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arXiv:0905.3373 · Physical Review A

Scalable quantum computation via local control of only two qubits

Daniel Klaus Burgarth, Koji Maruyama, Michael Murphy, Simone Montangero, Tommaso Calarco, Franco Nori, Martin Bodo Plenio

Published Apr 22, 2010• 103 citations
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Abstract

We apply quantum control techniques to a long spin chain by acting only on two qubits at one of its ends, thereby implementing universal quantum computation by a combination of quantum gates on these qubits and indirect swap operations across the chain. It is shown that the control sequences can be computed and implemented efficiently. We discuss the application of these ideas to physical systems such as superconducting qubits in which full control of long chains is challenging.

DOI
10.1103/physreva.81.040303

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We apply quantum control techniques to a long spin chain by acting only on two qubits at one of its ends, thereby implementing universal quantum computation by a combination of quantum gates on these qubits and indirect swap operations across the chain. It is shown that the control sequences can be computed and implemented efficiently. We discuss the application of these ideas to physical systems such as superconducting qubits in which full control of long chains is challenging.
We propose a platform to implement a scalable universal quantum computer based on a 2D array of superconducting qubits. Notably, calculations in our scheme are enabled by a set of only three global driving signals, irrespective of the number of qubits, ensuring full scalability of the computation. In stark contrast with the existing literature, global control in our scheme is achieved by leveraging the longitudinal ZZ coupling between neighboring qubits. We show how this enables information flow, one-and two-qubit gates through a series of three global pulses that act together on different subsets of the physical qubits in our system. These findings provide an alternative route to the realization of scalable and fault-tolerant superconducting quantum computers with reduced wiring, bringing them one step closer to solving practical problems in our daily lives.
Heisenberg spin chains can act as quantum wires transferring quantum states either perfectly or with high fidelity. Gaussian packets of excitations passing through dual rails can encode the two states of a logical qubit, depending on which rail is empty and which rail is carrying the packet. With extra interactions in one or between different chains, one can introduce interaction zones in arrays of such chains, where specific one- or two-qubit gates act on any qubit which passes through these interaction zones. Therefore, universal quantum computation is made possible in a static way where no external control is needed. This scheme will then pave the way for a scalable way of quantum computation where specific hardware can be connected to make large quantum circuits. Our scheme is an improvement of a recent scheme where we borrowed an idea from quantum electrodynamics to replace nonlocal interactions between spin chains with local interactions mediated by an ancillary chain.
Universal quantum computation requires the implementation of arbitrary control operations on the quantum register. In most cases, this is achieved by external control fields acting selectively on each qubit to drive single-qubit operations. In combination with a drift Hamiltonian containing interactions between the qubits, this allows the implementation of arbitrary gate operations. Here, we demonstrate an alternative scheme that does not require local control for all qubits: we implement one- and two-qubit gate operations on a set of target qubits indirectly, through a combination of gates on directly controlled actuator qubits with a drift Hamiltonian that couples actuator and target qubits. Experiments are performed on nuclear spins, using radio-frequency pulses as gate operations and magnetic-dipole couplings for the drift Hamiltonian.
It is shown that anisotropic spin chains with gapped bulk excitations and magnetically ordered ground states offer a promising platform for quantum computation, which bridges the conventional single-spin-based qubit concept with recently developed topological Majorana-based proposals. We show how to realize the single-qubit Hadamard, phase, and $\ensuremath{\pi}/8$ gates as well as the two-qubit controlled-not (cnot) gate, which together form a fault-tolerant universal set of quantum gates. The gates are implemented by judiciously controlling Ising exchange and magnetic fields along a network of spin chains, with each individual qubit furnished by a spin-chain segment. A subset of single-qubit operations is geometric in nature, relying on control of anisotropy of spin interactions rather than their strength. We contrast topological aspects of the anisotropic spin-chain networks to those of ppp-wave superconducting wires discussed in the literature.
Abstract. Quantum processors that combine the long decoherence times of spin qubits together with fast optical manipulation of excitons have recently been the subject of several proposals. I show here that arbitrary single- and entangling twoqubit gates can be performed in a chain of perpetually coupled spin qubits solely by using laser pulses to excite higher lying states. It is also demonstrated that universal quantum computing is possible even if these pulses are applied globally to a chain; by employing a repeating pattern of four distinct qubit units the need for individual qubit addressing is removed. Some current experimental qubit systems would lend themselves to implementing this idea. PACS numbers: 03.67.-a, 03.67.Lx, 78.67.HcGlobal Optical Control of a Quantum Spin Chain 2 1.