Optimality and Complexity in Measured Quantum-State Stochastic Processes

• URL: http://arxiv.org/abs/2205.03958v1
• Date: Sun, 8 May 2022 21:43:06 GMT
• Title: Optimality and Complexity in Measured Quantum-State Stochastic Processes
• Authors: A. Venegas-Li and J. P. Crutchfield
• Abstract summary: We show that optimal prediction requires using an infinite number of temporal features. We identify the mechanism underlying this complicatedness as generator nonunifilarity. This makes it possible to quantitatively explore the influence that measurement choice has on a quantum process' degrees of randomness.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Temporal sequences of quantum states are essential to quantum computation protocols, as used in quantum key distribution, and to quantum computing implementations, as witnessed by substantial efforts to develop on-demand single-photon sources. To date, though, these sources emit qubit sequences in which the experimenter has little or no control over the outgoing quantum states. The photon stream emitted by a color center is a familiar example. As a diagnostic aid, one desires appropriate metrics of randomness and correlation in such quantum processes. If an experimentalist observes a sequence of emitted quantum states via either projective or positive-operator-valued measurements, the outcomes form a time series. Individual time series are realizations of a stochastic process over the measurements' classical outcomes. We recently showed that, in general, the resulting stochastic process is highly complex in two specific senses: (i) it is inherently unpredictable to varying degrees that depend on measurement choice and (ii) optimal prediction requires using an infinite number of temporal features. Here, we identify the mechanism underlying this complicatedness as generator nonunifilarity -- the degeneracy between sequences of generator states and sequences of measurement outcomes. This makes it possible to quantitatively explore the influence that measurement choice has on a quantum process' degrees of randomness and structural complexity using recently introduced methods from ergodic theory. Progress in this, though, requires quantitative measures of structure and memory in observed time series. And, success requires accurate and efficient estimation algorithms that overcome the requirement to explicitly represent an infinite set of predictive features. We provide these metrics and associated algorithms.

Related papers

• Quantum complexity phase transitions in monitored random circuits [0.29998889086656577]
  We study the dynamics of the quantum state complexity in monitored random circuits. We find that the evolution of the exact quantum state complexity undergoes a phase transition when changing the measurement rate.
  arXiv  Detail & Related papers  (2023-05-24T18:00:11Z)
• Statistical learning on randomized data to verify quantum state k-designs [0.0]
  Random ensembles of pure states have proven to be extremely important in various aspects of quantum physics. generating a fully random ensemble is experimentally challenging but approximations are just as useful. verifying their degree of randomness can be an expensive task, similar to performing full quantum state tomography on many-body systems.
  arXiv  Detail & Related papers  (2023-05-02T14:46:28Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Importance sampling for stochastic quantum simulations [68.8204255655161]
  We introduce the qDrift protocol, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.
  arXiv  Detail & Related papers  (2022-12-12T15:06:32Z)
• Anticipative measurements in hybrid quantum-classical computation [68.8204255655161]
  We present an approach where the quantum computation is supplemented by a classical result. Taking advantage of its anticipation also leads to a new type of quantum measurements, which we call anticipative. In an anticipative quantum measurement the combination of the results from classical and quantum computations happens only in the end.
  arXiv  Detail & Related papers  (2022-09-12T15:47:44Z)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• The randomized measurement toolbox [3.2095357952052854]
  We review recently developed protocols for probing the properties of complex many-qubit systems. In all these protocols, a quantum state is repeatedly prepared and measured in a randomly chosen basis. We discuss a range of use cases that have already been realized in quantum devices.
  arXiv  Detail & Related papers  (2022-03-21T22:33:18Z)
• Preparing random states and benchmarking with many-body quantum chaos [48.044162981804526]
  We show how to predict and experimentally observe the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system. Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a wider context.
  arXiv  Detail & Related papers  (2021-03-05T08:32:43Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• Variationally Scheduled Quantum Simulation [0.0]
  We investigate a variational method for determining the optimal scheduling procedure within the context of adiabatic state preparation. In the absence of quantum error correction, running a quantum device for any meaningful amount of time causes a system to become susceptible to the loss of relevant information. Our variational method is found to exhibit resilience against control errors, which are commonly encountered within the realm of quantum computing.
  arXiv  Detail & Related papers  (2020-03-22T14:47:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.