scholarly journals Classical Simulation of Quantum Systems?

Physics ◽  
2016 ◽  
Vol 9 ◽  
Author(s):  
James Franson
Keyword(s):  
Quantum Systems ◽  
Classical Simulation

A LOGIC FOR QUANTUM COMPUTATION AND CLASSICAL SIMULATION OF QUANTUM ALGORITHMS

2008 ◽  
Vol 06 (02) ◽  
pp. 255-280
Author(s):  
M. K. PATRA
Keyword(s):  
Quantum Computation ◽  
General Formula ◽  
Quantum Algorithms ◽  
Quantum Systems ◽  
Quantum Circuits ◽  
Finite Dimensional ◽  
Classical Simulation ◽  
Complex Extension

The semantics of a language for reasoning about finite-dimensional quantum systems is presented. This language can express most important classes of assertions about quantum systems, including formulas for outputs of all combinational quantum circuits/algorithms. The main result of this paper is an algorithm for efficient translation of a formula of language into an equivalent formula in another decidable language ℝℂ, which is the language of reals and its complex extension. An important consequence is a descriptive characterization of quantum circuits that can be efficiently simulated classically. We illustrate this with examples of two classes of quantum circuits which are known to have efficient classical simulation. The algorithm for deciding the satisfiability of a general formula can be adapted for the simulation.

scholarly journals From estimation of quantum probabilities to simulation of quantum circuits

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 223 ◽  
Author(s):  
Hakop Pashayan ◽  
Stephen D. Bartlett ◽  
David Gross
Keyword(s):  
Quantum System ◽  
Additional Assumption ◽  
Quantum Systems ◽  
Quantum Circuits ◽  
Computational Power ◽  
Quantum Probabilities ◽  
Output Distribution ◽  
Classical Simulation ◽  
Classical Computer ◽  
Promising Avenue

Investigating the classical simulability of quantum circuits provides a promising avenue towards understanding the computational power of quantum systems. Whether a class of quantum circuits can be efficiently simulated with a probabilistic classical computer, or is provably hard to simulate, depends quite critically on the precise notion of ``classical simulation'' and in particular on the required accuracy. We argue that a notion of classical simulation, which we call EPSILON-simulation (or ϵ-simulation for short), captures the essence of possessing ``equivalent computational power'' as the quantum system it simulates: It is statistically impossible to distinguish an agent with access to an ϵ-simulator from one possessing the simulated quantum system. We relate ϵ-simulation to various alternative notions of simulation predominantly focusing on a simulator we call a poly-box. A poly-box outputs 1/poly precision additive estimates of Born probabilities and marginals. This notion of simulation has gained prominence through a number of recent simulability results. Accepting some plausible computational theoretic assumptions, we show that ϵ-simulation is strictly stronger than a poly-box by showing that IQP circuits and unconditioned magic-state injected Clifford circuits are both hard to ϵ-simulate and yet admit a poly-box. In contrast, we also show that these two notions are equivalent under an additional assumption on the sparsity of the output distribution (poly-sparsity).

scholarly journals Stabiliser states are efficiently PAC-learnable

2018 ◽  
Vol 18 (7&8) ◽  
pp. 541-552
Author(s):  
Andrea Rocchetto
Keyword(s):  
Wave Function ◽  
Fundamental Property ◽  
Computational Learning Theory ◽  
Quantum Systems ◽  
Quantum States ◽  
Computational Learning ◽  
Sample Complexity ◽  
Classical Simulation ◽  
Probably Approximately Correct ◽  
State Tomography

The exponential scaling of the wave function is a fundamental property of quantum systems with far reaching implications in our ability to process quantum information. A problem where these are particularly relevant is quantum state tomography. State tomography, whose objective is to obtain an approximate description of a quantum system, can be analysed in the framework of computational learning theory. In this model, Aaronson (2007) showed that quantum states are Probably Approximately Correct (PAC)-learnable with sample complexity linear in the number of qubits. However, it is conjectured that in general quantum states require an exponential amount of computation to be learned. Here, using results from the literature on the efficient classical simulation of quantum systems, we show that stabiliser states are efficiently PAC-learnable. Our results solve an open problem formulated by Aaronson (2007) and establish a connection between classical simulation of quantum systems and efficient learnability.

Coherent population trapping in quantum systems

1993 ◽  
Vol 163 (9) ◽  
pp. 1 ◽  
Author(s):  
B.D. Agap'ev ◽  
M.B. Gornyi ◽  
B.G. Matisov ◽  
Yu.V. Rozhdestvenskii
Keyword(s):  
Quantum Systems ◽  
Coherent Population Trapping ◽  
Population Trapping

Relaxation of interacting open quantum systems

2018 ◽  
Vol 189 (05) ◽  
Author(s):  
Vladislav Yu. Shishkov ◽  
Evgenii S. Andrianov ◽  
Aleksandr A. Pukhov ◽  
Aleksei P. Vinogradov ◽  
A.A. Lisyansky
Keyword(s):  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum

Entanglement

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Physical Condition ◽  
Physical System ◽  
Polarization State ◽  
Quantum Systems ◽  
Ghz State ◽  
Mathematical Representation ◽  
Entangled State ◽  
Physical Relation

Often a pair of quantum systems may be represented mathematically (by a vector) in a way each system alone cannot: the mathematical representation of the pair is said to be non-separable: Schrödinger called this feature of quantum theory entanglement. It would reflect a physical relation between a pair of systems only if a system’s mathematical representation were to describe its physical condition. Einstein and colleagues used an entangled state to argue that its quantum state does not completely describe the physical condition of a system to which it is assigned. A single physical system may be assigned a non-separable quantum state, as may a large number of systems, including electrons, photons, and ions. The GHZ state is an example of an entangled polarization state that may be assigned to three photons.

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