Quantum computing

The qubit duet

Small, but consistent, steps are being taken towards the realization of a quantum computer. The demonstration of the coupling of two quantum bits in a solid-state device moves us closer to that goal.

Basic steps towards the creation of a quantum computer have been taken, with the demonstrations of elementary data storage and manipulation using photons and atoms1 or trapped ions2,3 as the quantum bits, or 'qubits'. Solid-state qubits (made, for example, from tiny samples of superconducting material) are an attractive alternative, however, as they could be more easily built into working devices, profiting from the highly developed methods of nanotechnology. So far, solid-state qubits have lagged behind in the race to build the first quantum computer, handicapped by decoherence which implies the breakdown of the quantum information-storing state within the qubit. But new designs have improved the quality of individual qubits, and the next step, to connect qubits together, has now been taken: on page 823 of this issue, Pashkin et al.4 report the coupling — or rather 'entangling' — of two solid-state qubits.

Quantum computing exploits two resources offered by the laws of quantum mechanics: the principle of superposition of states and the concept of entanglement. Superposition is a 'one-particle' property; entanglement is a characteristic of two (or more) particles, or, more generally, of two quantum degrees of freedom. Consider a particle with spin — the angular momentum degree of freedom inherent to many elementary particles, such as the electron. With reference to a given axis (say along the z direction), the spin of the particle can point in two opposite directions, say 'up' and 'down', and the spin states can be denoted |↑〉 and |↓〉. But, by the laws of quantum mechanics, the particle can exist in a superposition of these two states, corresponding to arbitrary rotations away from the axis. The symmetric and antisymmetric states, represented as [|↑〉 ± |↓〉], are then examples of superpositions in which the spin points along the x axis.

Next, consider a two-particle state: there are now four 'basis states', |↑↑〉, |↓↓〉, |↑↓〉 and |↓↑〉, where the first (second) arrow indicates the state of the first (second) particle. Again, superpositions can be made of these states, including, in particular, the four 'maximally entangled Bell states', shown in Fig. 1. Such Bell states have the paradoxical property that the particles always 'know' about each other, even if they are separated by huge distances5; this property is commonly associated with the 'non-locality' of quantum mechanics. Entanglement such as this is a basic ingredient of quantum computation (Fig. 2) and hence is no longer just a toy for laboratory science6,7 but also a tool for the technological world. But how can specific entangled states be constructed on demand?

Figure 1: Bell states for a two-particle system.
figure1

The arrows represent the spin state of each particle (coded red and blue), which may be either 'up' or 'down'.

Figure 2: Quantum logic.
figure2

The quantum state of an individual qubit is described as a complex superposition of two basis states, here denoted by |↑〉 and |↓〉. a, Acting on a single qubit, the operation known as 'Hadamard' transforms |↑〉 or |↓〉 into the symmetric or antisymmetric superpositions [|↑〉 ± |↓〉]. b, Adding one non-trivial two-qubit operation to the set of single-qubit rotations defines a complete and universal set of gate operations. The operation 'Controlled NOT' flips the target spin (red) if the control spin (blue) points downwards (or else leaves the target unchanged). c, Two-qubit states are complex superpositions of the four basis states |↑↑〉, |↓↓〉, |↑↓〉 and |↓↑〉. Applying the two operations 'Hadamard' and 'Controlled NOT' to one of the two-qubit basis states produces a maximally entangled Bell state.

For a deterministic entanglement of two quantum degrees of freedom, the two constituents must interact in a controlled manner. This has already been achieved in atomic optics, by manipulating a pair of trapped beryllium atoms using a sequence of laser pulses8. But now the solid-state camp is catching up: Pashkin et al.4 have brought two superconducting qubits into a controlled state of interaction.

These qubits encode information using charge rather than spin. In a superconductor, charge is carried by pairs of electrons, known as Cooper pairs. In Pashkin and colleagues' experiment, the qubits are micrometre-size specks of superconductor, each connected to a superconducting 'reservoir'. By quantum mechanical tunnelling, a Cooper pair might jump from the reservoir onto a qubit. Then, analogous to the spin 'up' and 'down' states, the qubit can be in a state with no excess Cooper pairs, or one excess Cooper pair — or a superposed state of both. The superconducting energy gap, which is a natural barrier against the dissociation of Cooper pairs, protects these solid-state qubits from decoherence.

Using lithography and evaporation techniques, Pashkin et al. fabricated two qubits on an insulating wafer, connected through a capacitor (see Fig. 1 on page 824). Each qubit coupling to the superconducting reservoir (called a Josephson junction) results in a mixing between the charge states of that qubit, and the capacitive connection between the qubits leads to the mixing of two-particle states, and hence entanglement of the qubit pair. Following the principle demonstrated by Nakamura et al.9 for a single qubit, Pashkin et al.4 trace the evolution of the mixing of these two-particle states over time, monitoring the charge oscillations produced with a current probe.

Although they have not yet been able to create and measure a specific entangled state, a numerical analysis shows that the qubit pair does evolve through a maximally entangled state, bringing us closer to the construction of a solid-state quantum logic gate to produce deterministic entanglement. The next step could be to introduce time-controlled switching of the interaction and subsequent readout, measuring the degree of entanglement through the amplitudes of the final state expressed in the Bell-state basis10.

Astounding progress has been made over the past few years in the experimental development of quantum computing. In quantum atom optics, entanglement of four particles has been achieved11 and entangled ions are being used to test quantum mechanical relations known as Bell's inequalities12. Shor's factorization algorithm has been implemented13 with a seven-qubit molecule using NMR techniques, successfully identifying the factors of 15 as 3 and 5. From their first appearance a few years ago9,14,15, superconducting qubits have already matured into effective and efficient devices16,17, and now Pashkin et al.4 have demonstrated the first step towards their deterministic entanglement. These are firm foundations for the development of a solid-state quantum processor, but considerable effort will be needed to direct the complex choreography of a real quantum algorithm.

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Correspondence to Gianni Blatter.

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Blatter, G. The qubit duet. Nature 421, 796–797 (2003). https://doi.org/10.1038/421796a

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