# Quantum information processing

- Introduction
- Environment engineering for superconducting qubits
- Photonic quantum computer with microwaves
- Electron spin qubit in silicon
- Entanglement-enhanced quantum cryptography

**Introduction**

Part of QCD activities are focused on theoretical and computational problems in quantum information science as well as on experimental realizations of quantum information processing. We have a successful history in designing quantum gate decompositions for arbitrary quantum circuits. For example, we have designed the first two asymptotically optimal decompositions for arbitrary many-qubit quantum gates [Phys. Rev. Lett. 92, 177902 (2004); Phys. Rev. Lett. 93, 130502 (2004)] and we were the first to discover the most efficient decomposition known to date [in Trends in Quantum Computing Research (Nova Science Publishers Inc., New York, 2006)]. We have also studied the implementation of quantum gates in a noisy environment through numerical optimization of the Hamiltonian control sequences [Phys. Rev. A 77, 032334 (2008); Phys. Rev. A 75, 012308 (2007)], and enhancing quantum cryptography using entanglement. Furthermore, we have studied with our international collaborators the implementation of qubits using the electron spin of phosphorous donor atoms embedded into silicon nanostructures.

Our current theoretical efforts are focused on engineering the environment of superconducting qubits and design of quantum gates for a photonic quantum computer in the microwave regime. On the experimental side, we are currently investigating the use of microwave photons in quantum computing, namely, the single-photon detector used to measure the photonic qubits.

**Environment engineering for superconducting qubits**

Superconducting qubits provide great potential in implementing a large-scale quantum computer in future. They come in many forms and operating principles ranging from a simple charge qubit to the so-called fluxonium, but all the designs suffer from an uncontrollable coupling to some thermal environment introducing decoherence. The typical treatment to this problem is to try and decouple the system from the environment as efficiently as possible. However, we take a slightly different theoretical approach to the problem and introduce a controllable coupling between the qubit and a resistive environment in Refs. [Sci. Rep. 3, 1987 (2013); J. Low Temp. Phys. 173, 152-169 (2013)]. The temperature of the resistor can be modified and monitored via SIN thermometry but the main benefit of the approach comes from the in situ control of the qubit-bath coupling strength implemented by either coplanar-waveguide cavities or a sequence of LC resonators mediating the interaction. The control allows us to switch between rapid ground-state initialization and unhindered qubit evolution at will. In particular, the effective qubit temperature can be lowered significantly by executing a strong coupling to an artificial low-temperature resistive bath. In the future, we plan on implementing such control experimentally and turn our theoretical attention to studying the non-Markovian properties of such systems.

**Fig.** Contour plot of the qubit-like decay rate as a function of the frequencies of both the qubit and the bare left cavity.

**Photonic quantum computer with microwaves**

Single photons are the basic building block of a quantum computer based on the linear optical quantum computing (LOQC) paradigm. Our long term goal is to develop components for such a photonic quantum computer based on microwave photons confined on chips. In our theory work, we focus on taking advantage of non-linear effects that are strong for microwaves but weak or unobservable for optical light. Experimentally we are working toward constructing a single-photon microwave detector, which is one of the principal tools used in LOQC.

**Electron spin qubit in silicon**

Together with the Centre for Quantum Computation and Communication (CQC2T), we have studied valence electron spins of individual phosphorus donors in silicon with the aim to build robust qubits. These nanoelectronic devices are fabricated with the silicon metal-oxide-silicon field-effect transistor (MOSFET) technology together with ion implantation. The MOSFET channel is made only a few tens of nanometers long and it can be broken with a single barrier gate or with two barrier gates to form a quantum dot.

For the first time, we were able to reach the single-electron regime in silicon dots [Appl. Phys. Lett. 95, 242102 (2009)]. We have also implanted single phosphorus donor atoms below a single barrier gate breaking the MOSFET channel and tuned the device such that the conductance of the device can be tuned with a single gate voltage. If there is current flowing through the system, all of it is passing through the potential well created by a single phosphorus donor [Nano Lett. 10, 11 (2010)]. Thus this device works as a single-atom transistor.

By implanting the donors in the vicinity of a quantum dot, we were able to use the dot as a sensor for the charge state of the phosphorus. By tuning the device to a correct working point, we succeeded in utilizing so-called spin to charge conversion to measure [Nature (London) 467, 687 (2010)] and the spin state of the single electron confined in the potential well of a single phosphorus atom. Figure below shows a layout of the device used in the experiment. This was a major step towards spin-based quantum information processing in silicon. In fact, this technology led to the development of an electron spin qubit [Nature (London) 489, 541 (2012)] and a high-fidelity, single-atom quantum memory in silicon [Nature (London) 496, 334 (2013)].

**Fig.** Scanning electron micrograph of metallic electrodes on silicon oxide. The electrodes are isolated from each other so that there is no electric current flowing through them. A schematic illustration has been added to the figure representing the electron layer induced below the silicon oxide (source and drain) together with so-called quantum dot (SET island) which works as a charge detector. Furthermore, the dashed blue line shows a region where phosphorus donors have been placed in the silicon with the magnetic moment of the outermost electron pointing either up or down. The energy of spin-up state is higher than the energy of spin-down state in magnetic field. By controlling the voltage on a nearby plunger gate, the system can be brought at will into a working point where spin-up electron has enough energy to tunnel into the charge detector but the spin-down state of the same electron remains bound to the phosphorus. The detector is very sensitive to changes in the charge state of the phosphorus yielding noticeable current (ISET) after the spin-up electron moves. Thus the spin state of the electron can be measure by a single shot at any chosen time.

**Entanglement-enhanced quantum cryptography**

We have studied the benefits of multi-qubit entanglement in quantum cryptography [Phys. Rev. A 78, 032314 (2008)]. We have developed a new BB84-type protocol for quantum key distribution, and analyzed its main characteristics both theoretically and by numerical simulation. Our protocol offers protection against malicious attackers by prohibiting their access to the full space of the entangled state. Thus far, the protocol promises some improvement over existing BB84-type protocols, but is vulnerable to photon loss. In addition, understanding the effects of quantum noise is essential for practical realizations of quantum cryptography.

**Fig.** Quantum circuit for a two-qubit entanglement-enhanced protocol under a restricted intercept-resend attack.