The race to develop quantum computers has really heated up in the last few years. State-of-the-art systems can now run simple algorithms using many qubitsor quantum bits which are the building blocks of quantum computers.

Much of this success has been achieved with so-called gate-based quantum computers. These computers use physical components, particularly superconducting circuits, to host and control qubits. This approach is similar to conventional, device-based classical computers. The two computing architectures are thus relatively compatible and can be used together. In addition, future quantum computers can be created by using the technologies used to create conventional computers.

But the Optical Quantum Computing Research Team at the RIKEN Center for Quantum Computing is taking a very different approach. Instead of optimizing gate-based quantum computers, Atsushi Sakaguchi, Jun-ichi Yoshikawa and Team Leader Akira Furusawa developed quantum computing based on measurement.

## Computing based on measurement

Quantum computers based on measurement process information in a complex quantum state known as a cluster state, which consists of three (or more) qubits linked by a non-classical phenomenon called entanglement. Entanglement is when the properties of two or more quantum particles remain entangled, even when separated by large distances.

Measurement-based quantum computers work by making a measurement of the first qubit of the state of the cluster. The result of this measurement determines what measurement the second entangled qubit will make, a process called feedforward. This then determines how to measure the third. In this way, any quantum gate or circuit can be implemented by appropriately choosing a series of measurements.

Schemes based on measurement are very efficient when used in optical quantum computers, because it is easy to trap many quantum states in an optical system. This makes a measurement-based quantum computer potentially more scalable than a gate-based quantum computer. For the latter, the qubits must be precisely made and oriented for uniformity and physically connected to each other. These issues can be solved automatically by using a measurement based optical quantum computer.

Importantly, measurement-based quantum computing offers programmability in optical systems. “We can change the operation just by changing the measurement,” Sakaguchi said. “This is much easier than changing the hardware, because gated-based optical systems are required.”

But feedforward is important. “Feedforward is a control method where we feed measurement results to different parts of the system as a form of control,” Sakaguchi explained. “In measurement-based quantum computation, feedforward is used to compensate for the inherent randomness of quantum measurements.

The Optical Quantum Computing Research Team and their colleagues from The University of Tokyo, Palack University in the Czech Republic, the Australian National University and the University of New South Wales, Australia have now demonstrated a more advanced form of feedforward: nonlinear feedforward. Nonlinear feedforward is required to implement full potential gates in optics-based quantum computers. The findings are published in the journal *Communication in Nature*.

“We are now experimentally demonstrating nonlinear quadrature measurement using a new nonlinear feedforward technology,” Sakaguchi explained. “This type of measurement has previously been an obstacle to realizing universal quantum operations in optical measurement-based quantum computation.”

**Optical computers**

Optical quantum computers use qubits made of wave packets of light. At other institutions, some of the current RIKEN team previously built the large optical cluster states needed for quantum computation based on measurements. Linear feedforward is also achieved to perform simple gate operations, but more advanced gates require nonlinear feedforward.

A theory for the practical implementation of nonlinear quadrature measurement was proposed in 2016. But this method presents two major practical difficulties: creating a special ancillary state (which the team achieved in 2021) and perform a nonlinear feedforward operation.

The team overcame the latter challenge using complex optics, special electro-optic materials and ultrafast electronics. To do this they take advantage of digital memories, where the desired nonlinear functions are precomputed and recorded in memory. “After the measurement, we convert the optical signal into an electrical one,” Sakaguchi explained. “In linear feedforward, we amplify or attenuate the signal, but we have to do more complex processing for nonlinear feedforward.”

The main advantage of this nonlinear feedforward technique is its speed and flexibility. The process must be fast enough that the output can be synchronized with the optical quantum state.

“Now that we have shown that we can do nonlinear feedforward, we want to apply it to actual quantum computation based on measurement and quantum error correction using our previously developed system,” Sakaguchi said. “And we hope to increase the speed of our nonlinear feedforward for high-speed optical quantum computation.”

“But the key message is that, even if superconducting circuit-based methods become more popular, optical systems are a good candidate for quantum-computer hardware,” he added.

**More information:**

Atsushi Sakaguchi et al, Nonlinear feedforward enabling quantum computation, *Communication in Nature* (2023). DOI: 10.1038/s41467-023-39195-w

**Citation**: Researchers develop a different measurement approach based on quantum computing (2023, December 21) retrieved on December 22, 2023 from https://phys.org/news/2023-12-approach-measurement-based -quantum.html

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