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Physical Review A

Constructing two-qubit gates with minimal couplings

Haidong Yuan, Robert Zeier, Navin Khaneja, Seth Lloyd

Published Apr 7, 2009• 5 citations
Publisher

Abstract

Couplings between quantum systems are frequently less robust and harder to implement than controls on individual systems; thus, constructing quantum gates with minimal interactions is an important problem in quantum computation. In this paper we study the optimal synthesis of two-qubit quantum gates for the tunable coupling scheme of coupled superconducting qubits and compute the minimal interaction time of generating any two-qubit quantum gate.

DOI
10.1103/physreva.79.042309

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Couplings between quantum systems are frequently less robust and harder to implement than controls on individual systems; thus, constructing quantum gates with minimal interactions is an important problem in quantum computation. In this paper we study the optimal synthesis of two-qubit quantum gates for the tunable coupling scheme of coupled superconducting qubits and compute the minimal interaction time of generating any two-qubit quantum gate.
Optimal construction of quantum operations is a fundamental problem in the realization of quantum computation. We here introduce a newly discovered quantum gate, B, that can implement any arbitrary two-qubit quantum operation with minimal number of both two- and single-qubit gates. We show this by giving an analytic circuit that implements a generic nonlocal two-qubit operation from just two applications of the B gate. Realization of the B gate is illustrated with an example of charge-coupled superconducting qubits for which the B gate is seen to be generated in shorter time than the CNOT gate.
Superconducting qubits now offer coherence times exceeding 100 $\ensuremath{\mu}$s and single-qubit gate fidelities above 99.9%, but realizing a large-scale quantum computer is still impeded by the quality of two-qubit gates, with typical fidelities of 95--99%. Here a simple, broadly applicable scheme to improve two-qubit gates using a tunable coupler is proposed. It simplifies the coupling scheme, and reduces unwanted interactions typically present in schemes in which the interactions are always on. Numerical simulations show that this approach should allow two-qubit gate fidelities greater than 99.9%, when implemented using state-of-the-art superconducting qubits.
We construct a minimal robust controlled-not gate with an Ising-type interaction by which elementary two-qubit gates are implemented. It is robust against inaccuracy of the coupling strength and the obtained quantum circuits are constructed with the minimal number (N=3N=3N=3) of elementary two-qubit gates and several one-qubit gates. It is noteworthy that all the robust circuits can be mapped to one-qubit circuits robust against a pulse length error. We also prove that a minimal robust swap gate cannot be constructed with N=3N=3N=3 but requires N=6N=6N=6 elementary two-qubit gates.
Building a quantum computer is a daunting challenge since it requires good control but also good isolation from the environment to minimize decoherence. It is therefore important to realize quantum gates efficiently, using as few operations as possible, to reduce the amount of required control and operation time and thus improve the quantum state coherence. Here we propose a superconducting circuit for implementing a tunable system consisting of a qutrit coupled to two qubits. This system can efficiently accomplish various quantum information tasks, including generation of entanglement of the two qubits and conditional three-qubit quantum gates, such as the Toffoli and Fredkin gates. Furthermore, the system realizes a conditional geometric gate which may be used for holonomic (non-adiabatic) quantum computing. The efficiency, robustness and universality of the presented circuit makes it a promising candidate to serve as a building block for larger networks capable of performing involved quantum computational tasks.
Building a quantum computer is a daunting challenge since it requires good control but also good isolation from the environment to minimize decoherence. It is therefore important to realize quantum gates efficiently, using as few operations as possible, to reduce the amount of required control and operation time and thus improve the quantum state coherence. Here we propose a superconducting circuit for implementing a tunable system consisting of a qutrit coupled to two qubits. This system can efficiently accomplish various quantum information tasks, including generation of entanglement of the two qubits and conditional three-qubit quantum gates, such as the Toffoli and Fredkin gates. Furthermore, the system realizes a conditional geometric gate which may be used for holonomic (non-adiabatic) quantum computing. The efficiency, robustness and universality of the presented circuit makes it a promising candidate to serve as a building block for larger networks capable of performing involved quantum computational tasks.
We develop a method to synthesize a class of entangling multi-qubit gates for a quantum computing platform with fixed Ising-type interaction with all-to-all connectivity. The only requirement on the flexibility of the interaction is that it can be switched on and off for individual qubits. Our method yields a time-optimal implementation of the multi-qubit gates. We numerically demonstrate that the total multi-qubit gate time scales approximately linear in the number of qubits. Using this gate synthesis as a subroutine, we provide compilation strategies for important use cases: (i) we show that any Clifford circuit on n qubits can be implemented using at most 2 n multi-qubit gates without requiring ancilla qubits, (ii) we decompose the quantum Fourier transform in a similar fashion, (iii) we compile a simulation of molecular dynamics, and (iv) we propose a method for the compilation of diagonal unitaries with time-optimal multi-qubit gates, as a step towards general unitaries. As motivation, we provide a detailed discussion on a microwave controlled ion trap architecture with magnetic gradient induced coupling (MAGIC) for the generation of the Ising-type interactions.