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Quantum dynamics as a tunable micron-size resonator
Abstract
We present a theoretical analysis of the quantum dynamics of a superconducting circuit based on a highly asymmetric Cooper pair transistor (ACPT) in parallel to a dc-SQUID. Starting from the full Hamiltonian we show that the circuit can be modeled as a charge qubit (ACPT) coupled to an anharmonic oscillator (dc-SQUID). Depending on the anharmonicity of the SQUID, the Hamil-tonian can be reduced either to one that describes two coupled qubits or to the Jaynes-Cummings Hamiltonian. Here the dc-SQUID can be viewed as a tunable micron-size resonator. The coupling term, which is a combination of a capacitive and a Josephson coupling between the two qubits, can be tuned from the very strong-to the zero-coupling regimes. It describes very precisely the tunable coupling strength measured in this circuit [1] and explains the 'quantronium' as well as the adiabatic quantum transfer read-out.
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The creation and manipulation of multipartite entangled states is important for advancements in quantum computation and communication, and for testing our fundamental understanding of quantum mechanics and precision measurements. Multipartite entanglement has been achieved by use of various forms of quantum bits (qubits), such as trapped ions, photons, and atoms passing through microwave cavities. Quantum systems based on superconducting circuits have been used to control pair-wise interactions of qubits, either directly, through a quantum bus, or via controllable coupling. Here, we describe the first demonstration of coherent interactions of three directly coupled superconducting quantum systems, two phase qubits and a resonant cavity. We introduce a simple Bloch-sphere-like representation to help one visualize the unitary evolution of this tripartite system as it shares a single microwave photon. With careful control and timing of the initial conditions, this leads to a protocol for creating a rich variety of entangled states. Experimentally, we provide evidence for the deterministic evolution from a simple product state, through a tripartite W-state, into a bipartite Bell-state. These experiments are another step towards deterministically generating multipartite entanglement in superconducting systems with more than two qubits.
Quantum state tomography is an important tool in quantum information science for complete characterization of multiqubit states and their correlations. Here we report a method to perform a joint simultaneous readout of two superconducting qubits dispersively coupled to the same mode of a microwave transmission line resonator. The nonlinear dependence of the resonator transmission on the qubit state dependent cavity frequency allows us to extract the full two-qubit correlations without the need for single-shot readout of individual qubits. We employ standard tomographic techniques to reconstruct the density matrix of two-qubit quantum states.
The interaction of matter and light is one of the fundamental processes occurring in nature, and its most elementary form is realized when a single atom interacts with a single photon. Reaching this regime has been a major focus of research in atomic physics and quantum optics for several decades and has generated the field of cavity quantum electrodynamics. Here we perform an experiment in which a superconducting two-level system, playing the role of an artificial atom, is coupled to an on-chip cavity consisting of a superconducting transmission line resonator. We show that the strong coupling regime can be attained in a solid-state system, and we experimentally observe the coherent interaction of a superconducting two-level system with a single microwave photon. The concept of circuit quantum electrodynamics opens many new possibilities for studying the strong interaction of light and matter. This system can also be exploited for quantum information processing and quantum communication and may lead to new approaches for single photon generation and detection.
Demonstration of quantum entanglement, a key resource in quantum computation arising from a nonclassical correlation of states,
requires complete measurement of all states in varying bases. By using simultaneous measurement and state tomography, we demonstrated
entanglement between two solid-state qubits. Single qubit operations and capacitive coupling between two super-conducting
phase qubits were used to generate a Bell-type state. Full two-qubit tomography yielded a density matrix showing an entangled
state with fidelity up to 87%. Our results demonstrate a high degree of unitary control of the system, indicating that larger
implementations are within reach.
Short dephasing times pose one of the main challenges in realizing a quantum computer. Different approaches have been devised to cure this problem for superconducting qubits, a prime example being the operation of such devices at optimal working points, so-called "sweet spots." This latter approach led to significant improvement of $T_2$ times in Cooper pair box qubits [D. Vion et al., Science 296, 886 (2002)]. Here, we introduce a new type of superconducting qubit called the "transmon." Unlike the charge qubit, the transmon is designed to operate in a regime of significantly increased ratio of Josephson energy and charging energy $E_J/E_C$. The transmon benefits from the fact that its charge dispersion decreases exponentially with $E_J/E_C$, while its loss in anharmonicity is described by a weak power law. As a result, we predict a drastic reduction in sensitivity to charge noise relative to the Cooper pair box and an increase in the qubit-photon coupling, while maintaining sufficient anharmonicity for selective qubit control. Our detailed analysis of the full system shows that this gain is not compromised by increased noise in other known channels.
In this study is carried out an analysis of the classical and quantum complexity of the defined by the author formalized circuits and is shown, that the circuits require several classic computations. The formalized circuits of Raychev have almost the same quantum complexity as the non-general circuits. Since the represented circuit models are independent of the techniques for matrix decomposition and the processes for global optimization, used to find the quantum circuits for a given operator, on quantum computers can be made simulations with a high accuracy for the unitary propagators of molecular Hamiltonians. As an instance, we show how to be constructed a circuit model for a hydrogen molecule.
In this report is proposed an approach for constructing a quantum circuit, containing O(𝑛2) Toffoli gates, CNOT gates and single qubit gates that implements а 𝐶𝑛(X) gate for n > 3, without using work qubits. For solving the problem is constructed a 𝐶𝑛 𝑁𝑁𝑁 gate from linear number of Toffoli gates and single qubit gates, without using ancilla bits.
in this research are offered two versions of an algorithm for superdense encoding of а 4-dimensional qubit vector. The algorithm for switching of 4-bit packages in a full quantum network with multiple network nodes includes superdense encoding and is implemented as quantum logic circuit. The proposed two algorithmic solutions and the applied quantum circuit open new perspectives for more effective methods for establishment of a full quantum switching network.
This report describes an approach for representation of quantum entanglement through state matrix. The proposed approach could be used to allow encoding of more information. The Singular Value Decomposition is useful as a measure for entanglement because the unitary operations preserve it.
In this report is examined an algorithm for ensuring a spare quantum traffic, which requires the exchange of only one pair of qubits in order to be reached to a solution of the problem related to ensuring a spare traffic. Here we show two different approaches of the unitary dynamics that can enable the directional control, enhancement, and suppression of quantum transport. This opens new prospects for more efficient methods to transport a quantum information.
This paper present a divide based simultable quantum circuit for spatial optimized coding, which is using only elementary quantum gates. The proposed approach provides the techniques for spatial optimized quantum algorithms. This approach might be useful only as a tool for spatial optimization of quantum algorithms, it is not particularly valuable for saving bandwidth.
In this report is examined the construction of controlled operators, that include more than one control or target bit. In the research is examined a general class of n qubit operators, that use one or more control bits to conditionally apply an operator to a single target qubit. The conditional nature of these operators is controlled by a boolean function f, that acts on a set of control bits C.
In this report is considered the generalization of the principles, which manage the formalization of controlled qubit operators. The research builds on the standard external data sources, for development of a generalized system for conditional operators. Certain controlled operators are viewed as linear combinations of universal operators. This system provides a generalized scheme for the type of the controlled operators, which could be encountered in a circuit, composed entirely of elementary operators.
In this report is examined the generalization of the principles, that control the formalization of a single qubit operator. The set of the identical operators is used in order to be captured the types of operators, occurring at the application of negating operators in the n qubit space.
This report describes an approach for encoding and decoding of discrete information about basic states at the input of operators in the phase of their outputs. The decoding is considered as a special case of interference with four different forms of decoding that reflect the classes of identity and negation operators. If an operator decode another, he is able to read the information encoded in the phase space, and reduce the encoded bits to state or its negation. Decoding relationships have been developed both as regards the parameters of the operator and in terms of Boolean functions encoding. This further leads to an increase in the level of abstraction. The approach of the proposed system differs from previous discussions of phase encoding, making encoding a substantial part of all operators so that the correct encoded information can be determined from the parameters of the operators.
The Boolean functions are a classic way for capturing one of the most basic computations. In this dissertation they are used as a means for specifying an information which is coded in the phase space of a quantum state. This, in turn, may serve for understanding of key examples of disturbance at quantum calculations based on the chain model. Here are examined the main properties and algebraic structures of single qubit Boolean functions and their composition, the combination of primitive Boolean functions with the operator for excluding or, ⊕ , as well as the expression of these functions and their negation as an expression, using ⊕ and B = {0, 1}, the set of the single-byte strings.
The formalization of qubit operators has two main objectives. The first one is to present all qubit operators as linear combinations of 〖Ехt〗_1 and 〖Nехt〗_1, i.e. identity and negation. Both classes are analogous to the classic operators and therefore the formalization of single qubit operators with these classes, acting as main operators, provides means for operation with primitive operators, set in the classical concepts for calculations. The second objective is to be separated the parts of the phase of the state to be separated from those of the amplitude in such a way, so as to be set out the key models at the disturbance, generated by the operators.
A central component of the quantum calculations is the logical summary of the classic concept for the operators for identity and negation. The characteristic of the quantum states and operators, based on this summary, is in the basis of the logic of the formalized qubit operators. In this report is examined the general idea for the states of identity and negation. Also specific examples from these classes are discussed.
Superconducting resonators are a promising element for many applications in quantum information processing, such as memory, state transfer, and qubit-qubit coupling. Here I introduce a new application---multi-level quantum logic using superpositions of Fock states. A circuit-QED implementation of single and coupled-resonator gates will be presented and theoretically analyzed. This scheme, using experimentally demonstrated interactions, will be compared with traditional qubit operations.
For the past three decades or so the flexible flow shop (FFS) scheduling problem has attracted many researchers. Numerous research articles have been published on this topic. This study reviews research on the FFS scheduling problem from the past and the present. The solution approaches reviewed range from the optimum to heuristics and to artificial intelligence search techniques. I not only discuss the details from the selected methods and compare them, but also provide insights and suggestions for future research.
Accurate and precise detection of multi-qubit entanglement is key for the
experimental development of quantum computation. Traditionally, non-classical
correlations between entangled qubits are measured by counting coincidences
between single-shot readouts of individual qubits. We report entanglement
metrology using a single detection channel with direct access to
ensemble-averaged correlations between two superconducting qubits. Following
validation and calibration of this joint readout, we demonstrate full quantum
tomography on both separable and highly-entangled two-qubit states produced on
demand. Using a subset of the measurements required for full tomography, we
perform entanglement metrology with ~95% accuracy and ~98% precision despite
~10% fidelity of single measurements. For the highly entangled states, measured
Clauser-Horne-Shimony-Holt operators reach a maximum value of 2.61+/-0.04 and
entanglement witnesses give a lower bound of ~88% on concurrence. In its
present form, this detector will be able to resolve future improvements in the
production of two-qubit entanglement and is immediately extendable to 3 or 4
qubits.
A Bell inequality is derived for a state of n spin-1/2 particles which superposes two macroscopically distinct states. Quantum mechanics violates this inequality by an amount that grows exponentially with n.
We present an experimental realization of the transmon qubit, an improved superconducting charge qubit derived from the Cooper pair box. We experimentally verify the predicted exponential suppression of sensitivity to 1/f charge noise [J. Koch et al., Phys. Rev. A 76, 042319 (2007)]. This removes the leading source of dephasing in charge qubits, resulting in homogenously broadened transitions with relaxation and dephasing times in the microsecond range. Our systematic characterization of the qubit spectrum, anharmonicity, and charge dispersion shows excellent agreement with theory, rendering the transmon a promising qubit for future steps towards solid-state quantum information processing. Comment: 4+ pages, 4 figures
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