Adiabatic evolution of a coupled-qubit Hamiltonian

Corato, V.; Silvestrini, P.; Stodolsky, L.; Wosiek, J.

doi:10.1103/physrevb.68.224508

Cited by 9 publications

(9 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…According to the estimate given in ref [2], adiabaticity is guaranteed when the sweep time t sweep is sufficiently long such that…”

Section: Adiabaticitymentioning

confidence: 99%

“…For the SQUID these would be the four possible states arising from the current circulating clockwise or counterclockwise in two SQUIDs, and as explained in ref [3] this can be so arranged that the result of the sweep of one of the φ ext depends on the state of the other SQUID, thus providing the conditions for a CNOT gate [15]. We recall [2] [3] the Hamiltonian for this problem…”

Section: Two Variable Systemmentioning

confidence: 99%

“…states remains unchanged (control bit is zero), while the other pair reverses (control bit is one). This is accomplished by having the energy eigenstates (1,2,3,4), each one concentrated in a different potential well, move from one set of locations to another [3]. Since for relatively large φ ext each well represents a distinct state of the SQUID currents, one physical configuration of the two qubits is mapped to another.…”

Section: Cnot Configurationsmentioning

confidence: 99%

See 2 more Smart Citations

Simulations of quantum gates with decoherence

et al. 2007

Self Cite

View full text Add to dashboard Cite

Methods and results for numerical simulations of one and two interacting rf-SQUID systems suitable for adiabatic quantum gates are presented. These are based on high accuracy numerical solutions to the static and time dependent Schroedinger equation for the full SQUID Hamiltonian in one and two variables. Among the points examined in the static analysis is the range of validity of the effective two-state or "spin 1/2" picture. A range of parameters is determined where the picture holds to good accuracy as the energy levels undergo gate manipulations. Some general points are presented concerning the relations between device parameters and "good" quantum mechanical state spaces.The time dependent simulations allow the examination of suitable conditions for adiabatic behavior, and permits the introduction of a random noise to simulate the effects of decoherence. A formula is derived and tested relating the random noise to the decoherence rate. Sensitivity to device and operating parameters for the logical gates NOT and CNOT are examined, with particular attention to values of the tunnel parameter β slightly above one. It appears that with values of β close to one, a quantum CNOT gate is possible even with rather short decoherence times.Many of the methods and results will apply to coupled double-potential well systems in general.

show abstract

“…According to the estimate given in ref [2], adiabaticity is guaranteed when the sweep time t sweep is sufficiently long such that…”

Section: Adiabaticitymentioning

confidence: 99%

Section: Two Variable Systemmentioning

confidence: 99%

Section: Cnot Configurationsmentioning

confidence: 99%

See 1 more Smart Citation

Simulations of quantum gates with decoherence

et al. 2007

Self Cite

View full text Add to dashboard Cite

show abstract

“…Identification with SQUID parameters: Eqns [1,2] arise by standard methods in the analysis of two rf SQUID loops coupled by a mutual inductance L 12 [8]. The Josephson relation leads to f (φ) = cosφ, to which our f (φ) = 1 − units corresponds to τ adiab ≈ 500/E 0 ≈ 2.7 · 10 −9 s in seconds.…”

mentioning

confidence: 99%

Design of adiabatic logic for a quantum CNOT gate

et al. 2003

View full text Add to dashboard Cite

We examine the realization of a quantum CNOT gate by adiabatic operations. The principles of such systems and their analysis are briefly discussed and a model consisting of two weakly coupled double-potential well qubits is studied numerically. Regions of the parameter space with suitable well-defined sets of wavefunctions are found, in which then an adiabatic sweep of an external bias produces the switching behavior of CNOT. Results are presented on the adiabatic condition and the identification with the parameters of a flux-coupled two-SQUID system is given. For typical parameters adiabatic times in the nanosecond regime are obtained.The basic element of the "quantum computer" [1] is the quantum bit (qubit), a two level system, exhibiting quantum coherence between the states. Many physical realizations of the qubit have been proposed [2]. To manipulate the qubit quantum gates [3] are necessary, logic devices capable of operating on linear combinations of input states. First there is the simple NOT, a one bit operation which can be viewed as an inversion operation on a qubit. The next step is to construct gates of a conditional character. A simple case to consider is the two-bit operation "controlled NOT" or CNOT. To realize such device it is natural to consider using an interaction between the physical elements constituting the qubit.Among the possible mechanisms for manipulating coupled qubits adiabatic procedures are, as explained below, of special interest. Furthermore, it has been suggested that adiabatic procedures may be robust with respect to certain kinds of errors [4]. In particular with superconducting devices, Averin [5] has suggested using small Josephson junctions in the coulomb blockade regime, and we have mentioned the possibility of using SQUID qubits with flux coupling [6]. In this letter we will explain some general principles for studying such systems and to present numerical calculations relevant to their behavior and design.CNOT is a two-qubit operation and we will represent it by two interacting double-potential well systems. Each double well system may be though of as an approximately independent qubit since we shall keep the coupling weak. Qualitatively, we will use the procedure of performing an adiabatic NOT [6] on the first qubit while trying to influence its behavior by the state of the second. We find a region of parameter space where this works.Hamiltonian: We take the following model hamiltonian

show abstract

“…Firstly, the majority of entangling gate designs proposed in the literature assume resonant qubits [2,3,4,5,6,7,8,9]. (However, see Refs.…”

Section: Introductionmentioning

confidence: 99%