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 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.

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 Path-optimized nonadiabatic geometric quantum computation on superconducting qubits

2021 ◽  
Author(s):  
Cheng-Yun Ding ◽  
Li-Na Ji ◽  
Tao Chen ◽  
Zheng-Yuan Xue
Keyword(s):  
Quantum Computation ◽  
Large Scale ◽  
Fault Tolerant ◽  
High Fidelity ◽  
Noise Resistance ◽  
Geometric Phases ◽  
Single Qubit ◽  
Phase Gate ◽  
New Perspective ◽  
Geometric Quantum Computation

Abstract Quantum computation based on nonadiabatic geometric phases has attracted a broad range of interests, due to its fast manipulation and inherent noise resistance. However, it is limited to some special evolution paths, and the gate-times are typically longer than conventional dynamical gates, resulting in weakening of robustness and more infidelities of the implemented geometric gates. Here, we propose a path-optimized scheme for geometric quantum computation on superconducting transmon qubits, where high-fidelity and robust universal nonadiabatic geometric gates can be implemented, based on conventional experimental setups. Specifically, we find that, by selecting appropriate evolution paths, the constructed geometric gates can be superior to their corresponding dynamical ones under different local errors. Numerical simulations show that the fidelities for single-qubit geometric Phase, $\pi/8$ and Hadamard gates can be obtained as $99.93\%$, $99.95\%$ and $99.95\%$, respectively. Remarkably, the fidelity for two-qubit control-phase gate can be as high as $99.87\%$. Therefore, our scheme provides a new perspective for geometric quantum computation, making it more promising in the application of large-scale fault-tolerant quantum computation.

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.

The Solovay-Kitaev algorithm

2006 ◽  
Vol 6 (1) ◽  
pp. 81-95
Author(s):  
C.M. Dawson ◽  
M.A. Nielsen
Keyword(s):  
Fault Tolerant ◽  
Quantum Gate ◽  
Quantum Gates ◽  
Single Qubit ◽  
Classical Algorithm ◽  
Shor's Algorithm ◽  
Finite Set ◽  
Qubit Gate

This pedagogical review presents the proof of the Solovay-Kitaev theorem in the form of an efficient classical algorithm for compiling an arbitrary single-qubit gate into a sequence of gates from a fixed and finite set. The algorithm can be used, for example, to compile Shor's algorithm, which uses rotations of $\pi / 2^k$, into an efficient fault-tolerant form using only Hadamard, controlled-{\sc not}, and $\pi / 8$ gates. The algorithm runs in $O(\log^{2.71}(1/\epsilon))$ time, and produces as output a sequence of $O(\log^{3.97}(1/\epsilon))$ quantum gates which is guaranteed to approximate the desired quantum gate to an accuracy within $\epsilon > 0$. We also explain how the algorithm can be generalized to apply to multi-qubit gates and to gates from SU(d).

scholarly journals DECOMPOSITION OF UNITARY MATRICES AND QUANTUM GATES

2013 ◽  
Vol 11 (01) ◽  
pp. 1350015 ◽  
Author(s):  
CHI-KWONG LI ◽  
REBECCA ROBERTS ◽  
XIAOYAN YIN
Keyword(s):  
General Scheme ◽  
Quantum Gate ◽  
Quantum Gates ◽  
Unitary Matrix ◽  
Additional Structure ◽  
Unitary Matrices ◽  
Decomposition Scheme ◽  
Single Qubit ◽  
Matlab Program

A general scheme is presented to decompose a d-by-d unitary matrix as the product of two-level unitary matrices with additional structure and prescribed determinants. In particular, the decomposition can be done by using two-level matrices in d - 1 classes, where each class is isomorphic to the group of 2 × 2 unitary matrices. The proposed scheme is easy to apply, and useful in treating problems with the additional structural restrictions. A Matlab program is written to implement the scheme, and the result is used to deduce the fact that every quantum gate acting on n-qubit registers can be expressed as no more than 2n-1(2n-1) fully controlled single-qubit gates chosen from 2n-1 classes, where the quantum gates in each class share the same n - 1 control qubits. Moreover, it is shown that one can easily adjust the proposed decomposition scheme to take advantage of additional structure evolving in the process.

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