Illustration of a typical measurement and feedback setup consisting of an open quantum system and a detector with finite bandwidth γ. The detector continuously measures any observable system. The measurement intensity λ determines the measurement reaction. A continuous feedback is applied using the measurement result D to control the system’s Liouville superoperator L(D). A time trace visualizes the trajectory of the system state S

As the size of modern technologies shrinks to the nanoscale, strange quantum effects such as quantum tunneling, superposition and entanglement become prominent. This opens the door to a new era of quantum technologies that can exploit quantum effects. Many everyday technologies make use of feedback control on a daily basis. An important example is a pacemaker. A pacemaker should monitor the user’s heartbeat and apply electrical signals to control it only when needed. However, physicists do not yet have a comparable understanding of feedback control at the quantum level. Now physicists have developed a “master equation” to help engineers understand feedback on the quantum scale.The results are published in the journal physical review letter.

“It is important to investigate how feedback control can be used in quantum technology to develop efficient and fast methods for controlling quantum systems, which can be steered in real time with high precision. ,” said co-author Björn Annby. Andersson, a quantum physicist at Lund University in Sweden, said:

An example of an important feedback control process in quantum computing is quantum error correction. Quantum computers encode information into physical qubits, such as photons of light or atoms. However, the quantum properties of qubits are fragile, and the encoded information can be lost if the qubits are perturbed by vibrations or fluctuating electromagnetic fields. This means that physicists should be able to detect and correct such errors, for example using feedback control. This error correction can be implemented by measuring the state of the qubit. It also applies feedback and corrects any deviations from expectations it detects.

But feedback control at the quantum level presents its own challenges, due to the vulnerabilities that physicists are trying to mitigate. Its delicate nature means that even the feedback process itself can break the system. “It’s enough to interact weakly with the measured system while maintaining the properties we want to exploit,” says Amby Anderson.

It is therefore important to develop a complete theoretical understanding of quantum feedback control and establish its fundamental limits. However, most of the existing theoretical models of quantum feedback control require computer simulations and usually give only quantitative results for a particular system. “It’s hard to draw general, qualitative conclusions,” says Amby Anderson. “The few models that can provide a qualitative understanding are applicable only to a narrow class of feedback control systems. This type of feedback is usually called linear feedback.”

‘pen and paper’

Amby Anderson and his colleagues have now developed a master equation called the “quantum Fokker-Planck equation”. This allows physicists to use feedback control to track the evolution of any quantum system over time. “The equations can describe scenarios beyond linear feedback,” says Annby-Andersson. “In particular, the equations can be solved with pen and paper, rather than having to resort to computer simulations.”

The team applied the equation to a simple feedback model and tested it. This confirmed that the equations provide physically plausible results and also demonstrated how feedback control could be used to harvest energy in microscopic systems. “This equation is a promising starting point for future research into how to manipulate energy using microscopic information,” said Annby-Andersson.

The team is currently investigating a system that uses feedback to manipulate the energy of ‘quantum dots’ — tiny semiconductor crystals just a billionth of a meter in diameter. “An important future direction is the use of equations as a tool for inventing new feedback protocols that can be used for quantum technologies,” she says.

Quantum computers work with 0 and more than 1

For more information:
Björn Annby-Andersson et al., Quantum Fokker-Planck Master Equations for Continuous Feedback Control, physical review letter (2022). DOI: 10.1103/PhysRevLett.129.050401

Provided by the Foundational Questions Institute

Quote: The Master Equations to Boost Quantum Technologies (26 August 2022) will be published on 26 August 2022 at https://phys.org/news/2022-08-master-equation-boost-quantum-technologies.html obtained from

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