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arXiv:0804.2290 · Physical Review Letters

Efficient Quantum Circuits for One-Way Quantum Computing

Tetsufumi Tanamoto, Yu-xi Liu, Xuedong Hu, Franco Nori

Published Mar 9, 2009• 68 citations
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Abstract

While Ising-type interactions are ideal for implementing controlled phase flip gates in one-way quantum computing, natural interactions between solid-state qubits are most often described by either the XY or the Heisenberg models. We show an efficient way of generating cluster states directly using either the imaginary SWAP (iSWAP) gate for the XY model, or the sqrt[SWAP] gate for the Heisenberg model. Our approach thus makes one-way quantum computing more feasible for solid-state devices.

DOI
10.1103/physrevlett.102.100501

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APS March Meeting Abstracts•Mar 1, 2004•0 citations
While Ising-type interactions are ideal for implementing controlled phase flip gates in one-way quantum computing, natural interactions between solid-state qubits are most often described by either the XY or the Heisenberg models. We show an efficient way of generating cluster states directly using either the imaginary SWAP (iSWAP) gate for the XY model, or the sqrt[SWAP] gate for the Heisenberg model. Our approach thus makes one-way quantum computing more feasible for solid-state devices.
Based on the iSWAP gate generated from the XY interaction between solid-state qubits, we present an efficient quantum circuit for the implementation of discrete quantum Fourier transform. The relatively cumbersome and expensive controlled- R k gate and SWAP gate operations required for implementing discrete quantum Fourier transform in the naive quantum circuit are replaced only by iSWAP gate operation. The scheme can be realized using any physical system with XY interaction and it would be a useful step towards the implementation of more complex quantum computation in solid-state qubits.
The two-qubit interaction Hamiltonian of a given physical implementation determines whether or not a two-qubit gate such as the controlled-NOT (CNOT) gate can be realized easily. It can be shown that, e.g., with the XY\mathrm{XY}XY interaction more than one two-qubit operation is required in order to realize the CNOT operation. Here we propose a two-qubit gate for the XY\mathrm{XY}XY interaction which combines the CNOT and SWAP operations. By using this gate quantum circuits can be implemented efficiently, even if only nearest-neighbor coupling between the qubits is available.
Highly entangled states called cluster states are a universal resource for measurement-based quantum computing (QC). Here we propose an efficient method for producing large cluster states using superconducting quantum circuits. We show that a large cluster state can be efficiently generated in just one step by turning on the interqubit coupling for a short time. Because the interqubit coupling is only switched on during the time interval for generating the cluster state, our approach is also convenient for preparing the initial state for each qubit and for implementing one-way QC via single-qubit measurements. Moreover, the cluster state is robust against parameter variations.
We study the low energy states of finite spin chains with isotropic (Heisenberg) and anisotropic (XY and Ising-like) antiferromagnetic exchange interaction with uniform and nonuniform coupling constants. We show that for an odd number of sites a spin cluster qubit can be defined in terms of the ground state doublet. This qubit is remarkably insensitive to the placement and coupling anisotropy of spins within the cluster. One- and two-qubit quantum gates can be generated by magnetic fields and intercluster exchange, and leakage during quantum gate operation is small. Spin cluster qubits inherit the long decoherence times and short gate operation times of single spins. Control of single spins is hence not necessary for the realization of universal quantum gates.
Recently, fault tolerant quantum computation such as surface coding and topological quantum computation has been paid attention to due to high threshold against computational errors compared with that of conventional gate-model quantum computation.These schemes use a two or three-dimensional cluster state as universal resources for quantum computation.We can generate a cluster state by performing controlled-phase gates on an initial state prepared in |+⟩ state, where the control-phase gates are realized by nearest neighbor Ising type interactions.There are many proposal to realize Ising type interaction such as ultracold atoms in an optical lattice, superconducting charge qubits, superconducting spin qubits, resonator wave guides, nitrogen-vacancy centers, and quantum dots.Among many candidates, we especially discuss superconducting flux qubits.Superconducting flux qubits have a strong anharmonicity, so that we can perform high-speed single-qubit rotation with excellent fidelity.Usually, implementation of high-fidelity two-qubit gates is the hardest part for the realization of quantum computation.Two qubit gates require in-situ turn on/off the interaction between qubits by the external control apparatus.Since imperfection of the interaction control tends to induce spatially correlated errors between qubits, sophisticated technology is required to suppress such error rate below the threshold of fault tolerant quantum computation.Up to now, the generation of a large cluster state using solid-state qubit has not been demonstrated in a scalable manner yet.One of the main obstacles is the requirement for independent control of two-qubit gates that are necessary for the scalable quantum information processing.For a superconducting flux qubit, existing method uses applied magnetic field to control the interaction.It is known that the application of magnetic field to local area is difficult.Thus, it is hard to implement local control of the interaction without cross-talk problem where unwanted errors occurs between qubits.Firstly, we propose a novel way to control a number of two-qubit gates independently without using the on/off switching of locally applied magnetic field.Specifically, we assume the superconducting flux qubits that are inductively coupled with each other via always-on Ising interaction.Unlike the previous method to change the interaction strength with unitary operations, we fully make use of non-unitary properties of projective measurements so that we can effectively turn on/off the interaction via quantum feedforward.Also, we show how to generate a two or three-dimensional cluster state that are universal resource for fault tolerant quantum computation with constant stepsize operations.The on/off switching of locally applied magnetic field is not necessary to First of all, I would like to thank my adviser Professor Hiroshi Imai for his valuable comments and continuous support during the last five years.
The construction of a solid-state quantum computer remains a coveted, yet elusive goal. Among the most promising scalable candidates are the spin-based approaches, where qubits are represented by electron spins in quantum dots, or by donor-atom nuclear or electron spins, or by combinations thereof. It has been widely assumed that one-qubit gates in these systems, which are based on single-spin addressing, suffer from severe technical difficulties, including slow speed of operation, heating, and device and materials complexity, such as g-factor engineering. For this reason a variety of approaches have been suggested to circumvent one-qubit gates, including encoding the state of a qubit into two or more spins. These approaches inevitably introduce substantial overhead. Here we show that one-qubit gates can in fact be generated using only modest and presently feasible technological requirements. Our solution uses only global magnetic fields and controllable Heisenberg exchange interactions, thus circumventing the need for single-spin addressing. We explicitly show how to build up one-qubit gates from these components using simple pulse sequences. This should substantially simplify the implemention of spin-based solid state quantum computers.