High fidelity universal set of quantum gates using non-adiabatic rapid passage

2009 ◽  
Vol 9 (3&4) ◽  
pp. 290-316
Author(s):  
R. Li ◽  
M. Hoover ◽  
F. Gaitan
Keyword(s):  
Electric Fields ◽  
Quantum Interference ◽  
Fault Tolerant ◽  
Quantum Gates ◽  
High Fidelity ◽  
Interference Effects ◽  
Adiabatic Rapid Passage ◽  
The One ◽  
Parameter Values ◽  
Rapid Passage

Numerical simulation results are presented which suggest that a class of non-adiabatic rapid passage sweeps first realized experimentally in 1991 should be capable of implementing a universal set of quantum gates \uniset\ that operate with high fidelity. The gates constituting \uniset\ are the Hadamard and NOT gates, together with variants of the phase, $\pi /8$, and controlled-phase gates. The universality of \uniset\ is established by showing that it can construct the universal set consisting of Hadamard, phase, $\pi /8$, and controlled-NOT gates. Sweep parameter values are provided which simulations indicate will produce the different gates in \uniset , and for which the gate error probability $P_{e}$ satisfies: (i)~$P_{e}<10^{-4}$ for the one-qubit gates; and (ii)~$P_{e}<1.27\times 10^{-3}$ for the modified controlled-phase gate. The sweeps in this class are non-composite and generate controllable quantum interference effects that allow the gates in \uniset\ to operate non-adiabatically while maintaining high fidelity. These interference effects have been observed using NMR, and it has previously been shown how these rapid passage sweeps can be applied to atomic systems using electric fields. Here we show how these sweeps can be applied to both superconducting charge and flux qubit systems. The simulations suggest that the universal set of gates \uniset\ produced by these rapid passage sweeps shows promise as possible elements of a fault-tolerant scheme for quantum computing.

scholarly journals High-fidelity single-qubit gates using non-adiabatic rapid passage

2007 ◽  
Vol 7 (7) ◽  
pp. 594-608
Author(s):  
R. Li ◽  
M. Hoover ◽  
F. Gaitan
Keyword(s):  
Quantum Interference ◽  
Fault Tolerant ◽  
Quantum Gates ◽  
High Fidelity ◽  
Interference Effects ◽  
Adiabatic Rapid Passage ◽  
Single Qubit ◽  
The One ◽  
Error Probabilities ◽  
Rapid Passage

Numerical simulation results are presented which suggest that a class of non-adiabatic rapid passage sweeps first realized experimentally in 1991 should be capable of implementing a set of quantum gates that is universal for one-qubit unitary operations and whose elements operate with error probabilities $P_{e}<10^{-4}$. The sweeps are non-composite and generate controllable quantum interference effects which allow the one-qubit gates produced to operate non-adiabatically while maintaining high accuracy. The simulations suggest that the one-qubit gates produced by these sweeps show promise as possible elements of a fault-tolerant scheme for quantum computing.

High-fidelity universal quantum gates

2010 ◽  
Vol 10 (11&12) ◽  
pp. 936-946
Author(s):  
Ran Li ◽  
Frank Gaitan
Keyword(s):  
Quantum Interference ◽  
Error Probability ◽  
Quantum Gates ◽  
High Fidelity ◽  
Interference Effects ◽  
Single Family ◽  
Adiabatic Rapid Passage ◽  
Universal Quantum ◽  
Parameter Values ◽  
Rapid Passage

Twisted rapid passage is a type of non-adiabatic rapid passage that generates controllable quantum interference effects that were first observed experimentally in $2003$. It is shown that twisted rapid passage sweeps can be used to implement a universal set of quantum gates $\calGU$ that operate with high-fidelity. The gate set $\calGU$ consists of the Hadamard and NOT gates, together with variants of the phase, $\pi /8$, and controlled-phase gates. For each gate $g$ in $\calGU$, sweep parameter values are provided which simulations indicate will produce a unitary operation that approximates $g$ with error probability$P_{e} < 10^{-4}$. Note that \textit{all\/} gates in $\calGU$ are implemented using a \textit{single family\/} of control-field, and the error probability for each gate falls below the rough-and-ready estimate for the accuracy threshold $P_{a}\sim 10^{-4}$.

scholarly journals QUANTUM INTERFERENCE EFFECTS IN SLOWLY ROTATING NUT SPACE–TIME

2009 ◽  
Vol 18 (01) ◽  
pp. 107-118 ◽  
Author(s):  
V. S. MOROZOVA ◽  
B. J. AHMEDOV
Keyword(s):  
Phase Shift ◽  
Quantum Interference ◽  
Relativistic Quantum ◽  
Additional Term ◽  
Space Time ◽  
Sagnac Effect ◽  
Interference Effects ◽  
General Relativistic ◽  
Shift Effect ◽  
The One

General relativistic quantum interference effects in a slowly rotating NUT space–time, such as the Sagnac effect and the phase shift effect of interfering particles in a neutron interferometer, are considered. It was found that in the case of the Sagnac effect, the influence of the NUT parameter is becoming important due to the fact that the angular velocity of the locally nonrotating observer must be larger than the one in the Kerr space–time. In the case of neutron interferometry, it is found that due to the presence of the NUT parameter, an additional term in the phase shift of interfering particles emerges. This term can be, in principle, detected by a sensitive interferometer and the derived results could be further used in experiments to detect the gravitomagnetic charge. Finally, as an example, we apply the obtained results to the calculation of the UCN (ultra-cold neutrons) energy level modification in a slowly rotating NUT space–time.

scholarly journals Analytical solution of one-dimensional Pennes’ bioheat equation

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1084-1092
Author(s):  
Hongyun Wang ◽  
Wesley A. Burgei ◽  
Hong Zhou
Keyword(s):  
Analytical Solution ◽  
Radiofrequency Energy ◽  
Bioheat Equation ◽  
Surface Cooling ◽  
One Dimensional ◽  
The Fourier Transform ◽  
The One ◽  
Parameter Values ◽  
Mathematical Derivation ◽  
Effect Of Surface

Abstract Pennes’ bioheat equation is the most widely used thermal model for studying heat transfer in biological systems exposed to radiofrequency energy. In their article, “Effect of Surface Cooling and Blood Flow on the Microwave Heating of Tissue,” Foster et al. published an analytical solution to the one-dimensional (1-D) problem, obtained using the Fourier transform. However, their article did not offer any details of the derivation. In this work, we revisit the 1-D problem and provide a comprehensive mathematical derivation of an analytical solution. Our result corrects an error in Foster’s solution which might be a typo in their article. Unlike Foster et al., we integrate the partial differential equation directly. The expression of solution has several apparent singularities for certain parameter values where the physical problem is not expected to be singular. We show that all these singularities are removable, and we derive alternative non-singular formulas. Finally, we extend our analysis to write out an analytical solution of the 1-D bioheat equation for the case of multiple electromagnetic heating pulses.

scholarly journals High-fidelity composite quantum gates for Raman qubits

2020 ◽  
Vol 2 (4) ◽  
Author(s):  
Boyan T. Torosov ◽  
Nikolay V. Vitanov
Keyword(s):  
Quantum Gates ◽  
High Fidelity

scholarly journals Electron Symmetry Breaking during Attosecond Charge Migration Induced by Laser Pulses: Point Group Analyses for Quantum Dynamics

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 205
Author(s):  
Dietrich Haase ◽  
Gunter Hermann ◽  
Jörn Manz ◽  
Vincent Pohl ◽  
Jean Christophe Tremblay
Keyword(s):  
Laser Pulse ◽  
Symmetry Breaking ◽  
Electric Fields ◽  
Quantum Dynamics ◽  
Point Group ◽  
Laser Pulses ◽  
Charge Migration ◽  
Laser Control ◽  
The One ◽  
Superposition States

Quantum simulations of the electron dynamics of oriented benzene and Mg-porphyrin driven by short (<10 fs) laser pulses yield electron symmetry breaking during attosecond charge migration. Nuclear motions are negligible on this time domain, i.e., the point group symmetries G = D6h and D4h of the nuclear scaffolds are conserved. At the same time, the symmetries of the one-electron densities are broken, however, to specific subgroups of G for the excited superposition states. These subgroups depend on the polarization and on the electric fields of the laser pulses. They can be determined either by inspection of the symmetry elements of the one-electron density which represents charge migration after the laser pulse, or by a new and more efficient group-theoretical approach. The results agree perfectly with each other. They suggest laser control of symmetry breaking. The choice of the target subgroup is restricted, however, by a new theorem, i.e., it must contain the symmetry group of the time-dependent electronic Hamiltonian of the oriented molecule interacting with the laser pulse(s). This theorem can also be applied to confirm or to falsify complementary suggestions of electron symmetry breaking by laser pulses.

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