Quantum Computing

Abstract

We propose that multi-second coherence times in a quantum processor should be achievable — not through incremental improvements, but through a ~57 cm single-crystal sapphire disc hosting 4000 qubits in a self-stabilizing aperiodic spiral. Unlike traditional processors with discrete connections, this design depends on a continuous sapphire plane — where the medium itself enforces the wave physics needed for coherence.

Electromagnetic wave interference is already a solved problem in military phased-array antennas, where spiral geometries precisely control wave interactions across hundreds of elements (analogous to qubits), creating stable interference patterns.

Qubit stability is wave-driven. This is evident in recent experimental results, where Willow's 7×7 lattice-based surface code demonstrated exponential suppression of logical errors, extending logical qubit lifetimes beyond their best physical qubits. Wave physics dictates stability. Therefore, interference engineering — not just localized error correction — must define quantum processor design.

We propose replacing the traditional qubit lattice with an Archimedean spiral — a continuous curve where qubits are placed along a path defined by r=a+bθ, expanding outward with uniform spacing between turns. By optimizing for the effective wavelength in the continuous sapphire substrate (~1.6 cm at 6 GHz) rather than free-space values (that arise from typical substrate setups), we tailor interference patterns for on-chip propagation. Using established half-wavelength spacing (0.8 cm) from planar antenna design, our architecture scales from 49 qubits (6.4 cm diameter) to 400 qubits (18.4 cm diameter), and ultimately to 4000 qubits (57 cm diameter) — all requiring an unbroken sapphire plane to maintain consistent wave propagation.

At 6 GHz, the quantum environment reshapes itself 6 billion times per second. In conventional architectures, these oscillations propagate chaotically, scattering error across the system. But in our design, aperiodic spiral placement locks interference into a self-stabilizing wave structure inside the uniform sapphire substrate. We introduce a Bessel-function-based metric to quantify this effect, demonstrating substantially reduced residual wave overlap compared to regular lattices. Since each of these 6 billion cycles compounds the benefit of improved error suppression, even modest reductions in per-cycle error rates yield exponential gains in coherence times.

With sufficient precision in fabrication and tuning, this approach offers an extraordinary possibility: A single wave system driving all qubits in perfect harmony, with destructive interference precisely where needed — creating a naturally stable quantum environment.

Introduction

Quantum coherence in superconducting qubits is notoriously fragile. Superconducting quantum bits (qubits) easily lose their quantum state information by interacting with the environment, leading to decoherence and errors. Even with state-of-the-art devices achieving ~99.9% fidelity per operation, this error rate is many orders of magnitude too high – practical quantum computing demands error probabilities on the order of 10⁻¹² (about one in a trillion). Decoherence remains a central obstacle in quantum computing, requiring advances in hardware and error mitigation.

One often overlooked factor in hardware design is the physical geometry of the qubit layout. The spatial arrangement of qubits on a chip can strongly influence crosstalk, mode structure, and thus coherence. For example, qubits that are placed too closely can unintentionally couple to each other or to shared wiring modes, causing crosstalk errors. Conversely, increasing the distance between qubits tends to reduce such unwanted interactions – recent measurements show that crosstalk levels drop as qubit spacing increases.

This suggests that by carefully choosing the geometric layout of qubits, one can mitigate some sources of decoherence and improve overall quantum coherence.

Currently, most superconducting quantum processors use a regular two-dimensional lattice (grid) to position qubits. This choice is partly driven by the needs of quantum error-correcting codes (like the surface code), which require qubits to be arranged with nearest-neighbor connectivity in a planar array. A prominent example is Google's Willow quantum processor, which encodes a single logical qubit in a 7×7 lattice of physical qubits (97 physical qubits in total for one logical qubit).

By scaling up the lattice from smaller sizes (3×3 to 5×5 to 7×7), the Willow chip demonstrated a dramatic reduction in the logical error rate: it achieved the first clear observation of exponential error suppression as the number of physical qubits increased.

In essence, each time the code distance was increased (from a 3×3 to a 5×5 to a 7×7 array of qubits), the encoded qubit became roughly twice as stable (halving the error rate).

This milestone illustrates how adding more qubits in a well-engineered lattice can significantly boost quantum coherence via error correction.

Figure 1 is from the Willow paper: Quantum error correction below the surface code threshold:

Encouraged by such progress, we are motivated to ask whether geometry itself can be optimized to enhance coherence, beyond the standard lattice approach. A regular grid is convenient but may not be the optimal arrangement from an electromagnetic standpoint – its periodic structure can support resonances and correlated noise channels that degrade qubit performance. In the following, we explore an alternative placement strategy: an Archimedean spiral pattern for qubit layout. The hypothesis is that this non-periodic, carefully spaced spiral geometry can intrinsically reduce interference and crosstalk, providing a new route to preserving quantum coherence in superconducting qubit systems.