# Pioneering algorithm for accurate Qubit calculation

Scientists developed the ACE algorithm to study the interactions of qubits and changes in their quantum state, simplifying quantum dynamics computation and paving the way for advances in quantum computing and telephony.

### Practical quantum computing is another step closer.

The researchers introduced a new algorithm called Automated Compression of Arbitrary Environments (ACE) designed to study the interactions of qubits with their surrounding environment and subsequent changes in their quantum state. By simplifying the computation of quantum dynamics, this algorithm, based on the Feynman interpretation of quantum mechanics, offers new ways to understand and harness quantum systems. Potential applications include advances in quantum telephony and computing, providing more accurate predictions about quantum coherence and entanglement.

Conventional computers use qubits, represented by zeros and ones, to transmit information, while quantum computers use quantum bits (qubits) instead. Similar to bits, qubits have two main states or values: 0 and 1. However, unlike a bit, a qubit can exist in both states at the same time.

While this may seem like a baffling irony, it can be explained by a simple analogy with a coin. A classical bit can be represented as an outstretched coin with a head or tails (one or zero) facing upwards, while a qubit can be thought of as a spinning coin, which also has heads and tails, but whether it is heads or tails can be determined as soon as it stops spinning, i.e. loses its original state.

When a spinning coin stops, it can serve as an analogy for a quantum analogy, in which one of two states of a qubit is determined. in Quantitative statistics, different qubits must be linked together, for example, states 0(1) of one qubit must be uniquely associated with states 0(1) of another qubit. When the quantum states of two or more objects become interconnected, it is called quantum entanglement.

#### Quantum entanglement challenge

The main difficulty with quantum computing is that qubits are surrounded by, and interact with, an environment. This interaction can cause the quantum entanglement of qubits to deteriorate, causing them to separate from each other.

The similarity of two currencies can help understand this concept. If two identical coins are spun at once and then turned off soon after, they may end up with the same side up, whether heads or tails. This synchronization between coins can be compared to quantum entanglement. However, if the coins keep spinning for a longer period of time, they will eventually lose synchronization and will no longer end up with the same side – head or tail – facing upwards.

Loss of synchronization occurs because spinning coins gradually lose energy, mainly due to friction with the table, and each coin does this in a unique way. In the quantum realm, friction, or the loss of energy due to interaction with the environment, eventually leads to quantum decoherence, which means a loss of synchronization between qubits. This results in qubits dephasing, in which the phase of the quantum state (represented by the angle of rotation of the coin) changes randomly over time, causing a loss of quantum information and making quantum computing impossible.

Effective representation is determined entirely automatically and is not based on any approximations or preconceived assumptions. Credit: Alexei Vagov

#### Quantum coherence and dynamics

The main challenge many researchers face today is maintaining quantum coherence for longer periods. This can be achieved by accurately describing the evolution of a quantum state over time, also known as quantum dynamics.

Scientists from the MIEM HSE Center for Quantum Metamaterials, in collaboration with colleagues from Germany and the United Kingdom, have proposed an algorithm called Automated Compression of Arbitrary Environments (ACE) as a solution to study the interaction of qubits with their environment and the resulting changes in their quantum state over time.

#### An insight into quantum dynamics

“The almost infinite number of vibration modes or degrees of freedom in the environment makes computing quantum dynamics particularly difficult. Indeed, this task involves calculating the dynamics of a single quantum system while it is surrounded by trillions of others. Direct calculation is impossible in this case, as no computer can deal with it.

However, not all changes in the environment hold equal significance: those that occur at a sufficient distance from our quantum system are unable to affect its dynamics in major ways. The division into ‘relevant’ and ‘irrelevant’ environmental degrees of freedom lies at the basis of our method,” says Alexei Vagof, co-author of the paper, and director of the MIEM HSE Center for Quantitative Metamaterials.

#### Feynman interpretation and the ACE algorithm

According to the interpretation of quantum mechanics proposed by the famous American physicist Richard Feynman, calculating the quantum state of a system involves calculating the sum of all possible ways in which the state can be achieved. This explanation assumes that a quantum particle (the system) can move in all possible directions, including forward or backward, right or left, and even back in time. The quantum probabilities of all these trajectories must be added to calculate the final state of the particle.

The problem is that there are many possible trajectories for even a single particle, not to mention the entire environment. Our algorithm makes it possible to consider only paths that contribute significantly to qubit dynamics while eliminating those that are negligible. In our method, the evolution of the qubit and its environment are captured by tensors, which are matrices or tables of numbers that describe the state of the entire system at different points in time. We then select only those parts of the tensors that are relevant to the dynamics of the system,” explains Alexey Vagov.

#### Conclusion: Implications of the ACE algorithm

The researchers assert that the automated compression algorithm for arbitrary environments is publicly available and implemented as computer code. According to the authors, it opens up completely new possibilities for the accurate computation of the dynamics of multiple quantum systems. In particular, this method makes it possible to estimate the time until entanglement Photon Pairs in quantum telephony lines will become unentangled, which is how far a quantum particle can teleport, or how long it can take for a quantum computer’s qubits to lose coherence.

Reference: “Simulation of Open Quantum Systems by Automated Compression of Random Environments” By Moritz Sigorek, Michael Kozacchi, Aleksey Fagov, Vollrath-Martin Akst, Brendon W. Lovett, Jonathan Keeling, and Eric M. Guger, March 24, 2022, Available here. nature physics.
DOI: 10.1038/s41567-022-01544-9