To mitigate these detrimental effects, researchers have adopted a strategy of encoding information into logical qubits, which are themselves constructed from multiple physical qubits. This redundancy, coupled with continuous error correction, aims to preserve quantum information over extended periods, rendering it relatively stable. However, merely storing information is insufficient for harnessing the power of quantum computation. To execute quantum algorithms, qubits must be actively manipulated through quantum gates, the fundamental building blocks of quantum operations. The challenge has been to perform these operations without introducing new errors, a task proving significantly more arduous than maintaining qubit stability in a quiescent state.

Addressing this critical hurdle, a team spearheaded by D-PHYS Professor Andreas Wallraff, in collaboration with researchers from the Paul Scherrer Institute (PSI) and theorists led by Professor Markus Müller at RWTH Aachen University and Forschungszentrum Jülich, has unveiled a groundbreaking method. Their work, recently published in Nature Physics, demonstrates the ability to perform quantum operations between superconducting logical qubits while simultaneously correcting errors. This achievement represents a pivotal advancement towards the realization of fault-tolerant quantum computing, a paradigm where computations can proceed reliably without being undermined by incessant errors.

The intricacies of quantum error correction diverge significantly from its classical counterpart. Classical computers can readily protect information by copying bits. Multiple identical bits can be stored, and if one errs, a comparison and majority vote can reliably determine the correct value. This straightforward duplication is impossible in quantum systems due to the fundamental principle of the no-cloning theorem, which prohibits the exact replication of an arbitrary unknown quantum state. "With qubits, things are a lot more complicated," explains Dr. Ilya Besedin, a postdoctoral researcher in Wallraff’s group and a co-leading author of the study alongside PhD student Michael Kerschbaum. Quantum information cannot be copied; instead, it must be distributed across a network of entangled qubits. Furthermore, quantum systems are susceptible to phase flip errors, a phenomenon absent in classical computing and requiring dedicated correction mechanisms.

A prevalent and effective approach to error correction in quantum computing utilizes surface codes. Within this framework, the information of a single logical qubit is dispersed across several physical data qubits. Error detection is achieved through repeated measurements of specialized quantum elements called stabilizers. These stabilizers, which work in concert with the data qubits to form the logical qubit, provide insights into the integrity of the quantum information. The stabilizers are monitored using additional qubits that are coupled to the data qubits. Their measurements reveal whether a bit flip or a phase flip has occurred between successive checks. Z-type stabilizers are designed to detect changes in the bit value, while X-type stabilizers are sensitive to alterations in the phase. Crucially, the data qubits themselves are never directly measured, ensuring that they can safely store the corrected quantum state without collapsing it.

The complexity escalates when researchers aim to perform logical operations, such as a controlled-NOT (CNOT) gate, between two logical qubits. Errors can arise during the execution of the operation itself, and these must also be rectified. "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," states Kerschbaum. However, in superconducting quantum processors, qubits are fixed in their positions, and interactions are typically limited to neighboring qubits. This physical constraint significantly restricts the ways in which operations can be implemented.

To surmount these limitations, the team ingeniously employed a technique known as lattice surgery. In their experimental setup, the researchers began with a single logical qubit encoded across seventeen physical qubits. The data qubits and stabilizers were arranged in a roughly square configuration. Over a series of carefully timed cycles, stabilizers were measured approximately every 1.66 microseconds, enabling the continuous correction of both bit flips and phase flips.

At a critical juncture in the experiment, three data qubits situated along the central axis of the square were measured. This strategic measurement effectively bifurcated the surface code into two distinct halves. Concurrently, the measurements of the X-type stabilizers were temporarily suspended. "The end result of this operation was that we had two logical qubits entangled with each other," elucidates Besedin. During this splitting process, bit flip errors continued to be corrected. Following the division, bit flip error correction resumed independently on each of the two resulting halves. While this specific operation does not, in isolation, generate a CNOT gate, it serves as a foundational building block 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," remarks Besedin, underscoring the fundamental nature of their achievement. He further elaborates, "To the best of our knowledge, this is the first time lattice surgery has been performed on superconducting qubits, and we still have some way to go. For instance, 41 physical qubits would be required to make the splitting operation on one logical qubit stable against phase flips too." Despite these ongoing challenges, this demonstration of lattice surgery on superconducting qubits represents a monumental stride towards the ambitious objective of constructing useful quantum computers equipped with thousands of qubits, paving the way for a new era of scientific and technological discovery.