Exact CNOT Gates with a Single Nonlocal Rotation for Quantum-Dot Qubits

Abstract

We investigate capacitively coupled two-qubit quantum gates based on quantum dots. For exchange-only coded qubits electron spin $S$ and its projection $S_z$ are exact quantum numbers. Capacitive coupling between qubits, as distinct from interqubit exchange, preserves these quantum numbers. We prove, both analytically and numerically, that conservation of the spins of individual qubits has dramatic effect on performance of two-qubit gates. By varying the level splittings of individual qubits, $J_a$ and $J_b$, and the interqubit coupling time $t$, we can find an infinite number of triples $(J_a,J_b,t)$ for which the two-qubit entanglement, in combination with appropriate single-qubit rotations, can produce an exact CNOT gate. This statement is true for practically arbitrary magnitude and form of capacitive interqubit coupling. Our findings promise a large decrease in the number of nonlocal (two-qubit) operations in quantum circuits.

11 pages, 4 figures, Added 2 references

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Cited by in corpus (13)

• Semiconductor Spin Qubits
• Three-electron spin qubits
• Entangling distant resonant exchange qubits via circuit quantum electrodynamics
• Coupling of three-spin qubits to their electric environment
• Programmable two-qubit gates in capacitively coupled flopping-mode spin qubits
• Characterisation of an exchange-based two-qubit gate for resonant exchange qubits
• Generation of Schrödinger's cat states in a planar semiconductor heterostructure
• Cyclic groups and quantum logic gates
• Benchmarking of dynamically corrected gates for the exchange-only spin qubit in $1/f$ noise environment
• Two-qubit logical operations in three quantum dots system
• Two-qubit sweet spots for capacitively coupled exchange-only spin qubits
• Universal control of superexchange in linear triple quantum dots with an empty mediator
• All-electric single electron spin-to-charge conversion