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Building logical qubits in a superconducting quantum computing system
Jay M. Gambetta, Jerry M. Chow, Matthias Steffen
TL;DR
The paper addresses how to build a quantum memory whose encoded logical qubit remains stable against local errors despite the control–coherence conflict in physical qubits. It reviews superconducting-qubit systems using the rotated surface code, their control and readout technology, and engineering challenges. The authors conclude that O(100)-qubit systems are within reach and that this route can support a useful logical-memory demonstration.
Problem
Physical qubits must interact strongly for control and detection while remaining coherent, and a sufficiently stable logical memory has not yet been demonstrated.
Method
The review examines superconducting-qubit coherence, control, readout, rotated-surface-code architecture, and engineering requirements for medium-sized systems.
Results
The review identifies O(100)-qubit systems as within reach and presents the rotated surface code with superconducting qubits as a promising route toward useful logical memory.
Takeaways & Limitations
Progress requires integrating engineering solutions with quantum architectural considerations, especially scalable control, readout, verification, and substrate design.
Abstract
from arXiv · showhide
The technological world is in the midst of a quantum computing and quantum information revolution. Since Richard Feynman's famous "plenty of room at the bottom" lecture, hinting at the notion of novel devices employing quantum mechanics, the quantum information community has taken gigantic strides in understanding the potential applications of a quantum computer and laid the foundational requirements for building one. We believe that the next significant step will be to demonstrate a quantum memory, in which a system of interacting qubits stores an encoded logical qubit state longer than the incorporated parts. Here, we describe the important route towards a logical memory with superconducting qubits, employing a rotated version of the surface code. The current status of technology with regards to interconnected superconducting-qubit networks will be described and near-term areas of focus to improve devices will be identified. Overall, the progress in this exciting field has been astounding, but we are at an important turning point where it will be critical to incorporate engineering solutions with quantum architectural considerations, laying the foundation towards scalable fault-tolerant quantum computers in the near future.
I. INTRODUCTION
Quantum computing seeks computational advantages from entanglement and superposition, but controlling interacting qubits while preserving coherence remains a fundamental challenge. Quantum error correction and fault-tolerant architectures are therefore needed to realize stable logical qubits and quantum memory.
- Motivation: Quantum computers exploit entanglement and superposition to explore computational paths and use interference to select answers.Shor’s algorithm is presented as an example for factoring.
- Motivation: The central hardware conflict is providing strong qubit interactions and external control while preserving quantum coherence.This conflict limits direct use of physical qubits for long, difficult, large-scale computations.
- Quantum error correction: Quantum error correction encodes information in larger physical subsystems and uses redundant entangled states with non-local measurements to extract noise entropy.The approach avoids learning individual physical-qubit states while defining fault-tolerant logical qubits.
- Quantum error correction: The two-dimensional surface code offers an approximately 6.7 × 10^-3 error threshold, nearest-neighbor interactions, simple syndrome circuits, and several fault-tolerant logic methods.Its supported methods include transversal gates, code deformation, and lattice surgery.
- System requirements: Building a quantum computer requires controllable, sufficiently isolated physical qubits, a fault-tolerant architecture, and universal logical operations with initialization and measurement.These requirements connect device-level capabilities to reliable logical computation.
- Scope: The review targets a medium-sized superconducting system and the challenges of reaching O(100) qubits to advance quantum error correction toward a useful fault-tolerant quantum memory.It situates near-term progress between demonstrated small networks and larger systems beyond full classical emulation.
II. THE QUANTUM COMPUTING SYSTEM AND FAULT-TOLERANT ARCHITECTURE
The proposed system separates physical qubits and controls from a logical layer, using a rotated surface code to encode and protect logical information. A classical QEC processor orchestrates syndrome extraction, feedback, and hardware operations, while superconducting implementation requires suitable connectivity and control.
- System architecture: The system has physical and logical layers, with a classical QEC processor controlling physical qubits and applying feedback from measurement outcomes.The logical layer defines encoded qubits and performs logical operations for algorithms.
- Rotated surface code: The rotated surface code uses d^2 data qubits and d^2 − 1 X- and Z-parity stabilizers, leaving one unconstrained degree of freedom as the logical qubit.Logical X and Z operations are represented by operator chains joining their corresponding code boundaries.
- Error correction: The QEC processor repeatedly extracts syndrome bits, identifies error-chain endpoints, and uses minimum-weight perfect matching to determine corrective operations.In each cycle, d^2 − 1 syndrome bits are extracted; unchanged values indicate no detected change.
- Hardware realization: The physical layer places the qubit processor at 15 mK, while room-temperature microwave electronics are filtered and attenuated before reaching the qubits.Cryogenic amplification supports high-fidelity readout and the QEC processor orchestrates control and readout.
- Hardware realization: Quantum buses couple syndrome bits to data qubits, with each bus connecting four data qubits and each qubit connecting to two buses for the required lattice tiling.Directional gates and this connectivity require at least five distinct qubit frequencies for selective two-qubit operations.
- Logical operations: The review focuses on superconducting-qubit technology implementing the rotated surface code and the challenges of constructing a fully error-corrected physical-qubit surface.Logical Hadamard is transversal up to code rotation, while lattice surgery provides a lower-overhead cNOT implementation.
III. COHERENCE OF SUPERCONDUCTING QUBITS
Superconducting qubits rely on Josephson-junction circuits whose anharmonicity isolates computational energy levels, while coherence times and material losses constrain operation quality. The review connects device design, error mechanisms, and emerging multi-qubit implementations.
- Qubit fundamentals: Superconducting qubits combine inductors, capacitors, and Josephson junctions, whose nonlinearity creates anharmonic energy levels for isolating |0⟩ and |1⟩.Typical transition energies lie in the microwave regime, around 4–6 GHz.
- Experimental progress: IBM devices progressed from 2-qubit gate studies and 3-qubit parity measurements to 4-qubit code demonstrations and 8-qubit studies of both parity checks.The devices use combinations of qubits, quantum buses, and readout resonators.
- Coherence: Coherence metrics T1 and T2 quantify energy relaxation and dephasing, and shorter coherence times reduce quantum-operation accuracy.T1 corresponds to decay from |1⟩ to |0⟩, while T2 concerns loss of phase in a superposition.
- Loss mechanisms: Electromagnetic modes coupled to a qubit affect T1, while stray high-frequency radiation can generate quasiparticles.Reducing residual electromagnetic coupling and stray radiation is therefore part of coherence improvement.
- Loss mechanisms: Dielectric loss appears to limit T1 for many superconducting qubits through bulk loss and microscopic two-level systems coupled to electric fields.Individual TLSs can produce avoided level crossings and other undesirable effects.
- Device design: Transmon designs target 5–5.4 GHz transition frequencies, approximately −346 MHz anharmonicity, and charge dispersion below 30 KHz.The stated design targets also include Cq ∼65 fF and I0 ∼27 nA.
IV. CONTROL OF SUPERCONDUCTING QUBITS
Superconducting-qubit control combines microwave single-qubit rotations with several classes of entangling gates, each trading coherence, crosstalk, speed, and circuit complexity. Two-qubit gate fidelity remains a central bottleneck for fault-tolerant operation.
- Arbitrary single-qubit gates plus one two-qubit gate are sufficient for universal quantum control.
- DRAG pulse shaping corrects higher-level effects in weakly anharmonic transmons and has demonstrated single-qubit gate fidelity of 5(2) × 10−4.
- Superconducting entangling gates divide into dynamically flux-tunable gates and fixed-frequency microwave-activated gates.
- Dynamically tunable gates offer negligible interaction during single-qubit operations and maximized interaction during two-qubit operations, but add flux-noise, leakage, and control-complexity risks.
- Fixed-frequency gates can park qubits at coherence sweet-spots, while some schemes require local microwave addressability and face additional tradeoffs.
- Two-qubit gate errors include 6 × 10−3 for DP, 1.4(2)×10−2 for CR, and 2.3×10−2 for RIP; the field targets errors below 10−4.
V. READOUT OF SUPERCONDUCTING QUBITS
Superconducting-qubit readout uses resonator-mediated dispersive shifts to infer qubit states from reflected microwave signals. Improvements increasingly target post-resonator circuitry, filtering, and quantum-limited amplification.
- Dispersive coupling shifts the resonator frequency according to the qubit state, allowing microwave interrogation of the reflected signal.
- Readout improvement focuses substantially on filters and amplifiers placed after the resonator.
- Purcell filters reduce spontaneous emission by modifying the qubit’s coupled external environment at its frequency.
- Quantum-limited parametric amplifiers boost readout signals using Josephson-based three-wave or four-wave mixing.
VI. TECHNICAL CHALLENGES AHEAD
The paper identifies an O(100)-physical-qubit system as a near-term milestone for quantum error-correction experiments and emphasizes that scaling requires coordinated architectural and engineering advances. Key challenges span device geometry, microwave integrity, fabrication, hardware, calibration, verification, software, and QEC overhead.
- An O(100) physical-qubit lattice could support quantum error-correction experiments and provide a stepping stone toward systems containing 10^4 to 10^8 physical qubits.
- Breaking the plane: Scaling beyond a single plane requires three-dimensional integration that remains cryogenically compatible while preserving coherence and gate fidelities.
- Substrate modes: Larger substrates host lower-frequency electromagnetic modes that can increase crosstalk or reduce coherence times; metallic vias are a potential but constrained remedy.
- On-Chip Microwave Integrity: Improperly connected ground planes can create slot-line modes and spurious resonances, producing crosstalk and reduced coherence.
- Josephson-Junction Reproducibility & Accuracy: Josephson-junction critical-current fluctuations of about 10% produce approximately 280 MHz qubit-frequency variation, causing collisions, correlated interactions, leakage, and addressability errors.
- Extensible Control and Readout Hardware: O(100) networks require lower-cost customized control and readout electronics without sacrificing noise performance, low latency, full state discrimination, fast measurement, or reset.
- System Calibration: Robust, extensible calibration becomes critical as connected-qubit systems increase correlated-error possibilities and calibration complexity.
- Verification & Validation: Verification methods often scale exponentially or provide partial information, motivating techniques that assess gates on subsets of larger qubit fabrics.
VII. CONCLUSION
The authors frame full-scale fault-tolerant quantum computing as a difficult but promising long-term goal, while identifying near-term systems beyond classical emulation. They highlight rotated surface code implementations with superconducting qubits as a promising route toward useful logical memory.
- Systems of O(100) qubits are within reach and beyond what can be emulated in full generality on a classical computer.
- A useful logical memory is presented as a culminating milestone for quantum-information hardware.
- The rotated surface code offers a promising route because of its network simplicity and compatibility with superconducting qubits.
- Superconducting-qubit technology has made rapid progress in coherence times, control, and readout, supporting this route toward logical memory.
- The authors characterize the remaining challenges as difficult but not insurmountable, requiring clever engineering and new insights.