We present a universal mechanism that, acting on any target qubit, propagates it to the state it had T time units before the experiment started. This protocol works by setting the target on a superposition of flight paths, where it is acted on by uncharacterized, but repeatable, quantum operations. Independently of the effect of each of these individual operations on the target, the successful interference of the paths causes it to leap to its past state. We prove that, for generic interaction effects, the protocol will herald a successful rewinding with probability 1 after some finite number of steps.
We present a universal mechanism that, acting on any target qubit, propagates it to the state it had T time units before the experiment started. This protocol works by setting the target on a superposition of flight paths, where it is acted on by uncharacterized, but repeatable, quantum operations. Independently of the effect of each of these individual operations on the target, the successful interference of the paths causes it to leap to its past state. We prove that, for generic interaction effects, the protocol will herald a successful rewinding with probability 1 after some finite number of steps.
In quantum mechanics, the unitary nature of time evolution makes it intrinsically reversible, given control over the system in question. Remarkably, there have been several recent demonstrations of protocols for reverting unknown unitaries in scenarios where even the interactions with the target system are unknown. These protocols are limited by their probabilistic nature, raising the fundamental question of whether time-reversal could be performed deterministically. Here we show that quantum physics indeed allows for this by exploiting the non-commuting nature of quantum operators, and demonstrate a recursive protocol for two-level quantum systems with an arbitrarily high probability of success. Using a photonic platform, we achieve an average rewinding fidelity of over 95%. Our protocol, requiring no knowledge of the quantum process to be rewound, is optimal in its running time, and brings quantum rewinding into a regime of practical relevance.
We consider a scenario where we wish to bring a closed system of known Hilbert space dimension d S (the target), subject to an unknown Hamiltonian evolution, back to its quantum state at a past time t 0 .The target is out of our control: This means that we ignore both its free Hamiltonian and how the system interacts with other quantum systems we may use to influence it.Under these conditions, we prove that there exist protocols within the framework of nonrelativistic quantum physics that reset the target system to its exact quantum state at t 0 .Each "resetting protocol" is successful with nonzero probability for all possible free Hamiltonians and interaction unitaries, save a subset of zero measure.When the target is a qubit and the interaction is sampled from the Haar measure, the simplest resetting circuits have a significant average probability of success and their implementation is within reach of current quantum technologies.Finally, we find that, in case the resetting protocol fails, it is possible to run a further protocol that, if successful, undoes both the natural evolution of the target and the effects of the failed protocol over the latter.By chaining in this fashion several such protocols, one can substantially increase the overall probability of a successful resetting.
Short-time approximations and path integrals can be dominated by high-energy or large-field contributions, especially in the presence of singular interactions, motivating regulators that are suppressive yet removable. Standard regulators typically impose such suppressions by hand (e.g. cutoffs, higher-derivative terms, heat-kernel smearing, lattice discretizations), while here we show that closely related smooth filters can arise as the conditional map produced by interference in a coherently controlled, postselected superposition of evolutions. A successful postselection implements a single heralded operator that is a coherent linear combination of time-evolution operators. For a Gaussian superposition of time translations in quantum mechanics, the postselected step is Vσ,Δt=e−iHΔte−21σ2Δt2H2, i.e.\ the desired unitary step multiplied by a Gaussian energy filter suppressing energies above order 1/(σΔt). This renders short-time kernels in time-sliced path-integral approximations well behaved for singular potentials, while the target unitary dynamics is recovered as σ→0 and (for fixed σ) also as Δt→0 at fixed t. In scalar QFT, a local Gaussian smearing of the quartic coupling induces a positive (σ2/2)φ8 term in the Euclidean action, providing a symmetry-compatible large-field stabilizer; it is naturally viewed as an irrelevant operator whose effects can be renormalized at fixed σ (together with a conventional UV regulator) and removed by taking σ→0. We give short-time error bounds and analyze multi-step success probabilities.
We show that there exist non-relativistic scattering experiments which, if successful, freeze out, speed up or even reverse the free dynamics of any ensemble of quantum systems present in the scattering region. This ``time translation'' effect is universal, i.e., it is independent of the particular interaction between the scattering particles and the target systems, or the (possibly non-Hermitian) Hamiltonian governing the evolution of the latter. The protocols require careful preparation of the probes which are scattered, and success is heralded by projective measurements of these probes at the conclusion of the experiment. We fully characterize the possible time translations which we can effect on multiple target systems through a scattering protocol of fixed duration. The core results are: a) when the target is a single system, we can translate it backwards in time for an amount proportional to the experimental runtime; b) when n targets are present in the scattering region, we can make a single system evolve n times faster (backwards or forwards), at the cost of keeping the remaining n−1 systems stationary in time. For high n our protocols therefore allow one to map, in short experimental time, a system to the state it would have reached with a very long unperturbed evolution in either positive or negative time.
Abstract For decades, researchers have sought to understand how the irreversibility of the surrounding world emerges from the seemingly time-symmetric, fundamental laws of physics. Quantum mechanics conjectured a clue that final irreversibility is set by the measurement procedure and that the time-reversal requires complex conjugation of the wave function, which is overly complex to spontaneously appear in nature. Building on this Landau-Wigner conjecture, it became possible to demonstrate that time-reversal is exponentially improbable in a virgin nature and to design an algorithm artificially reversing a time arrow for a given quantum state on the IBM quantum computer. However, the implemented arrow-of-time reversal embraced only the known states initially disentangled from the thermodynamic reservoir. Here we develop a procedure for reversing the temporal evolution of an arbitrary unknown quantum state. This opens the route for general universal algorithms sending temporal evolution of an arbitrary system backward in time.
Given a quantum gate implementing a d-dimensional unitary operation Ud, without any specific description but d, and permitted to use k times, we present a universal probabilistic heralded quantum circuit that implements the exact inverse Ud−1, whose failure probability decays, exponentially in k. The protocol employs an adaptive strategy, proven necessary for the exponential performance. It requires k≥d−1, proven necessary for exact implementation of Ud−1 with quantum circuits. Moreover, even when quantum circuits with indefinite causal order are allowed, k≥d−1 uses are required. We then present a finite set of linear and positive semidefinite constraints characterizing universal unitary inversion protocols and formulate a convex optimization problem whose solution is the maximum success probability for given k and d. The optimal values are computed using semidefinite programming solvers for k≤3 when d=2 and k≤2 for d=3. With this numerical approach we show for the first time that indefinite causal order circuits provide an advantage over causally ordered ones in a task involving multiple uses of the same unitary operation.