin-locked transmons through a chain of resonators, using the encoding to suppress unwanted dispersive coupling while retaining drive-activated interactions. Perturbative effective-Hamiltonian calculations give dual-rail dispersive coupling scaling as $\Delta^{-4}$ rather than the bare-transmon $\Delta^{-2}$, while the desired cross-resonance interaction remains $g_{CR}\sim\eta g\Omega/\Delta^2$. Balanced two-tone drives produce a Mølmer–Sørensen interaction, enabling pair-selective entangling gates and photon-number-based joint parity measurements, with different modes providing parallel channels.
Full-Hamiltonian simulations of two dual-rail qubits attached to three resonators yield gate infidelity $1.4\times10^{-3}$ at $152$ ns for mode lifetime $30\,\mu$s; photon loss contributes 81%. This excludes heralded transmon relaxation, whose erasure probability is $3.2\times10^{-3}$ for transmon lifetime $100\,\mu$s. Analytical error estimates combine photon loss, spectral crowding, and spectator erasure. With $J/2\pi=80$ MHz and mode lifetime $150\,\mu$s, they admit 13 encoded qubits on 25 resonators within a $10^{-3}$ gate-error budget, provided sufficient drive strength is available.
The results are theoretical; large-array capacity is estimated rather than demonstrated. Strong-drive operation requires numerical calibration beyond the perturbative regime. Parity-readout estimates assume unit detection efficiency, filtering, and QND operation. Stated unresolved errors include 5–26% photon-loss probabilities during readout and vacuum outcomes from displaced even-parity states that mimic odd parity; a continuously driven variant remains unstudied.
Little sign of AI-generated textOverclaimsStrong assumptions
Central claim may not hold: The abstract's fourth-order inverse-detuning suppression does not generally hold for the total spin-locked-transmon dispersive coupling, because the supplement derives a potentially dominant contribution proportional to Δ^−3 at fixed locking amplitude.
The proposed parity protocol's 1% photon-number decoding target excludes vacuum ambiguity and photon loss, which produce substantially larger complete-measurement errors at the stated operating parameters.
The supplemental parity protocol specifies a logical Z correction where a logical X correction is required to remove the photon-number-dependent relative phase between |++⟩ and |−−⟩.
Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.
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9 pages, 2 figures (main text with End Matter) + 23 pages of Supplemental Material
We show that encoding superconducting qubits as dual-rail or spin-locked transmons lets a metamaterial waveguide couple them all-to-all while suppressing the spurious entanglement that burdens shared-mode architectures, a step toward the non-local connectivity that quantum low-density parity-check codes require. In a bare-transmon architecture, the dispersive coupling between each populated mode and every idle qubit attached to it entangles spectators with the gate, and cancelling it by dynamical decoupling lengthens every gate. The encoding suppresses this coupling at the hardware level, from second to fourth order in the inverse qubit--mode detuning. A two-tone cross-resonance drive then generates a Mølmer-Sørensen interaction between encoded qubits, which we use for an entangling gate and a joint parity measurement, both selective and parallelizable through different modes. Simulating two dual-rail transmons sharing three resonators with a mode lifetime of 30μs, we find that heralding transmon relaxation as erasure leaves a gate infidelity of 1.4×10−3 at 152~ns, dominated by photon loss. Photon loss and mode crowding together bound the array size. The gate duration must exceed the inverse mode spacing, which shrinks as the array lengthens, while photon loss grows with gate duration. This bound grows linearly with the mode lifetime and with the inter-resonator coupling; at a lifetime of 150μs, five times the simulated value, and a coupling of 80~MHz, a 10−3 error budget admits 13 qubits on 25 resonators.
Shared-mode superconducting architectures offer nonlocal interactions, but populated bus modes dispersively entangle idle spectator qubits. This paper proposes coupling dual-rail or spin-locked transmons through a chain of resonators, using the encoding to suppress unwanted dispersive coupling while retaining drive-activated interactions. Perturbative effective-Hamiltonian calculations give dual-rail dispersive coupling scaling as Δ−4 rather than the bare-transmon Δ−2, while the desired cross-resonance interaction remains gCR∼ηgΩ/Δ2. Balanced two-tone drives produce a Mølmer–Sørensen interaction, enabling pair-selective entangling gates and photon-number-based joint parity measurements, with different modes providing parallel channels.
Full-Hamiltonian simulations of two dual-rail qubits attached to three resonators yield gate infidelity 1.4×10−3 at 152 ns for mode lifetime 30μs; photon loss contributes 81%. This excludes heralded transmon relaxation, whose erasure probability is 3.2×10−3 for transmon lifetime 100μs. Analytical error estimates combine photon loss, spectral crowding, and spectator erasure. With J/2π=80 MHz and mode lifetime 150μs, they admit 13 encoded qubits on 25 resonators within a 10−3 gate-error budget, provided sufficient drive strength is available.
The results are theoretical; large-array capacity is estimated rather than demonstrated. Strong-drive operation requires numerical calibration beyond the perturbative regime. Parity-readout estimates assume unit detection efficiency, filtering, and QND operation. Stated unresolved errors include 5–26% photon-loss probabilities during readout and vacuum outcomes from displaced even-parity states that mimic odd parity; a continuously driven variant remains unstudied.
Quantum error correction using erasure qubits offers higher fault-tolerant thresholds and improved scaling by converting dominant physical errors into detectable erasures. In superconducting circuits, erasure qubits can be constructed using the dual-rail approach, which, however, requires additional qubit-count overhead and tailored coupling elements. Here, we demonstrate a hardware-efficient scheme that operates transmon qutrits as erasure qubits, which is compatible with standard superconducting circuit-QED hardware. The logical states ∣0L⟩ and ∣1L⟩ are represented by the ground and second excited states, while the dominant relaxation errors can be detected via an ancilla qubit using a microwave-activated two-qutrit SWAP gate. We demonstrate a logical qubit T1 lifetime exceeding 500μs, post-selected with repeated mid-circuit erasure detection, which is ten times longer than the T1 time of the transmon physical qubit. Coherence times beyond 300μs are achieved using dynamical decoupling. Single-qubit gate operations reach average Clifford gate infidelity on the order of 10−4. We further demonstrate dual-purposing an ancilla qubit for both erasure detection and parity checking, showing heralded generation of Bell states between erasure qubits. These results suggest that mainstream architectures of transmon qubit arrays may already be capable of implementing erasure-based QEC strategies for hardware-efficient fault-tolerant quantum computing.
Tunable couplings are a central requirement for scalable quantum processing with superconducting quantum circuits. Practical quantum processors must dynamically reconfigure their interaction landscape to accommodate different quantum operations, including idle, single-qubit gates, two-qubit gates, readout, and reset, while maintaining high coherence and suppressing spurious couplings. While widely used tunable interaction approaches rely on single-mode mediation, they are often constrained by nearest-neighbor connectivity, limited on-off ratios, and stringent requirements on qubit frequency allocation. This thesis develops and studies novel strategies for tailoring tunable interactions by moving beyond single-mode mediation, spanning multimode engineered interactions and modeless interaction schemes ("many to no modes"), while accounting for realistic constraints in superconducting hardware. Using a microwave metamaterial waveguide realized by coupled resonator arrays, I demonstrate tunable dissipative interactions that allow on-demand, fast, and high switching-ratio photon emission from a transmon used as a multi-level quantum emitter. This capability is leveraged to achieve deterministic generation of multidimensional photonic cluster states, as well as unconditional reset and leakage reduction of frequency-tunable superconducting qubits. Complementary to these multimode dissipative tunable interactions, this thesis also introduces architectures that realize tunable interactions mediated by many coherent modes or by no mediating modes. I discuss a long-range interaction scheme between superconducting dual-rail qubits mediated by spatially extended eigenmodes of a coupled-resonator array bus. Finally, I propose and analyze a novel modeless coupling architecture based on a SQUID coupler which provides intrinsic cross-Kerr interactions, enabling fast, hybridization-free CZ gates for far-detuned pairs, and discuss its implications for miniaturization of superconducting quantum processors.
For useful quantum computation, error-corrected machines are required that can dramatically reduce the inevitable errors experienced by physical qubits. While significant progress has been made in approaching and exceeding the surface-code threshold in superconducting platforms, large gains in the logical error rate with increasing system size remain out of reach. This is due both to the large number of required physical qubits and the need to operate far below threshold. Importantly, by exploiting the biases and structure of the physical errors, this threshold can be raised. Erasure qubits achieve this by detecting certain errors at the hardware level. Dual-rail qubits encoded in superconducting cavities are a promising erasure qubit wherein the dominant error, photon loss, can be detected and converted to an erasure. In these approaches, the complete set of operations, including two qubit gates, must be high performance and preserve as much of the desirable hierarchy or bias in the errors as possible. Here, we design and realize a novel two-qubit gate for dual-rail erasure qubits based on superconducting microwave cavities. The gate is high-speed ($\sim$500 ns duration), and yields a residual gate infidelity after error detection below 0.1%. Moreover, we experimentally demonstrate that this gate largely preserves the favorable error structure of idling dual-rail qubits, making it ideal for error correction. We measure low erasure rates of $\sim$0.5% per gate, as well as low and asymmetric dephasing errors that occur at least three times more frequently on control qubits compared to target qubits. Bit-flip errors are practically nonexistent, bounded at the few parts per million level. This error asymmetry has not been well explored but is extremely useful in quantum error correction and flag-qubit contexts, where it can create a faster path to effective error-corrected systems.
The design of quantum hardware that reduces and mitigates errors is essential for practical quantum error correction (QEC) and useful quantum computation. To this end, we introduce the circuit-Quantum Electrodynamics (QED) dual-rail qubit in which our physical qubit is encoded in the single-photon subspace, [Formula: see text], of two superconducting microwave cavities. The dominant photon loss errors can be detected and converted into erasure errors, which are in general much easier to correct. In contrast to linear optics, a circuit-QED implementation of the dual-rail code offers unique capabilities. Using just one additional transmon ancilla per dual-rail qubit, we describe how to perform a gate-based set of universal operations that includes state preparation, logical readout, and parametrizable single and two-qubit gates. Moreover, first-order hardware errors in the cavities and the transmon can be detected and converted to erasure errors in all operations, leaving background Pauli errors that are orders of magnitude smaller. Hence, the dual-rail cavity qubit exhibits a favorable hierarchy of error rates and is expected to perform well below the relevant QEC thresholds with today's coherence times.
Qubits with predominantly erasure errors present distinctive advantages for quantum error correction (QEC) and fault-tolerant quantum computing. Logical qubits based on dual-rail encoding that exploit erasure detection have been recently proposed in superconducting circuit architectures, with either coupled transmons or cavities. Here, we implement a dual-rail qubit encoded in a compact, double-post superconducting cavity. Using an auxiliary transmon, we perform erasure detection on the dual-rail subspace. We characterize the behavior of the code space by a novel method to perform joint-Wigner tomography. This is based on modifying the cross-Kerr interaction between the cavity modes and the transmon. We measure an erasure rate of 3.981±0.003 (ms)^{-1} and a residual, postselected dephasing error rate up to 0.17 (ms)^{-1} within the code space. This strong hierarchy of error rates, together with the compact and hardware-efficient nature of this novel architecture, holds promise in realizing QEC schemes with enhanced thresholds and improved scaling.
Generating high-fidelity, tunable entanglement between qubits is crucial for realizing gate-based quantum computation. In superconducting circuits, tunable interactions are often implemented using flux-tunable qubits or coupling elements, adding control complexity and noise sources. Here, we realize a tunable ZZ interaction between two transmon qubits with fixed frequencies and fixed coupling, induced by driving both transmons off resonantly. We show tunable coupling over 1 order of magnitude larger than the static coupling, and change the sign of the interaction, enabling cancellation of the idle coupling. Further, this interaction is amenable to large quantum processors: the drive frequency can be flexibly chosen to avoid spurious transitions, and because both transmons are driven, it is resilient to microwave cross talk. We apply this interaction to implement a controlled phase (CZ) gate with a gate fidelity of 99.43(1)% as measured by cycle benchmarking, and we find the fidelity is limited by incoherent errors.