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Complete set of one qubit quantum gates using twisted rapid passage

M. Hoover

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

In this thesis, details are presented of a numeric simulation of non-adiabatic rapid passage sweeps that were first realized experimentally in 1991. The sweeps are non-composite and generate controllable interference effects which can be used to create high accuracy quantum gates. The simulation is used to optimize the sweep parameters in order to obtain a reliable set of one-qubit quantum gates. A set of sweep parameters was found that approximate the Hadamard, a modified pi/8, a modified phase, and the not gates with an error probability of less than 10^-4. These gates are significant because they form a set that can approximate an arbitrary one qubit unitary operation. The 10^-4 is also significant because is used a rough estimate for the accuracy required to implement fault-tolerant quantum logic.

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 2, 2010•0 citations
In this thesis, details are presented of a numeric simulation of non-adiabatic rapid passage sweeps that were first realized experimentally in 1991. The sweeps are non-composite and generate controllable interference effects which can be used to create high accuracy quantum gates. The simulation is used to optimize the sweep parameters in order to obtain a reliable set of one-qubit quantum gates. A set of sweep parameters was found that approximate the Hadamard, a modified pi/8, a modified phase, and the not gates with an error probability of less than 10^-4. These gates are significant because they form a set that can approximate an arbitrary one qubit unitary operation. The 10^-4 is also significant because is used a rough estimate for the accuracy required to implement fault-tolerant quantum logic.
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 that operate with high-fidelity. The gate set consists of the Hadamard and NOT gates, together with variants of the phase, pi/8, and controlled-phase gates. For each gate g in the universal set, sweep parameter values are provided which numerical simulations indicate will produce a unitary operation that approximates g with error probability less than 10**(-4). Note that all gates in the universal set are implemented using a single family of control-field, and the error probability for each gate falls below the rough-and-ready estimate for the accuracy threshold of 10**(-4).
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 Pe<10−4P_{e}<10^{-4}Pe​<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.
Twisted rapid passage is a type of non-adiabatic rapid passage that generates controllable quantum interference effects that were first observed experimentally in 200320032003. 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, π/8\pi /8π/8, and controlled-phase gates. For each gate ggg in $\calGU$, sweep parameter values are provided which simulations indicate will produce a unitary operation that approximates ggg with error probabilityPe<10−4P_{e} < 10^{-4}Pe​<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 Pa∼10−4P_{a}\sim 10^{-4}Pa​∼10−4.
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, π/8\pi /8π/8, and controlled-phase gates. The universality of \uniset\ is established by showing that it can construct the universal set consisting of Hadamard, phase, π/8\pi /8π/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 PeP_{e}Pe​ satisfies: (i)~Pe<10−4P_{e}<10^{-4}Pe​<10−4 for the one-qubit gates; and (ii)~Pe<1.27×10−3P_{e}<1.27\times 10^{-3}Pe​<1.27×10−3 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.
Twisted rapid passage is a type of non-adiabatic rapid passage that gives rise to controllable quantum interference effects that were first observed experimentally in 2003. We show that twisted rapid passage sweeps can be used to implement a universal set of quantum gates that operate with high-fidelity. For each gate in the universal set, sweep parameter values are provided which simulations indicate will yield a quantum gate with error probability P_{e} < 10**(-4). Note that all gates in this universal set are driven by a **single** type of control field (twisted rapid passage), and the error probability for each gate falls below the rough-and-ready estimate for the accuracy threshold P_{a} ~ 10**(-4). The simulations suggest that the universal gate set produced by twisted rapid passage shows promise for use in a fault-tolerant scheme for quantum computing.
Numerical simulation results are presented which suggest that a class of non-adiabatic rapid passage sweeps first realized experimentally in 1991, and which give rise to controllable quantum interference effects observed using NMR in 2003, should be capable of implementing a universal set of quantum gates Gu that operate with high-fidelity. Gu consists of the Hadamard and NOT gates, together with variants of the phase, π/8, and controlled-phase gates. Sweep parameter values are provided which simulations indicate will produce the different gates in Gu, and for each gate, yield an operation with error probability Pe < 10-4. The simulations suggest that the universal gate set produced by these rapid passage sweeps show promise as possible elements of a fault-tolerant scheme for quantum computing.