Time reversal of an unknown quantum state

Physicists have long sought to understand the irreversibility of the surrounding world and have attributed its rise to the time-symmetrical, fundamental laws of natural credit. According to quantum mechanics, the definitive irreversibility of conceptual time change requires extremely complex and implicit scenarios that are not likely to occur spontaneously in nature. Physicists have previously shown that although time variability is exponentially unpredictable in a natural environment, it is possible to design an algorithm to artificially return a time game to a known or specified state within an IBM quantum computer. However, this version of the inverted arrow-of-time includes only a known quantum state and is therefore compared to the quantum version of pressing the rewind on a video to “reverse the flow of time.”

In a new report now published in Communication Physics, Physicists AV Lebedev and VM Vinokur and colleagues in materials, physics and advanced engineering in the US and Russia, built on their previous work to develop a technical method to reverse the temporal evolution of any unknown quantum state. The technical work will open new avenues for general universal algorithms to reverse the temporal evolution of any system. This work only outlines the mathematical process of reversal without experimental implementations.

The arrow of time and the development of a protocol for time change

The arrow of time arises from the expression of the direction of time in a single route relative to the second law of thermodynamics, which implies that entropy growth stems from energy distribution of the system to the environment. Scientists can therefore consider energy dissipation relative to the disintegration of the system with the environment. Previous research focused only on the quantum finding of the arrow of time and on understanding the effects of the Landau-Neumann-Wigner hypothesis to quantify the complexity of the reversal of the arrow of time. on an IBM quantum computer. In the present work, scientists propose to use a thermodynamic reservoir at finite temperatures to form a stochastic bath with a high entropy to thermize a particular quantum system and increase experimental thermal disturbance as entropy in the system. Experimentally, however, the IBM computers do not support thermization, which is the first step in the currently proposed cycle.

In theory, the presence of the thermal reservoir unexpectedly made it possible to prepare high temperature thermal states of an auxiliary verb (alternative) quantum system elsewhere, ruled by the same Hamiltonian (an operator corresponding to the sum of kinetic energy and potential energy for all particles in the system). This allowed Lebedev and Vinokur to mathematically devise an evolutionary evolution operator to reverse the chronological dynamics in a given quantum system.

Universal procedure and the tool

The team defines the universal time-reversal process of an unknown quantum state using the density matrix of a quantum system (a mixed state); describe the evolution of the temporal system to return to its original state. The quantum state of the new system could remain unknown when implementing the arrow of time change. Unlike the previous protocol of time change of a known quantum state, the initial state also did not have to be of a purely uncorrelated state and could remain in a mixed state and correlate with past interactions with the environment. The team observed reduced time-reversal complexity for a mixed state with high entropy in the system.

Lebedev et al. used the inversion procedure previously described by S. Lloyd, Mohseni, and Rebentrost (LMR procedure) to construct or map the initial density matrix. The LMR procedure considered the combined scheme of the system in question and an ancilla to achieve reversible calculation. The experimental system will be equipped with a thermodynamic bath to thermize the ancilla and provide the desired state for reverse evolution. The harder the system, the more chaotic it would become. By using a heat reservoir to expose the utility to a very high temperature, Lebedev et al. paradoxically intended to experimentally observe the cold and ordered past of the primary system using the LMR formula. The authors reason that a universal algorithm for time change can turn a calculation in reverse, without a specific quantum state to return, as long as the algorithm facilitates the time movement to its point of origin.

Computational complexity of the time-reversal procedure

The work described only the mathematical analysis of time change without specifying experiments. In the course of time, the proposed system continued to maintain the forward evolution, ruled by its own Hamiltonian. The computational complexity of time change for an unknown quantum state was proportional to the square of the Hilbert space dimension of the system (an abstract vector space). To put this into practice, the experimental system will require a natural system that evolves under an unknown Hamiltonian in addition to thermization, which does not support quantum computers, paired with universal quantum ports to achieve time-lapse. As a result, practical implementation of this work will require an upgrade to existing quantum computers to meet the written requirements.

A route to upgrade the existing design of quantum chips

Lebedev et al. strive to upgrade the existing design of quantum chips to achieve a set of interactive qubits (quantum bits) that can thermize on demand in a high temperature environment. To accomplish this, superconducting qubits can be coupled to a transmission line where high temperature thermal radiation will be fed to set the qubits to a high temperature state. Next, they will require a second set of qubits that can store a quantum state similar to the original set of qubits. If the original set of qubits is then experimentally thermalized to implement the common LMR evolution, subsequent qubits may undergo time-reversed dynamics under the same Hamiltonian to achieve the original state. If precisely implemented, the proposed mechanism will also facilitate error correction of an upgraded quantum computer to confirm the correct function. Lebedev et al. propose the execution of the procedure on emerging computers with thermal qubits on demand.

In this way, Lebedev and Vinokur demonstrated the procedure for changing time from an unknown mixed quantum state. The process depends on the implementation of the LMR protocol and the existence of an ancilla system, whose dynamics can be controlled by the same Hamiltonian as the Hamiltonian of the reverse system. To complete the reversal procedure, the LMR protocol will subsequently need to be applied to the common state of the system and ancilla, prepared in a thermal state. The work developed a formula to mark the number of cycles that would need to be repeated to return the state of a particular system to previous states in the past. This number will depend on the complexity of the system and how far back in time it should go. When implementing the time reference protocol, the operating frequency of the LMR procedure should be high enough to transmit the evolution of forward time of the reverse system.

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