Variational Consistent Histories as a Hybrid Algorithm for Quantum Foundations

Abstract

Although quantum computers are predicted to have many commercial applications, less attention has been given to their potential for resolving foundational issues in quantum mechanics. Here we focus on quantum computers' utility for the Consistent Histories formalism, which has previously been employed to study quantum cosmology, quantum paradoxes, and the quantum-to-classical transition. We present a variational hybrid quantum-classical algorithm for finding consistent histories, which should revitalize interest in this formalism by allowing classically impossible calculations to be performed. In our algorithm, the quantum computer evaluates the decoherence functional (with exponential speedup in both the number of qubits and the number of times in the history), and a classical optimizer adjusts the history parameters to improve consistency. We implement our algorithm on a cloud quantum computer to find consistent histories for a spin in a magnetic field, and on a simulator to observe the emergence of classicality for a chiral molecule.

9+6 pages, 13 figures, published version

References in corpus (31)

• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• Decoherence, einselection, and the quantum origins of the classical
• The theory of variational hybrid quantum-classical algorithms
• A Quantum Approximate Optimization Algorithm
• Classical Equations for Quantum Systems
• Dynamics of a Quantum Phase Transition
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Quantum autoencoders for efficient compression of quantum data
• Quantum-assisted quantum compiling
• Learning the quantum algorithm for state overlap
• Variational Quantum State Diagonalization
• The SWAP test and the Hong-Ou-Mandel effect are equivalent
• Environment--Induced Decoherence, Classicality and Consistency of Quantum Histories
• Hund's paradox and the collisional stabilization of chiral molecules
• An Introduction to Consistent Quantum Theory
• A Review of the Decoherent Histories Approach to Quantum Mechanics
• Quasiclassical Equations of Motion for Nonlinear Brownian Systems
• Arrival Times, Complex Potentials and Decoherent Histories
• The Objective Past of a Quantum Universe: Redundant Records of Consistent Histories
• Predictability sieve, pointer states, and the classicality of quantum trajectories
• QVECTOR: an algorithm for device-tailored quantum error correction
• Time of arrival and localization of relativistic particles
• Quantum Arrival Time Formula from Decoherent Histories
• Quantum jumps as decoherent histories
• On the Definition of Decoherence
• Numerical Evidence for Approximate Consistency and Markovianity of some Quantum Histories in a Class of Finite Closed Spin Systems
• Variational Quantum Factoring
• Classicality of quantum information processing
• Global coherence of quantum evolutions based on decoherent histories: theory and application to photosynthetic quantum energy transport
• Consistent histories for tunneling molecules subject to collisional decoherence

Cited by in corpus (49)

• Variational Quantum Algorithms
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• Hybrid quantum-classical algorithms and quantum error mitigation
• Absence of Barren Plateaus in Quantum Convolutional Neural Networks
• Robust data encodings for quantum classifiers
• Variational Fast Forwarding for Quantum Simulation Beyond the Coherence Time
• Effect of barren plateaus on gradient-free optimization
• Diagnosing Barren Plateaus with Tools from Quantum Optimal Control
• Variational Quantum Linear Solver
• Noise Resilience of Variational Quantum Compiling
• Trainability of Dissipative Perceptron-Based Quantum Neural Networks
• Large gradients via correlation in random parameterized quantum circuits
• Equivalence of quantum barren plateaus to cost concentration and narrow gorges
• Variational Quantum State Eigensolver
• Barren plateaus preclude learning scramblers
• Higher Order Derivatives of Quantum Neural Networks with Barren Plateaus
• An Adaptive Optimizer for Measurement-Frugal Variational Algorithms
• Variational Quantum Fidelity Estimation
• Machine learning of noise-resilient quantum circuits
• Variational Quantum Algorithm for Estimating the Quantum Fisher Information
• Reformulation of the No-Free-Lunch Theorem for Entangled Data Sets
• Scaling of variational quantum circuit depth for condensed matter systems
• Variational Hamiltonian Diagonalization for Dynamical Quantum Simulation
• Strong bound between trace distance and Hilbert-Schmidt distance for low-rank states
• Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?
• Long-time simulations with high fidelity on quantum hardware
• Non-trivial symmetries in quantum landscapes and their resilience to quantum noise
• Operator Sampling for Shot-frugal Optimization in Variational Algorithms
• Retrieving information from a black hole using quantum machine learning
• Engineered dissipation to mitigate barren plateaus
• Wishart and random density matrices: Analytical results for the mean-square Hilbert-Schmidt distance
• Conditionally rigorous mitigation of multiqubit measurement errors
• Variational Quantum Cloning: Improving Practicality for Quantum Cryptanalysis
• Einselection, Equilibrium and Cosmology
• Experimental Quantum Learning of a Spectral Decomposition
• Stochastic approach for quantum metrology with generic Hamiltonians
• Qsun: an open-source platform towards practical quantum machine learning applications
• Random density matrices: Analytical results for mean root fidelity and mean square Bures distance
• Variational quantum computing for quantum simulation: principles, implementations, and challenges
• Adaptive shot allocation for fast convergence in variational quantum algorithms
• The topology of data hides in quantum thermal states
• Random density matrices: Analytical results for mean fidelity and variance of squared Bures distance
• Probing quantum chaos with the entropy of decoherent histories
• Decoherence of Histories: Chaotic Versus Integrable Systems
• Variational quantum cloning machine on an integrated photonic interferometer
• Emergence of non-Markovian Decoherent Histories in Integrable Environment: A "Tape Recorder" Model for Local Quantum Observables
• A Search for Classical Subsystems in Quantum Worlds