To combat this pervasive issue, a common strategy involves the concept of logical qubits. Instead of relying on individual, highly sensitive physical qubits, researchers encode the information of a single logical qubit across an ensemble of multiple physical qubits. This redundancy, coupled with continuous error correction protocols, allows for the preservation of quantum information over extended periods, achieving a degree of stability crucial for storage. However, maintaining stable quantum states is only one piece of the puzzle. The true power of quantum computation lies in actively manipulating qubits using quantum gates, the fundamental building blocks of quantum algorithms. The challenge intensifies when attempting to perform these operations without introducing new, detrimental errors. Applying quantum gates to logical qubits while simultaneously correcting errors has proven to be a significantly more formidable task than simply keeping qubits quiescent.

Now, a groundbreaking advancement by a team led by D-PHYS Professor Andreas Wallraff has introduced a novel method that directly addresses this critical challenge. Collaborating with researchers from the Paul Scherrer Institute (PSI) and theoretical physicists led by Professor Markus Müller at RWTH Aachen University and Forschungszentrum Jülich, the group has demonstrated a technique to execute quantum operations between superconducting logical qubits while actively correcting errors in real-time. Their seminal findings, recently published in the prestigious journal Nature Physics, represent a significant leap forward in the pursuit of fault-tolerant quantum computing – a future where quantum calculations can proceed reliably, unhindered by the constant threat of errors.

The distinction between error correction in classical and quantum computing is profound. Classical error correction relies on a principle that is fundamentally incompatible with quantum mechanics: redundancy through copying. In classical systems, information can be duplicated, and multiple identical bits can be stored. Later, these copies can be checked and compared. If one bit errs and flips, a majority vote can easily identify the correct value. This straightforward approach is impossible in the quantum realm due to the no-cloning theorem, which states that an arbitrary unknown quantum state cannot be copied perfectly.

"With qubits, things are a lot more complicated," explains Dr. Ilya Besedin, a postdoctoral researcher in Wallraff’s group and co-leading author of the study, alongside PhD student Michael Kerschbaum. Quantum information cannot be cloned. Instead, it must be distributed across a network of entangled qubits. Furthermore, quantum systems are plagued by phase flip errors, a phenomenon with no direct analogue in classical computing, necessitating entirely different correction mechanisms.

A leading approach to tackle these quantum errors involves the use of surface codes. In this architecture, the information of a single logical qubit is encoded and spread across several physical data qubits. Error detection is achieved through repeated measurements of auxiliary qubits known as stabilizers. These stabilizers, working in conjunction with the data qubits, form the logical qubit. The stabilizers are monitored using additional qubits that are coupled to the data qubits. Measuring the stabilizers provides crucial information about whether a bit flip or a phase flip has occurred since the last check. Specifically, Z-type stabilizers are employed to detect changes in the bit value, while X-type stabilizers are used to identify phase changes. A key advantage of this method is that the data qubits, which hold the precious quantum information, are never directly measured. This ensures that the quantum state, after error correction, remains intact and stable.

The complexity escalates dramatically when the goal shifts from maintaining stable qubits to performing logical operations, such as a controlled-NOT (CNOT) gate, between two logical qubits. Errors can arise not only from the environment but also during the operation itself, and these newly introduced errors must also be corrected. "Performing a logical operation in this fault-tolerant way would be relatively easy if we could move our qubits around and connect them arbitrarily to each other," remarks Kerschbaum. However, in current superconducting quantum processors, qubits are physically fixed in position. Interactions are typically limited to neighboring qubits, imposing significant constraints on how complex operations can be implemented.

To overcome these spatial limitations, the team ingeniously employed a technique known as lattice surgery. In their experimental setup, they began with a single logical qubit encoded across seventeen physical qubits. The data qubits and their associated stabilizers were arranged in a roughly square configuration. Over several carefully timed cycles, stabilizers were measured at regular intervals of 1.66 microseconds, ensuring continuous correction of both bit flips and phase flips.

The crucial innovation occurred at a pivotal moment: three data qubits situated at the center of the square arrangement were measured. This act effectively cleaved the surface code into two independent halves. Concurrently, the measurements of the X-type stabilizers, which detect phase flips, were temporarily halted. "The end result of this operation was that we had two logical qubits entangled with each other," explains Besedin. During this splitting process, bit flip errors continued to be corrected independently on each of the emerging halves. While this lattice surgery operation, in itself, does not directly generate a CNOT gate, it serves as a foundational primitive that can be combined with subsequent splitting and merging operations to construct more complex gates.

"One could say that the lattice surgery operation is the operation, and all the others can be constructed from it," emphasizes Besedin. He adds, "To the best of our knowledge, this is the first time lattice surgery has been performed on superconducting qubits." While acknowledging that further refinement is necessary – for instance, achieving stability against phase flips during the splitting operation would require 41 physical qubits – Besedin highlights the significance of this demonstration. This successful implementation of lattice surgery on superconducting qubits marks a critical stride towards the ambitious objective of building practical quantum computers with thousands of qubits, bringing the transformative potential of quantum computation closer to reality.