Illustration of the general measurement and feedback setup, which consists of an open quantum system and a detector with a limited bandwidth γ. The detector continuously measures an arbitrary observable system. The force of the measurement determines the measurement of the recoil. Continuous feedback is applied using the measurement result D to control the Liouville L(D) actuator of the system. Time traces depict the system state S

As modern technology shrinks to the nanoscale, strange quantum effects — such as quantum tunneling, superposition, and entanglement — are becoming prominent. This opens the door to a new era of quantum technologies, where quantum effects can be exploited. Many everyday techniques benefit from routine feedback control; An important example is the pacemaker, which must monitor the user’s heartbeat and apply electrical signals to control it, only when needed. But physicists do not yet have an equivalent understanding of feedback control at the quantum level. Now, physicists have developed a “key equation” that will help engineers understand the feedback on the quantum scale. Their results are published in the journal *physical review messages*.

“It is critical to investigate how this is done Feedback control It can be used in quantum technologies to develop efficient and rapid control methods Quantum Systemsso they can be guided in real time and with high precision,” says co-author Björn Annbe Andersen, a quantum physicist at Lund University in Sweden.

An example of an important process for controlling feedback in Quantitative Statistics he is Quantum Error Correction. A quantum computer encodes information about physical qubits, which could be photons of light or atoms, for example. But the quantum properties of qubits are fragile, so it is likely that the encoded information will be lost if the qubits are perturbed by vibrations or oscillations of electromagnetic fields. This means that physicists need to be able to detect and correct these errors, for example using feedback control. This error correction can be implemented by measuring the state of the qubits, and if a deviation from what is expected is detected, apply feedback to correct it.

But controlling feedback at the quantum level presents unique challenges, precisely because of the fragility that physicists are trying to mitigate. This sensitive nature means that even the feedback process itself can destroy the system. “It is only necessary to interact weakly with the measured system, and to preserve the properties we want to exploit,” Annby-Andersson says.

It is thus important to develop a complete theoretical understanding of quantum feedback control, to set its fundamental limits. But most current theoretical models of quantitative feedback control require computer simulations, which usually only provide quantitative results for particular systems. “It’s hard to draw general qualitative conclusions,” says Anneby 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 commonly referred to as linear feedback.”

**‘paper and pen’**

Annbe Anderson and his colleagues have now developed a key equation called the Fokker Planck quantum equation that enables physicists to track the evolution of any quantum system while controlling for feedback over time. “The equation can describe scenarios beyond linear feedback,” Annby-Andersson says. In particular, the equation can be solved with pen and paper, rather than having to rely on it computer simulation. ”

The team tested their equation by applying it to a simple feedback form. This confirmed that the equation provides physically plausible results and also demonstrated how energy can be harvested in microscopic systems, using feedback control. “The equation is a promising starting point for future studies of how to manipulate energy with the help of information at the microscopic level,” says Annby-Andersson.

The team is now looking at a system that uses feedback to manipulate energy in “quantum dots” — tiny semiconducting crystals a billionth of a meter across. “An important future direction is to use the equation as a tool to create new feedback protocols that can be used for quantum technologies,” says Annby-Andersson.

**more information:**

Björn Annby-Andersson et al, The main Quantum Fokker-Planck equation for continuous feedback control,

*physical review messages*(2022). DOI: 10.1103/ PhysRevLett.129.050401

Presented by the Institute for Foundational Questions

**the quote**: Key Equation Boost for Quantum Technologies (2022, Aug 26) Retrieved on Aug 28, 2022 from https://phys.org/news/2022-08-master-equation-boost-quantum-technologies.html

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