The team successfully executed large-scale algorithms on an error-corrected quantum computer utilizing 48 logical qubits. This represents a significant advance over previous demonstrations, which were limited to one or two logical qubits. This breakthrough signifies a transition from the era of physical qubits to the era of logical, error-corrected qubits, marking a new era in scalable fault-tolerant quantum computing. The research demonstrates enhanced computation stability and reliability through quantum error correction, operating logical qubits with a fidelity superior to the component physical qubits. The fidelity improves as the code distance increases, allowing the correction of more errors. Key developments that enabled this achievement include controlling hundreds of physical qubits (280 in this experiment), the ability to shuttle qubits without losing their quantum state, high-fidelity two-qubit gates with a fidelity of 99.5%, and hardware-efficient control that reduces complexity in performing logical operations. The introduction of a zoned architecture, with separate storage, entangling, and readout zones, and the ability to perform high-fidelity mid-circuit measurements and feedforward operations. This is critical for effective error correction in quantum computations. The approach offers a significant advantage over other modalities like superconducting qubits in terms of scalability and efficiency. It allows for an increase in qubits without a proportional rise in control signals, addressing a major challenge in quantum computing scalability.

These achievements indicate a major step forward in the field of quantum computing, particularly in addressing the challenges of error correction and scalability. While real world applications that offer a definite quantum speedup over classical resources remain out of reach on this machine, it does open the door to new potential use cases and breakthroughs.

Grover’s Algorithm for Database Search:
   – Description: Grover’s algorithm is used for unstructured database search, offering a quadratic speedup over classical algorithms. On a 48 qubit quantum computer, it could perform database searches in roughly √N steps, where N is the size of the database.
   – Metrics & Benchmarks: The classical approach requires O(N) time, whereas Grover’s algorithm operates in O(√N) time. This makes it significantly faster for large N, though the advantage diminishes as N decreases.
   – References: L.K. Grover’s original paper, “A fast quantum mechanical algorithm for database search” (Proceedings, 28th Annual ACM Symposium on the Theory of Computing, 1996), offers an in-depth explanation.

Quantum Simulation Algorithms:
   – Description: Quantum computers can simulate quantum systems naturally, which is a challenging task for classical computers. For a 48 qubit system, this could include simulating molecular structures or quantum material properties.
   – Metrics & Benchmarks: The FLOPS (Floating Point Operations Per Second) required for classical simulation of quantum systems grows exponentially with system size, while quantum computers perform these tasks inherently.
   – References: Richard Feynman’s seminal paper, “Simulating Physics with Computers” (International Journal of Theoretical Physics, 1982), provides foundational concepts.

Quantum Fourier Transform (QFT):
   – Description: QFT is essential for many quantum algorithms, including Shor’s algorithm. It is exponentially faster than its classical counterpart, the Fast Fourier Transform (FFT).
   – Metrics & Benchmarks: Classical FFT operates in O(N log N) time, while QFT on a quantum computer works in O((log N)^2) time.
   – References: The role of QFT in quantum algorithms is detailed in Nielsen and Chuang’s “Quantum Computation and Quantum Information”.

Quantum Machine Learning Algorithms:
   – Description: Quantum algorithms for machine learning, such as quantum support vector machines or quantum neural networks, can potentially offer speedups in processing large datasets.
   – Metrics & Benchmarks: Specific benchmarks are harder to define here, as the field is still exploratory, but theoretical models suggest polynomial to exponential speedups in data processing and training times.
   – References: “Quantum Machine Learning” by Peter Wittek provides an overview of the field.

In conclusion, a 48 logical qubit quantum computer can leverage these algorithms to perform tasks intractably difficult for classical computers, highlighting the transformative potential of quantum computing. However, it’s crucial to note that the practical realization of these advantages depends on factors beyond just qubit count, such as qubit fidelity, error rates, and system architecture.

Additional information about this demonstration is available in a press release issued by QuEra which is available here, an FAQ page available on the QuEra website here, and the paper posted on the Nature magazine website here and the same paper posted on arXiv here.

December 6, 2023