Researchers at QuTech—a collaboration between the TU Delft and TNO—have
reached a milestone in quantum error correction. They have integrated
high-fidelity operations on encoded quantum data with a scalable scheme for
repeated data stabilization. The researchers report their findings in the
December issue of Nature Physics.

### More qubits

Physical quantum bits, or qubits, are vulnerable to errors. These errors
arise from various sources, including quantum decoherence, crosstalk, and
imperfect calibration. Fortunately, the theory of quantum error correction
stipulates the possibility to compute while synchronously protecting quantum
data from such errors.

"Two capabilities will distinguish an error corrected quantum computer from
present-day noisy intermediate-scale quantum (NISQ) processors," says Prof
Leonardo DiCarlo of QuTech. "First, it will process quantum information
encoded in logical qubits rather than in physical qubits (each logical qubit
consisting of many physical qubits). Second, it will use quantum parity
checks interleaved with computation steps to identify and correct errors
occurring in the physical qubits, safeguarding the encoded information as it
is being processed." According to theory, the logical error rate can be
exponentially suppressed provided that the incidence of physical errors is
below a threshold and the circuits for logical operations and stabilization
are fault tolerant.

### All the operations

The basic idea thus is that if you increase the redundancy and use more and
more qubits to encode data, the net error goes down. The researchers at TU
Delft, together with colleagues at TNO, have now realized a major step
toward this goal, realizing a logical qubit consisting of seven physical
qubits (superconducting transmons). "We show that we can do all the
operations required for computation with the encoded information. This
integration of high-fidelity logical operations with a scalable scheme for
repeated stabilization is a key step in quantum error correction," says Prof
Barbara Terhal, also of QuTech.

First author and Ph.D. candidate Jorge Marques further explains, "Until now
researchers have encoded and stabilized. We now show that we can compute as
well. This is what a fault-tolerant computer must ultimately do: process and
protect data from errors all at the same time. We do three types of
logical-qubit operations: initializing the logical qubit in any state,
transforming it with gates, and measuring it. We show that all operations
can be done directly on encoded information. For each type, we observe
higher performance for fault-tolerant variants over non-fault-tolerant
variants." Fault-tolerant operations are key to reducing the build-up of
physical-qubit errors into logical-qubit errors.

### Long term

DiCarlo emphasizes the multidisciplinary nature of the work: "This is a
combined effort of experimental physics, theoretical physics from Barbara
Terhal's group, and also electronics developed with TNO and external
collaborators. The project is mainly funded by IARPA and Intel Corporation."

"Our grand goal is to show that as we increase encoding redundancy, the net
error rate actually decreases exponentially," DiCarlo concludes. "Our
current focus is on 17 physical qubits and next up will be 49. All layers of
our quantum computer's architecture were designed to allow this scaling."

### Reference:

J. F. Marques et al, Logical-qubit operations in an error-detecting surface
code, Nature Physics (2021).
DOI: 10.1038/s41567-021-01423-9

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