Optimizing quantum gates towards the scale of logical qubits
Paul V. Klimov, Andreas Bengtsson, Chris Quintana, Alexandre Bourassa, Sabrina Hong, A. Dunsworth, Kevin J. Satzinger, William P. Livingston, Volodymyr Sivak, Murphy Yuezhen Niu, Trond I. Andersen, Yaxing Zhang, Desmond Chik, Zijun Chen, Charles Neill, Catherine Erickson, Alejandro Grajales Dau, A. Megrant, P. Roushan, Alexander N. Korotkov, J. Kelly, Vadim Smelyanskiy, Yu Chen, Hartmut Neven
A foundational assumption of quantum error correction theory is that quantum gates can be scaled to large processors without exceeding the error-threshold for fault tolerance. Two major challenges that could become fundamental roadblocks are manufacturing high-performance quantum hardware and engineering a control system that can reach its performance limits. The control challenge of scaling quantum gates from small to large processors without degrading performance often maps to non-convex, high-constraint, and time-dynamic control optimization over an exponentially expanding configuration space. Here we report on a control optimization strategy that can scalably overcome the complexity of such problems. We demonstrate it by choreographing the frequency trajectories of 68 frequency-tunable superconducting qubits to execute single- and two-qubit gates while mitigating computational errors. When combined with a comprehensive model of physical errors across our processor, the strategy suppresses physical error rates by ~3.7× compared with the case of no optimization. Furthermore, it is projected to achieve a similar performance advantage on a distance-23 surface code logical qubit with 1057 physical qubits. Our control optimization strategy solves a generic scaling challenge in a way that can be adapted to a variety of quantum operations, algorithms, and computing architectures.
A foundational assumption of quantum error correction theory is that quantum gates can be scaled to large processors without exceeding the error-threshold for fault tolerance. Two major challenges that could become fundamental roadblocks are manufacturing high-performance quantum hardware and engineering a control system that can reach its performance limits. The control challenge of scaling quantum gates from small to large processors without degrading performance often maps to non-convex, high-constraint, and time-dynamic control optimization over an exponentially expanding configuration space. Here we report on a control optimization strategy that can scalably overcome the complexity of such problems. We demonstrate it by choreographing the frequency trajectories of 68 frequency-tunable superconducting qubits to execute single- and two-qubit gates while mitigating computational errors. When combined with a comprehensive model of physical errors across our processor, the strategy suppresses physical error rates by ~3.7× compared with the case of no optimization. Furthermore, it is projected to achieve a similar performance advantage on a distance-23 surface code logical qubit with 1057 physical qubits. Our control optimization strategy solves a generic scaling challenge in a way that can be adapted to a variety of quantum operations, algorithms, and computing architectures.
Quantum error correction [1–4] is essential for bridging the gap between the error rates of physical devices and the extremely low error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting processors [5–8] have focused primarily on the surface code [9], which offers a high error threshold but poses limitations for logical operations. The color code [10] enables more efficient logic, but it requires more complex stabilizer measurements and decoding. Measuring these stabilizers in planar architectures like superconducting qubits is challenging, and realizations of color codes [11–19] have not addressed performance scaling with code size on any platform. Here, we present a comprehensive demonstration of the color code on a superconducting processor [8]. Scaling the code distance from three to five suppresses logical errors by a factor of Λ 3/5 = 1.56(4). Simulations indicate this performance is below the threshold of the color code, and the color code may become more efficient than the surface code following modest device improvements. We test transversal Clifford gates with logical randomized benchmarking [20] and inject magic states [21], a key resource for universal computation, achieving fidelities exceeding 99 % with post-selection. Finally, we teleport logical states between color codes using lattice surgery [22]. This work establishes the color code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors in the near future.
Quantum computing holds the promise of solving problems that are intractable for classical computers, with applications ranging from optimization and materials simulation to cryptography. It achieves this by leveraging the exponentially scaling dimensionality of the space encoding quantum information and by executing algorithms on quantum registers in superposition states – a feature often referred to as quantum parallelism. However, while encoding information in computational units capable of exploring a continuous set of quantum states enables exponential scaling of computational power with system size, quantum systems are also more susceptible to errors than their classical counterparts. These errors take the form of both control errors, where miscalibration of the control pulses causes coherent errors on the qubit states, as well as incoherent errors due to energy relaxation and dephasing. Scaling quantum systems to run useful algorithms involving hundreds or thousands of logical qubits will require quantum error correction. In this approach, quantum information is redundantly encoded across an entangled state of many physical qubits. This has enabled experimental demonstrations across various platforms – including ion traps, superconducting circuits, and neutral atoms – showing that encoded quantum states can be preserved beyond the coherence times of the constituting physical qubits. However, quantum state preservation is only one component needed for scalable quantum computing. To execute algorithms, it is also necessary to implement quantum gates on and between encoded qubits, in a way that maintains fault tolerance by preserving the ability to correct errors as they occur during the computation. In the first part of this thesis, we demonstrate the implementation of an error-corrected quantum operation that entangles two logical qubits. This is achieved by performing lattice surgery on a distance-three surface code qubit, resulting in a logical Bell state encoded in distance-three repetition codes, which enable the correction of single bit-flip errors. We further introduce techniques to benchmark and characterize the performance of logical operations, including applying the protocol to arbitrary logical input states and performing logical quantum process tomography. Together, these results constitute one of the first realizations of error-corrected lattice surgery in superconducting circuits. While quantum error correction can correct errors provided they occur with sufficiently low frequency, it may fail when many qubits experience errors simultaneously. In the second part of this thesis, we therefore shift focus to a specific error mechanism known to cause correlated errors in superconducting circuits – quasiparticle-induced decoherence. In this case, various forms of energy deposition on the quantum device can break Cooper pairs into quasiparticles, which may subsequently diffuse to the tunnel junction and interact with the qubit state, thereby causing decoherence. In this thesis, we investigate the impact of quasiparticle tunneling on qubit performance, with a focus on infrared-induced quasiparticles. We compare the sensitivity of niobium-based qubits to those made from tantalum – a material that has gained interest in recent years following demonstrations of qubits with improved coherence times based on this material. Using a thermal radiator source, we show that the performance of tantalum qubits may be limited by infrared-induced quasiparticles in typical superconducting circuit experimental setups. By employing both ambient and in-line infrared filters, we investigate the effectiveness of different filtering strategies and develop best practices for engineering cryogenic environments for superconducting quantum processors. The results presented in this thesis contribute to the advancement of quantum computing based on superconducting circuits by implementing and characterizing quantum error-corrected operations, and by investigating quasiparticles as a source of decoherence, along with strategies to improve infrared filtering and signal conditioning in cryogenic environments for future fault-tolerant quantum computing.
Superconducting qubits are a leading platform for quantum computation, yet decoherence and scalability challenges continue to limit progress toward fault-tolerant systems. This review synthesizes research on architectures, noise sources, and error correction to clarify performance trade-offs and guide development. The transition from Transmon to Fluxonium has dramatically improved qubit performance, achieving millisecond-scale coherence times. However, this success reveals a fundamental limit of coherence now being primarily restricted by the physical properties of the materials, specifically dielectric losses occurring at the Josephson junction leads and within the surrounding materials. As overcoming these material limits becomes increasingly difficult, system-level engineering determines whether high-coherence qubits can scale.Scaling quantum systems is difficult because current cooling and control systems create too much heat and this forces a shift to integrated digital superconducting circuits and cryogenic light-based links. While these hardware challenges restrict scaling, experiments in error correction show that logical qubits can already outperform physical ones. For example, a distance-7 surface code improved logical qubit lifetime by 2.4×. Achieving practical fault tolerance, however, requires moving beyond simple error models. Future systems must combine techniques like Dynamical Decoupling and Machine Learning-based Optimal Control with dynamic classical control capable of handling complex, correlated faults such as Multi-Bit Burst Errors. Progress in materials, cryogenic system integration for control, and adaptive error management must advance together to realize scalable, high-fidelity quantum hardware.
Quantum computation holds the promise of solving certain complex problems exponentially faster than classical computers. However, the high prevalent noise in current quantum devices impedes the accurate execution of even basic algorithms. This can be remedied by protecting quantum information with a quantum error-correcting code, where the logical information of an algorithmic qubit is spread across multiple physical qubits. Individual quantum errors are then located and corrected by the fault-tolerant measurement of multi-qubit stabilizer operators (parity checks). Unfortunately, error correction and fault tolerance both impose large demands on the qubit overhead: hundreds to thousands of physical qubits per logical qubit.
We reduce the spacetime cost of fault tolerance by redesigning key building blocks of an error-corrected quantum computer. First, we develop a combinatorial proof with flag fault tolerance that exponentially reduces the extra qubits needed to measure a stabilizer of any size, while tolerating one fault. We leverage these proofs to then design state preparation circuits for the Steane and Golay codes with 100% yield. Next, we improve error correction on a planar layout by showing that a distance-four code encoding six logical qubits protects information as well as the distance-five surface code, using one-tenth as many physical qubits. Finally, we optimize the time overhead of logical gates in surface code quantum computers by protecting measurement results with a classical code, cutting computation time by a factor of two to six. Our hardware-agnostic optimizations of fault tolerance overheads thus suggest new routes to advance the timeline of error-free quantum computing.
Abstract Suppressing errors is the central challenge for useful quantum computing 1 , requiring quantum error correction (QEC) 2–6 for large-scale processing. However, the overhead in the realization of error-corrected ‘logical’ qubits, in which information is encoded across many physical qubits for redundancy 2–4 , poses substantial challenges to large-scale logical quantum computing. Here we report the realization of a programmable quantum processor based on encoded logical qubits operating with up to 280 physical qubits. Using logical-level control and a zoned architecture in reconfigurable neutral-atom arrays 7 , our system combines high two-qubit gate fidelities 8 , arbitrary connectivity 7,9 , as well as fully programmable single-qubit rotations and mid-circuit readout 10–15 . Operating this logical processor with various types of encoding, we demonstrate improvement of a two-qubit logic gate by scaling surface-code 6 distance from d = 3 to d = 7, preparation of colour-code qubits with break-even fidelities 5 , fault-tolerant creation of logical Greenberger–Horne–Zeilinger (GHZ) states and feedforward entanglement teleportation, as well as operation of 40 colour-code qubits. Finally, using 3D [[8,3,2]] code blocks 16,17 , we realize computationally complex sampling circuits 18 with up to 48 logical qubits entangled with hypercube connectivity 19 with 228 logical two-qubit gates and 48 logical CCZ gates 20 . We find that this logical encoding substantially improves algorithmic performance with error detection, outperforming physical-qubit fidelities at both cross-entropy benchmarking and quantum simulations of fast scrambling 21,22 . These results herald the advent of early error-corrected quantum computation and chart a path towards large-scale logical processors.
Current quantum processors are fragile, noisy and fairly limited in both quantity and quality with tens of qubits and physical error rates of around 10^-3. To realize practical quantum applications, however, error rates need to be below 10^-15 across millions of qubits. To bridge this gap and fully harness the potential of quantum computers, quantum error correction (QEC) is essential. QEC codes are designed to protect quantum information by redundantly encoding it onto multiple physical qubits. This encoding allows for the detection and correction of local errors affecting individual qubits, e.g., through stabilizer measurements. Importantly, if the physical error rates are below a specific threshold, QEC codes can exponentially suppress logical error rates by increasing the number of physical qubits involved. This is essential for achieving fault-tolerant computations, which are key to unlocking the full potential of quantum computers. The work presented in this thesis focuses on the implementation and optimization of small-scale QEC experiments using the surface code and flux-tunable superconducting qubits (Transmons). It addresses several key challenges: enhancing two-qubit gate fidelity in Surface-4 (Chapter 2), implementing an error-detection code with Surface-7 (Chapter 3), automating the calibration and benchmarking of the building blocks in Surface-17 (Chapter 4), reducing leakage into higher excited states with leakage reduction units (Chapter 5), assessing and enhancing the performance of logical qubits (Chapters 7 and 8).