Computing using a continuous-time evolution, based on the natural interaction Hamiltonian of the quantum computer hardware, is a promising route to building useful quantum computers in the near-term. Adiabatic quantum computing, quantum annealing, computation by continuous-time quantum walk, and special purpose quantum simulators all use this strategy. In this work, we carry out a detailed examination of adiabatic and quantum walk implementation of the quantum search algorithm, using the more physically realistic hypercube connectivity, rather than the complete graph, for our base Hamiltonian. We calculate optimal adiabatic schedules both analytically and numerically for the hypercube, and then interpolate between adiabatic and quantum walk searching, obtaining a family of hybrid algorithms. We show that all of these hybrid algorithms provide the quadratic quantum speed up when run with optimal parameter settings, which we determine and discuss in detail. We incorporate the effects of multiple runs of the same algorithm, noise applied to the qubits, and two types of problem misspecification, determining the optimal hybrid algorithm for each case. Our results reveal a rich structure of how these different computational mechanisms operate and should be balanced in different scenarios. For large systems with low noise and good control, quantum walk is the best choice, while hybrid strategies can mitigate the effects of many shortcomings in hardware and problem misspecification. arXiv:1709.00371v3 [quant-ph]

Thermalisation in closed quantum systems occurs through a process of dephasing due to parts of the system outside of the window of observation, gradually revealing the underlying thermal nature of eigenstates. In contrast, closed classical systems thermalize due to dynamical chaos. We demonstrate a deep link between these processes. Projecting quantum dynamics onto variational states using the time-dependent variational principle, results in classical chaotic Hamiltonian dynamics. We study an infinite spin chain in two ways—using the matrix product state ansatz for the wavefunction and for the thermofield purification of the density matrix—and extract the full Lyapunov spectrum of the resulting dynamics. We show that the entanglement growth rate is related to the Kolmogorov–Sinai entropy of dynamics projected onto states with appropriate entanglement, extending previous results about initial entanglement growth to all times. The Lyapunov spectra for thermofield descriptions of thermalizing systems show a remarkable semi-circular distribution.

A "no-knowledge" measurement of an open quantum system yields no information about any system observable; it only returns noise input from the environment. Surprisingly, performing such a noknowledge measurement can be advantageous. We prove that a system undergoing no-knowledge monitoring has reversible noise, which can be canceled by directly feeding back the measurement signal. We show how no-knowledge feedback control can be used to cancel decoherence in an arbitrary quantum system coupled to a Markovian reservoir that is being monitored. Since no-knowledge feedback does not depend on the system state or Hamiltonian, such decoherence cancellation is guaranteed to be general and robust, and can operate in conjunction with any other quantum control protocol. As an application, we show that no-knowledge feedback could be used to improve the performance of dissipative quantum computers subjected to local loss. "More signal, less noise" is the guiding philosophy of experimental science. Increasing measurement sensitivity is a proven strategy for pushing the frontiers of science and technology, yielding improved knowledge and control over nature. However, at the quantum scale physics pushes back by imposing a fundamental limit on the signal-to-noise ratio by virtue of Heisenberg's uncertainty principle [1,2]. Nevertheless, "more signal, less noise" also guides the design of protocols for the measurement and control of quantum systems, such as squeezed state photon [3] and atom [4] interferometry, optimal parameter estimation [5], weak measurement [6], measurement-based feedback control [5,7], and adaptive measurement [8]. In this Letter, we take the unorthodox "no signal, only noise" approach, and consider measurements that are pure noise, and therefore give no knowledge of the quantum state whatsoever. From a quantum control perspective, one intuitively expects such "no-knowledge" measurements to be unworthy of study, since robust feedback control requires at least some (and preferably good) knowledge of the system state. On the contrary, we show that a measurement-based feedback protocol based on no-knowledge monitoring can be used to remove decoherence-the bane of quantum technologyfrom an arbitrary quantum system coupled to a Markovian environment that can be monitored.Although the "no signal, only noise" approach is unorthodox, it has been considered within the context of channel correction. In Refs. [9][10][11], it was proven that coherence could be recovered in a noisy channel provided the conditional evolution was random unitary. Consequently, complete correction is, in principle, possible for systems with dimension d ≤ 3. Furthermore, it was proven that measurements that returned a small amount of knowledge ("little signal, mostly noise") provided a good error correction strategy, and a tradeoff relation between information extraction and correction efficacy was established [12]. Our no-knowledge feedback scheme is consistent with these results; however, it goes several steps further as (1) it concretely ...

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