High-fidelity universal quantum gates

Ran Li; Frank Gaitan

doi:10.26421/qic10.11-12-4

High-fidelity universal quantum gates

Quantum Information and Computation ◽

10.26421/qic10.11-12-4 ◽

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 $P_{a}\sim 10^{-4}$.

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

Quantum Information and Computation ◽

10.26421/qic9.3-4-7 ◽

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.

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

Quantum Information and Computation ◽

10.26421/qic7.7-3 ◽

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.

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