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Quantum physics

Tailor-made quantum states

Nature volume 459, pages 516517 (28 May 2009) | Download Citation

The ability to produce arbitrarily superposed quantum states is a prerequisite for creating a workable quantum computer. Such highly complex states can now be generated on demand in superconducting electronic circuitry.

As an innocent reductionist in elementary school, I dreamed of creating everything in the world by assembling atoms one by one, just like building with Lego blocks. Decades later, the dream has, to some extent, come true with the 'bottom-up' approach of nanotechnology in which, for example, single atoms can be manipulated and assembled using the tip of a scanning probe microscope. But physicists are now playing with even fancier — and often more fragile — 'quantum Lego blocks'. Using a bottom-up approach, Hofheinz et al.1 (page 546 of this issue) report on-demand synthesis of arbitrary quantum states in a superconducting resonator circuit. Starting from a vacuum (zero-photon) state, the authors pile up photons one by one in the resonator and create complex quantum states in an entirely deterministic way.

Quantum mechanics was founded and, to a great extent, developed during the last century. Despite its weird and counterintuitive predictions, such as the uncertainty principle and the superposition and entanglement of states, it has stood up to a number of tests, and has proved itself to be a rigorous foundation across a broad spectrum of physics fields, from particle physics to solid-state physics. But only relatively recently have people recognized that the paradoxical nature of quantum mechanics is in itself useful in many applications, such as quantum cryptography and quantum computation. This recognition has boosted research on technologies of quantum-state engineering in various types of physical setting, and the twenty-first century will hopefully be memorable for the implementation of such technologies.

Among physical systems currently being investigated, superconducting (zero-resistance) macroscopic circuits stand in a unique position. Although the naive expectation is that quantum mechanics is normally associated with single microscopic systems such as atoms, nuclei and electrons, it has been shown that quantum-mechanical behaviour can be observed and controlled in human-designed, superconducting circuits that are micrometres or even millimetres in size2.

The simplest example of a superconducting quantum circuit is a linear resonator consisting of an inductor and a capacitor. If proper parameters are chosen, such a circuit can store a number of energy quanta (photons) at a microwave frequency. Another example is a quantum bit (or qubit), which is an effective two-state system. It can be implemented using a Josephson junction — a tunnel junction between two superconductors — as a nonlinear inductor; the two states are the ground and the first excited state of the nonlinear circuit. Coherent control of quantum states in such circuits and their combinations3 is the basis of superconducting quantum-state engineering.

To synthesize quantum states in a resonator, Hofheinz et al.1 use a circuit (see Fig. 1a on page 546) in which a resonator is coupled to a qubit. Because it is not possible to create arbitrary quantum states in resonator circuits using classical control signals alone, the qubit is used as a 'forklift' to load photons one by one into the resonator. Each cycle consists of two sequential steps. First, the qubit, initially detuned off-resonant with the resonator, is excited by a microwave pulse. Then, the qubit energy level is tuned into resonance with the resonator, enabling coherent transfer of energy quanta. A similar technique was proposed for an optical cavity with an atom inside4, and was demonstrated for the motional states of an ion in a trap5. Hofheinz and colleagues have also previously reported6 generation of states with a certain number of photons (N-photon or Fock states) — with up to 15 photons7 — based on the same scheme. In their new study1, they perfect the scheme to precisely control not only the amplitude but also the phase of each quantum loading. This allows them to synthesize, in a completely deterministic manner, quantum states that are the largest-ever arbitrary superpositions of multiple N-photon states.

Another distinctive aspect of Hofheinz and colleagues' experiment is the quantitative characterization and visualization (Fig. 1) of the generated quantum states, which they attained using Wigner tomography. This method fully characterizes, by means of the Wigner function, the resonator's quantum state: just as tomography is used in medical diagnoses such as magnetic-resonance and X-ray imaging, Wigner tomography allows the quantum state to be completely reconstructed from a large number of measurements. In this case, such measurements were taken by using the same qubit, now as a diagnostic probe, to unload energy quanta from the resonator. In the past year, an analogous technique was used to characterize the quantum state of a microwave field in a three-dimensional cavity, using atoms passing through the cavity as probes of the radiation field8.

Figure 1: Synthesizing quantum states.
Figure 1

Hofheinz and colleagues1 demonstrate on-demand generation of arbitrary quantum states in a superconducting resonator. In a bottom-up approach, which starts with a vacuum state, the target quantum state is constructed in a completely controlled manner by pumping photons one by one into the resonator using a superconducting quantum bit. The generated, superposed quantum states are fully characterized by the Wigner function, a representation of the resonator state, and are visualized by Wigner tomograms: top, simulated tomograms of two example states; bottom, experimentally measured tomograms. The right panel displays the 'voodoo cat' state (see Supplementary Information in ref. 1), which can be described by the superposition of three states: 'alive', 'dead' and 'zombie'. Positive values of the Wigner function are shown in blue; negative values, which are a distinctive signature of the quantum nature of the state, are shown in red.

Comparison1 of the observed and simulated Wigner functions (Fig. 1) clearly indicates that the target quantum states were synthesized with high fidelity. The ability to accurately create and control superposed quantum states is the first requisite for quantum computing. Moreover, coupling between qubits and resonators, such as that achieved in this study, has already shown its value in the implementation of quantum gates — the analogues of logic gates in conventional computers — between remote qubits9,10.

That said, the complexity and accuracy of the quantum states achieved by the authors is limited by decoherence — that is, the vulnerability of the quantum superposition. In superconducting circuits, quantum coherence tends to be lost more quickly than in atoms. This is not surprising if one considers the macroscopic nature of the circuits, which makes them interact more strongly with their surroundings.

Efforts to achieve longer coherence times are ongoing, and include improving circuit design and reducing the number of defects in the materials from which circuit components are made. Studying the decay of coherence in a variety of quantum states will be a valuable approach to understanding what mechanism triggers decoherence itself and the crossover from quantum to classical behaviour7,8. For now, Hofheinz and colleagues' experiment has set the stage for further developments in quantum-state engineering in superconducting electronic circuitry, and has brought physicists a step closer to realizing a workable quantum computer.


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  1. Yasunobu Nakamura is at the NEC Nano Electronics Research Laboratories, Tsukuba, Ibaraki 305-8501, and the Institute of Physical and Chemical Research (RIKEN), Wako, Saitama 351-0198, Japan.

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