Physicists have long sought to understand the irreversibility of the world around them and have credited its appearance to the basic symmetrical laws of physics. According to quantum mechanics, the ultimate irreversibility of the conceptual reversal of time requires extremely complex and indisputable scenarios that are unlikely to occur spontaneously in nature. Physicists have previously shown that while reversing time is exponentially impossible in a natural environment ̵

1; it is possible to devise an algorithm to artificially reverse a time arrow into a known or given state within an IBM quantum computer. However, this version of the inverted time arrow only embraced a known quantum state and has therefore been compared to the quantum version of subtraction printing in a video to “reverse the flow of time”.In a new report now published in *Physics of communication*, Physicists AV Lebedev and VM Vinokur and their colleagues in advanced materials, physics and engineering in the US and Russia, built on their previous work to develop a technical method to reverse the temporary evolution of an arbitrary quantum state unknown. Technical work will open up new avenues for general universal algorithms to send the temporary evolution of an arbitrary system back in time. This work only describes the mathematical process of time reversal without experimental applications.

**Time arrow and developing a time return protocol**

The time arrow derives from the expression of the direction of time in a singular path in relation to the second law of thermodynamics, which implies that the increase in entropy stems from the distribution of energy of the system in the environment. Scientists, therefore, can consider the distribution of energy in relation to the confusion of the system with the environment. Previous research has focused solely on the time arrow quantum view and understanding the effects of the Landau-Neumann-Wigner hypothesis to measure the complexity of the time arrow return on an IBM quantum computer. In the present work, scientists propose the use of a thermodynamic reservoir at finite temperatures to form a stochastic bath with high entropy, to heat a certain quantum system, and to experimentally increase the thermal disorder or entropy in the system. However, experimentally, IBM computers do not support heating, which forms the first step in the currently proposed cycle.

In theory, the presence of the thermal reservoir suddenly made it possible to prepare the high-temperature thermal conditions of an (alternative) quantum auxiliary system elsewhere, governed by the same Hamiltonian (an operator corresponding to the sum of kinetic energy and potential energies for all particles in the system). This allowed Lebedev and Vinokur to mathematically create a backward time operator to reverse chronological dynamics in a given quantum system.

**Universal procedure and support system**

The team determined the universal time reversal process of an unknown quantum state using the density matrix of a quantum system (a mixed state); to describe the return of the evolution of the time system to return to its original state. The quantum state of the new system may remain unknown during the implementation of the time return arrow. In contrast to the previous time reversal protocol of a known quantum state, the initial state did not have to be of a purely unrelated state or it could remain in a mixed state and correlate with past interactions with the environment. The team noted the reduced complexity of the turnaround time for a mixed state of high entropy in the system.

Lebedev et al. was drawn into the detailed return procedure previously by S. Lloyd, Mohseni, and Rebentrost (LMR procedure) to construct or design the initial density matrix. The LMR procedure considered the combined adjustment of the system in question and an auxiliary to perform a reversible calculation. The experimental system will be equipped with a thermodynamic bath to heat the aniline and provide the desired state for reverse evolution. The hotter the system, the more chaotic it would become. Using a heat reservoir to expose the auxiliary system to an extremely high temperature, Lebedev et al. paradoxically aim to experimentally observe the cold and ordered past of the primary system using the LMR formula. The authors reason that a universal time reversal algorithm can do an inverse calculation without a specific quantum state to retrieve, as long as the algorithm facilitates the return of time to its point of origin.

**The computer complexity of the time-lapse procedure**

The work only describes the mathematical analysis of time change without specifying experimental applications. As it practiced the change of time, the proposed system continued to maintain evolution ahead ruled by Hamiltonian himself. The computational complexity of turning time for an unknown quantum state was proportional to the square of the spatial dimension of the Hilbert space of the system (an abstract vector space). To accomplish this in practice, the experimental system will require a natural system that evolves under an unknown Hamiltonian alongside thermalization, which quantum computers do not support, paired with universal quantum gates to achieve time reversal. As a result, the practical implementation of this work will require an update to existing quantum computers to meet the described requirements.

**A way to update the existing model of quantum chips**

Lebedev et al. therefore aim to update the existing model of quantum chips to achieve a set of interactive qubits (quantum pieces) that can terminate demand in a high temperature environment. To accomplish this, superconducting cubits can be coupled to a transmission line where high temperature thermal radiation will be fed to place the quotes in a high temperature state. After that, they will look for a second set of cubes that can maintain a quantum state similar to the original set of cubes. When the original set of domes is then terminated experimentally to implement the common LMR evolution, subsequent cubes will be able to undergo time-reversed dynamics under the same Hamiltonian to reach the original state. If implemented correctly, the proposed mechanism will also facilitate the error correction of an updated quantum computer to confirm its correct function. Lebedev et al. provide for the implementation of the procedure on emergency computers with demand-terminalized cubes.

In this way, Lebedev and Vinokur demonstrated the procedure of time reversal of an unknown mixed quantum state. The process relies on the execution of the LMR protocol and the existence of an anila system, the dynamics of which can be governed by the same Hamiltonian as the Hamiltonian of the returned system. To perform the protocol return procedure, the LMR protocol will need to be applied sequentially to the common state of the system and the aniline, prepared in a thermal state. The work developed a formula to underline the number of cycles that need to be repeated to turn the state of a given system back to previous states in the past. This number will depend on the complexity of the system and how far in time it is expected to go. When applying the turnaround protocol, the rate of operation of the LMR procedure must be high enough to overcome the evolution of the forward time of the return system.

Thermal chaos returns the quantum system to its unknown past

**More information:**

AV Lebedev et al. Return in time of an unknown quantum state,

*Physics of communication*(2020). DOI: 10.1038 / s42005-020-00396-0

Seth Lloyd et al. Analysis of the main quantum component, *Physics of nature* (2014). DOI: 10.1038 / nfys3029

Gonzalo Manzano et al. Quantum fluctuation theorems for arbitrary environments: Production of Adiabatic and Nonadiabatic Entropy, *Physical Review X* (2018). DOI: 10.1103 / PhysRevX.8.031037

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**citation**: Timely return of an unknown quantum state (2020, August 10) Retrieved 11 August 2020 from https://phys.org/news/2020-08-time-reversal-unknown-quantum-state.html

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