Simulation of n-qubit quantum systems. III. Quantum operations

2007 ◽  
Vol 176 (9-10) ◽  
pp. 617-633 ◽  
Author(s):  
T. Radtke ◽  
S. Fritzsche
Keyword(s):  
Quantum Systems ◽  
Quantum Operations

scholarly journals Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Esteban Castro-Ruiz ◽  
Flaminia Giacomini ◽  
Alessio Belenchia ◽  
Časlav Brukner
Keyword(s):  
Reference Frame ◽  
Reference Frames ◽  
Quantum Systems ◽  
Indefinite Metric ◽  
Causal Order ◽  
Quantum Operations ◽  
Unitary Dilation ◽  
Local Quantum ◽  
Fixed Space ◽  
Quantum Clocks

AbstractThe standard formulation of quantum theory relies on a fixed space-time metric determining the localisation and causal order of events. In general relativity, the metric is influenced by matter, and is expected to become indefinite when matter behaves quantum mechanically. Here, we develop a framework to operationally define events and their localisation with respect to a quantum clock reference frame, also in the presence of gravitating quantum systems. We find that, when clocks interact gravitationally, the time localisability of events becomes relative, depending on the reference frame. This relativity is a signature of an indefinite metric, where events can occur in an indefinite causal order. Even if the metric is indefinite, for any event we can find a reference frame where local quantum operations take their standard unitary dilation form. This form is preserved when changing clock reference frames, yielding physics covariant with respect to quantum reference frame transformations.

Lyapunov control on quantum systems

2014 ◽  
Vol 28 (30) ◽  
pp. 1430020 ◽  
Author(s):  
L. C. Wang ◽  
X. X. Yi
Keyword(s):  
Quantum System ◽  
Open Quantum System ◽  
Open Quantum Systems ◽  
Logic Gates ◽  
Quantum Systems ◽  
Open Quantum ◽  
Quantum Operations ◽  
Lyapunov Control ◽  
Decoherence Free Subspace ◽  
General Method

We review the scheme of quantum Lyapunov control and its applications into quantum systems. After a brief review on the general method of quantum Lyapunov control in closed and open quantum systems, we apply it into controlling quantum states and quantum operations. The control of a spin-1/2 quantum system, driving an open quantum system into its decoherence free subspace (DFS), constructing single qubit and two-qubit logic gates are taken to illustrate the scheme. The optimalization of the Lyapunov control is also reviewed in this article.

GEOMETRIC PHASES FOR MIXED STATES DURING UNITARY AND NON-UNITARY EVOLUTIONS

2003 ◽  
Vol 01 (01) ◽  
pp. 135-152 ◽  
Author(s):  
ARUN K. PATI
Keyword(s):  
Geometric Phase ◽  
Parallel Transport ◽  
Quantum Systems ◽  
Mixed States ◽  
Completely Positive Maps ◽  
Initial State ◽  
Unitary Evolution ◽  
Completely Positive ◽  
Quantum Operations ◽  
Positive Maps

Mixed states typically arise when quantum systems interact with the outside world. Evolution of open quantum systems in general are described by quantum operations which are represented by completely positive maps. We elucidate the notion of geometric phase for a quantum system described by a mixed state undergoing unitary evolution and non-unitary evolutions. We discuss parallel transport condition for mixed states both in the case of unitary maps and completely positive maps. We find that the relative phase shift of a system not only depends on the state of the system, but also depends on the initial state of the ancilla with which it might have interacted in the past. The geometric phase change during a sequence of quantum operations is shown to be non-additive in nature. This property can attribute a "memory" to a quantum channel. We explore these ideas and illustrate them with simple examples.

scholarly journals Quantum Horn's lemma, finite heat baths, and the third law of thermodynamics

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 54 ◽  
Author(s):  
Jakob Scharlau ◽  
Markus P. Mueller
Keyword(s):  
Crucial Role ◽  
Heat Bath ◽  
Quantum Systems ◽  
The Other ◽  
State Transitions ◽  
Quantum Operations ◽  
The Third ◽  
Third Law Of Thermodynamics ◽  
Quantum Version ◽  
Third Law

Interactions of quantum systems with their environment play a crucial role in resource-theoretic approaches to thermodynamics in the microscopic regime. Here, we analyze the possible state transitions in the presence of "small" heat baths of bounded dimension and energy. We show that for operations on quantum systems with fully degenerate Hamiltonian (noisy operations), all possible state transitions can be realized exactly with a bath that is of the same size as the system or smaller, which proves a quantum version of Horn's lemma as conjectured by Bengtsson and Zyczkowski. On the other hand, if the system's Hamiltonian is not fully degenerate (thermal operations), we show that some possible transitions can only be performed with a heat bath that is unbounded in size and energy, which is an instance of the third law of thermodynamics. In both cases, we prove that quantum operations yield an advantage over classical ones for any given finite heat bath, by allowing a larger and more physically realistic set of state transitions.

scholarly journals Quantum Zeno Effect in Open Quantum Systems

2021 ◽  
Author(s):  
Simon Becker ◽  
Nilanjana Datta ◽  
Robert Salzmann
Keyword(s):  
Open Quantum Systems ◽  
Quantum Systems ◽  
Quantum Zeno Effect ◽  
Quantum Dynamical Semigroup ◽  
Open Quantum ◽  
Quantum Operations ◽  
Zeno Effect ◽  
Quantum Dynamical ◽  
Dynamical Semigroup ◽  
First Time

AbstractWe prove the quantum Zeno effect in open quantum systems whose evolution, governed by quantum dynamical semigroups, is repeatedly and frequently interrupted by the action of a quantum operation. For the case of a quantum dynamical semigroup with a bounded generator, our analysis leads to a refinement of existing results and extends them to a larger class of quantum operations. We also prove the existence of a novel strong quantum Zeno limit for quantum operations for which a certain spectral gap assumption, which all previous results relied on, is lifted. The quantum operations are instead required to satisfy a weaker property of strong power-convergence. In addition, we establish, for the first time, the existence of a quantum Zeno limit for open quantum systems in the case of unbounded generators. We also provide a variety of physically interesting examples of quantum operations to which our results apply.

scholarly journals Asymptotic evolution of random unitary operations

Open Physics ◽  
2010 ◽  
Vol 8 (6) ◽  
Author(s):  
Jaroslav Novotný ◽  
Gernot Alber ◽  
Igor Jex
Keyword(s):  
Probability Distribution ◽  
Vector Space ◽  
Quantum Systems ◽  
Quantum Operations ◽  
Large Numbers ◽  
Asymptotic Dynamics ◽  
Low Dimensional

AbstractWe analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits.

scholarly journals Encoding Two-Qubit Logical States and Quantum Operations Using the Energy States of a Physical System

Technologies ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 1
Author(s):  
Dimitrios Ntalaperas ◽  
Nikos Konofaos
Keyword(s):  
Quantum Computer ◽  
Quantum Systems ◽  
Quantum States ◽  
Discrete Energy ◽  
Quantum Operations ◽  
Single Qubit ◽  
Use Of Resources ◽  
Energy States ◽  
Qubit Operations ◽  
Charge Degree

In this paper, we introduce a novel coding scheme, which allows single quantum systems to encode multi-qubit registers. This allows for more efficient use of resources and the economy in designing quantum systems. The scheme is based on the notion of encoding logical quantum states using the charge degree of freedom of the discrete energy spectrum that is formed by introducing impurities in a semiconductor material. We propose a mechanism of performing single qubit operations and controlled two-qubit operations, providing a mechanism for achieving these operations using appropriate pulses generated by Rabi oscillations. The above architecture is simulated using the Armonk single qubit quantum computer of IBM to encode two logical quantum states into the energy states of Armonk’s qubit and using custom pulses to perform one and two-qubit quantum operations.

scholarly journals Floquet-enhanced spin swaps

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Haifeng Qiao ◽  
Yadav P. Kandel ◽  
John S. Van Dyke ◽  
Saeed Fallahi ◽  
Geoffrey C. Gardner ◽  
...  
Keyword(s):  
Quantum Information Processing ◽  
Quantum Systems ◽  
Quantum Computers ◽  
Quantum Operations ◽  
Efficiency Of Algorithms ◽  
Order Of Magnitude ◽  
High Connectivity ◽  
Quantum Phenomena ◽  
Transfer Of Information ◽  
Time Crystals

AbstractThe transfer of information between quantum systems is essential for quantum communication and computation. In quantum computers, high connectivity between qubits can improve the efficiency of algorithms, assist in error correction, and enable high-fidelity readout. However, as with all quantum gates, operations to transfer information between qubits can suffer from errors associated with spurious interactions and disorder between qubits, among other things. Here, we harness interactions and disorder between qubits to improve a swap operation for spin eigenstates in semiconductor gate-defined quantum-dot spins. We use a system of four electron spins, which we configure as two exchange-coupled singlet–triplet qubits. Our approach, which relies on the physics underlying discrete time crystals, enhances the quality factor of spin-eigenstate swaps by up to an order of magnitude. Our results show how interactions and disorder in multi-qubit systems can stabilize non-trivial quantum operations and suggest potential uses for non-equilibrium quantum phenomena, like time crystals, in quantum information processing applications. Our results also confirm the long-predicted emergence of effective Ising interactions between exchange-coupled singlet–triplet qubits.

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