Automated Compression of Arbitrary Environments (ACE)

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• Scientific research on quantum computing
• Quantum Computers and Quantum Communications
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2023: Introducing an algorithm to accurately calculate quantum systems

Researchers at the Center for Quantum Metamaterials MIEM HSE together with colleagues from Germany Great Britain and proposed algorithm Automatic Compression of Arbitrary Environments (ACE). As TAdviser the HSE reported on February 9, 2023, the method provides qualitatively new possibilities for accurate calculations to study the dynamics of quantum systems. According to scientists, the algorithm will help in the design quantum computers of new communication systems.

Russian scientists have proposed an algorithm for accurately calculating the dynamics of quantum systems

As you know, in ordinary computers, bits - zeros and ones are responsible for transmitting information, in quantum computers they are replaced by quantum bits (qubits). Qubits, like bits, have two main values ​ ​ (states) - 0 and 1. However, unlike a bit, a qubit means that the system is in both states at the same time. It looks like an inexplicable paradox, but can be illustrated by a simple coin analogy. The classic bit 0 (1) is a coin lying with an eagle or a tails up. And the qubit is a rotating coin, it also has an eagle and a tails, but this can only be recognized after the rotation stops, that is, after the destruction of the original state of the coin. Stopping rotation is an analogue of a quantum measurement, as a result of which one of the two qubit states is selected. Quantum computing requires different qubits to be related: for example, states 0 (1) of one qubit are uniquely related to states 0 (1) of another. This relationship between states is called quantum entanglement.

According to the researchers, the main problem of quantum computing in practice arises from the fact that qubits are surrounded by the environment and interact with it. In the process of interaction, the quantum entanglement of qubits disappears - they unravel. You can understand this using the analogy with two coins. If two identical coins are simultaneously started to rotate, and then stopped at the same time after a short time, then the same results may fall out, for example, "tails - tails" or "eagle - eagle." This synchrony between coin rotation is analogous to quantum entanglement. However, if you give the coins to rotate longer, then their movement will gradually lose synchronicity. When stopping the tails (eagles) of one coin, it will no longer fall out synchronously with the tails (eagles) of the other.

The loss of synchronicity occurs due to the fact that when the coin rotates, it loses energy due to friction with the table, and this happens in different ways. In the quantum world, friction (loss of energy due to interaction with the environment) over time leads to a loss of synchronicity, or quantum coherence of qubits. There is a phasing of qubits: the phase of the quantum state (the angle of rotation of the coin) changes almost randomly in time, which leads to the loss of quantum information, and quantum computing becomes impossible, "said the Center for Quantum Metamaterials of the Higher School of Economics.

The main task that many researchers are working on is to maintain the coherence of the quantum state for as long as possible, and for this it is necessary to be able to describe its evolution over time (quantum dynamics) as accurately as possible.

Scientists from the Center for Quantum Metamaterials of MIEM, together with colleagues from Germany and Great Britain, proposed their solution for studying the interaction of a qubit with an environment and changing its quantum state over time - the algorithm "Automatic compression of arbitrary environments."

"The difficulty in calculating quantum dynamics is that the medium has an almost infinite number of oscillatory modes - degrees of freedom. In fact, you need to calculate the dynamics of one quantum system surrounded by trillions of others. Direct calculation is impossible here, no computer can cope with this. However, not all changes to the environment are equally important. The part of the environment that is far from our quantum system does not greatly affect its dynamics. This division into "important" and "unimportant" degrees of freedom of the environment is at the heart of our method, "explained Alexei Vagov, one of the authors of the article, director of the Center for Quantum Metamaterials at the Higher School of Economics.

In the interpretation of quantum mechanics proposed by the famous American physicist Richard Feynman, in order to calculate the quantum state of the system, it is necessary to calculate the sum of all possible paths along which this state can be achieved. According to this approach, a quantum particle (system) can move forward or backward, right or left, even forward in time or backward. To calculate the final state of a particle, one must add the quantum probabilities of all such trajectories.

"The problem is that there are too many such paths, even if the particle is one, and what can we say - for the whole environment. Our algorithm offers a method of how to take into account only such trajectories that contribute to the dynamics of the qubit, discarding those whose contribution to this dynamics is negligible, - said Alexey Vagov. - In our method, the evolution of the qubit and the medium is the product of tensors - matrices or tables of numbers representing the state of the entire system at different points in time. And then we select only those parts of the tensors that are important for the dynamics of the system. "

Scientists emphasize that the algorithm "Automatic compression of arbitrary environments" is implemented in the form of computer code, which is in the public domain. According to the authors of the article, it opens up qualitatively new possibilities for accurate calculations to study the dynamics of a large number of quantum systems. With it, for example, it is possible to calculate how quickly the pairs of entangled photons in the transmission lines of quantum telephony unravel, how far the quantum particle can be "teleported" or for how long the qubits of a quantum computer are unfastered.

The results of the work are published in the journal Nature Physics.