Ludovico Lami of QuSoft and the University of Amsterdam and Mark M. Wilde of Cornell have achieved a major breakthrough in the field of quantum computing by developing a formula that predicts the impact of environmental noise. This formula is critical in the creation of quantum computers that can work in imperfect real-world conditions.

#### The choreography of quantum computing

Quantum computing utilizes the laws of quantum mechanics for computation purposes. Unlike conventional computers that operate using bits that are either 0 or 1, quantum computers utilize quantum bits (qubits) which can be in a superposition of 0 and 1 simultaneously.

This allows quantum computers to perform certain types of calculations much faster than classical computers. For example, a quantum computer can factor very large numbers in a fraction of the time it would take a classical computer.

While one could naively attribute such an advantage to the ability of a quantum computer to perform numerous calculations in parallel, the reality is more complicated. The quantum wave function of the quantum computer (which represents its physical state) possesses several branches, each with its own phase. A phase can be thought of as the position of the hand of a clock, which can point in any direction on the clock face.

At the end of its computation, the quantum computer recombines the results of all computations it simultaneously carried out on different branches of the wave function into a single answer. “The phases associated with the different branches play a key role in determining the outcome of this recombination process, not unlike how the timing of a ballerina’s steps plays a key role in determining the success of a ballet performance,” explains Lami.

#### Disruptive environmental noise

A significant obstacle to quantum computing is environmental noise. Such noise can be likened to a little demon that alters the phase of different branches of the wave function in an unpredictable way. This process of tampering with the phase of a quantum system is called dephasing and can be detrimental to the success of a quantum computation.

Dephasing can occur in everyday devices such as optical fibers, which are used to transfer information in the form of light. Light rays traveling through an optical fiber can take different paths; since each path is associated with a specific phase, not knowing the path taken amounts to an effective dephasing noise.

In their new publication in *Nature Photonics*, Lami and Wilde analyze a model, called the bosonic dephasing channel, to study how noise affects the transmission of quantum information. It represents the dephasing acting on a single mode of light at a definite wavelength and polarisation.

The number quantifying the effect of the noise on quantum information is the quantum capacity, which is the number of qubits that can be safely transmitted per use of a fiber. The new publication provides a full analytical solution to the problem of calculating the quantum capacity of the bosonic dephasing channel, for all possible forms of dephasing noise.

#### Longer messages overcome errors

To overcome the effects of noise, one can incorporate redundancy in the message to ensure that the quantum information can still be retrieved at the receiving end. This is similar to saying “Alpha, Beta, Charlie” instead of “A, B, C” when speaking on the phone. Although the transmitted message is longer, the redundancy ensures that it is understood correctly.

The new study quantifies exactly how much redundancy needs to be added to a quantum message to protect it from dephasing noise. This is significant because it enables scientists to quantify the effects of noise on quantum computing and develop methods to overcome these effects.

Reference: “Exact solution for the quantum and private capacities of bosonic dephasing channels” by Ludovico Lami and Mark M. Wilde, 6 April 2023, *Nature Photonics*.

DOI: 10.1038/s41566-023-01190-4

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