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Bulletin of the American Physical Society

Properties and Gate Control of the 0-Pi Qubit, Part 2: Gate Control

Agustín Di Paolo, Arne L. Grimsmo, Peter Groszkowski, Jens Koch, Alexandre Blais

Published Mar 17, 2017• 0 citations
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Related papers

Properties and Gate Control of the 0-Pi Qubit, Part 1: Disorder and Coherence

Peter Groszkowski, Agustín Di Paolo, Arne L. Grimsmo +2 more

Bulletin of the American Physical Society•Mar 17, 2017•0 citations

All You Need is pi: Quantum Computing with Hermitian Gates

Ben Zindorf, Sougato Bose

Universal gate sets for quantum computation, when single and two qubit operations are accessible, include both Hermitian and non-Hermitian gates. Here we utilize the fact that any single-qubit operator may be implemented as two Hermitian gates, and thus a purely Hermitian universal set is possible. This implementation can be used to prepare high fidelity single-qubit states in the presence of amplitude errors, and helps to achieve a high fidelity single-qubit gate decomposition using four Hermitian gates. An implementational convenience can be that non-identity single-qubit Hermitian gates are equivalent to π rotations up to a global phase. We show that a gate set comprised of π rotations about two fixed axes, along with the CNOT gate, is universal for quantum computation. Moreover, we show that two π rotations can transform the axis of any multi-controlled unitary, a special case being a single CNOT sufficing for any controlled π rotation. These gates simplify the process of circuit compilation in view of their Hermitian nature. We exemplify by designing efficient circuits for a variety of controlled gates, and achieving a CNOT count reduction for the four-controlled Toffoli gate in LNN-restricted qubit connectivity.

arXiv:2402.12356•Quantum•Dec 2, 2025•1 citation

Improving control and coherence of the 0-π qubit

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The synthesis of a quantum circuit

Alexis De Vos, Stijn De Baerdemacker

As two basic building blocks for any quantum circuit, we consider the 1-qubit NEGATOR(θ) circuit and the 1-qubit PHASOR(θ) circuit, extensions of the NOT gate and PHASE gate, respectively: NEGATOR(π) = NOT and PHASOR(π) = PHASE.Quantum circuits (acting on w qubits) consisting of controlled NEGATORs are represented by matrices from XU(2 w ); quantum circuits (acting on w qubits) consisting of controlled PHASORs are represented by matrices from ZU(2 w ).Here, XU(n) and ZU(n) are subgroups of the unitary group U(n): the group XU(n) consists of all n × n unitary matrices with all line sums equal to 1 and the group ZU(n) consists of all n × n unitary diagonal matrices with first entry equal to 1.We conjecture that any U(n) matrix can be decomposed into four parts: U = e iα Z1XZ2, where both Z1 and Z2 are ZU(n) matrices and X is an XU(n) matrix.For n = 2 w , this leads to a decomposition of a quantum computer into simpler blocks.

Cambridge University Press eBooks•Jan 1, 2014•4 citations

All-Microwave Control and Dispersive Readout of Gate-Defined Quantum Dot Qubits in Circuit Quantum Electrodynamics

Pasquale Scarlino, David J. van Woerkom, Anna Stockklauser +8 more

Developing fast and accurate control and readout techniques is an important challenge in quantum information processing with semiconductor qubits. Here, we study the dynamics and the coherence properties of a GaAs/AlGaAs double quantum dot charge qubit strongly coupled to a frequency-tunable high-impedance resonator. We drive qubit transitions with synthesized microwave pulses and perform qubit readout through the state-dependent frequency shift imparted by the qubit on the dispersively coupled resonator. We perform Rabi oscillation, Ramsey fringe, energy relaxation, and Hahn-echo measurements and find significantly reduced decoherence rates down to γ_{2}/2π∼3 MHz corresponding to coherence times of up to T_{2}∼50 ns for charge states in gate-defined quantum dot qubits. We realize Rabi π pulses of width down to σ∼0.25 ns.

arXiv:1711.01906•Physical Review Letters•May 22, 2019•67 citations
Universal gate sets for quantum computation, when single and two qubit operations are accessible, include both Hermitian and non-Hermitian gates. Here we utilize the fact that any single-qubit operator may be implemented as two Hermitian gates, and thus a purely Hermitian universal set is possible. This implementation can be used to prepare high fidelity single-qubit states in the presence of amplitude errors, and helps to achieve a high fidelity single-qubit gate decomposition using four Hermitian gates. An implementational convenience can be that non-identity single-qubit Hermitian gates are equivalent to π rotations up to a global phase. We show that a gate set comprised of π rotations about two fixed axes, along with the CNOT gate, is universal for quantum computation. Moreover, we show that two π rotations can transform the axis of any multi-controlled unitary, a special case being a single CNOT sufficing for any controlled π rotation. These gates simplify the process of circuit compilation in view of their Hermitian nature. We exemplify by designing efficient circuits for a variety of controlled gates, and achieving a CNOT count reduction for the four-controlled Toffoli gate in LNN-restricted qubit connectivity.
As two basic building blocks for any quantum circuit, we consider the 1-qubit NEGATOR(θ) circuit and the 1-qubit PHASOR(θ) circuit, extensions of the NOT gate and PHASE gate, respectively: NEGATOR(π) = NOT and PHASOR(π) = PHASE.Quantum circuits (acting on w qubits) consisting of controlled NEGATORs are represented by matrices from XU(2 w ); quantum circuits (acting on w qubits) consisting of controlled PHASORs are represented by matrices from ZU(2 w ).Here, XU(n) and ZU(n) are subgroups of the unitary group U(n): the group XU(n) consists of all n × n unitary matrices with all line sums equal to 1 and the group ZU(n) consists of all n × n unitary diagonal matrices with first entry equal to 1.We conjecture that any U(n) matrix can be decomposed into four parts: U = e iα Z1XZ2, where both Z1 and Z2 are ZU(n) matrices and X is an XU(n) matrix.For n = 2 w , this leads to a decomposition of a quantum computer into simpler blocks.
Developing fast and accurate control and readout techniques is an important challenge in quantum information processing with semiconductor qubits. Here, we study the dynamics and the coherence properties of a GaAs/AlGaAs double quantum dot charge qubit strongly coupled to a frequency-tunable high-impedance resonator. We drive qubit transitions with synthesized microwave pulses and perform qubit readout through the state-dependent frequency shift imparted by the qubit on the dispersively coupled resonator. We perform Rabi oscillation, Ramsey fringe, energy relaxation, and Hahn-echo measurements and find significantly reduced decoherence rates down to γ_{2}/2π∼3 MHz corresponding to coherence times of up to T_{2}∼50 ns for charge states in gate-defined quantum dot qubits. We realize Rabi π pulses of width down to σ∼0.25 ns.