Session Y30: Quantum Computing, Quantum Algorithms, and Quantum Simulation

Phase Slips in Topological Superconductor Wire Devices

We make a detailed study of phase slips in topological superconducting wires and devices based on topological wires. We begin by investigating a device composed of a topological superconducting wire connected to a non-topological wire (T-S). In the T-segment only slips of the phase by multiples of 4$\pi $ are allowed, while in the S-segment slips by 2$\pi $ are also allowed. We show that near the interface, 2$\pi $ phase slips are also allowed and we comment on the consequences of such phase slips for the Aharonov-Casher effect. We also consider an implementation of a q-bit consisting of a T-S-T device, where the quantum information is stored in the parity of the two topological segments via the four Majorana modes. We show that the central S-segment of this type of device can support 2$\pi $ phase-slips which result in the decoherence of the q-bit.   

String localization and delocalization in the disordered toric code

Topological quantum memories based on the toric code model have the ability to protect quantum information by self correcting a large class of errors. However, excitations such as a string of spin flips, when allowed to perform a quantum walk, can change the logical state encoded in the system every time they wind around the torus. It has been proposed that by adding randomness to the local spin exchange couplings, one can localize these string excitations and avoid logical errors. In our work, we investigate this proposal numerically through the use of an efficient time-dependent numerical quantum evolution method. We determine the dependence of the winding time on the torus size and on the amount of randomness. We study the effect of dephasing in the quantum evolution of the string excitations and show that a transition to delocalization can occur.   

Implementing quantum gates through scattering between an electron and a magnetic impurity in a graphene nanoribbon

We study the feasibility of implementing quantum logic gates and generate entanglement when a ballistic electron is scattered by a magnetic impurity fixed in a graphene nanoribbon. Because electrons in graphene behaves like massless Dirac Fermions, we use the Dirac equation to describe the system. In our model we consider the ballistic electron spin as a relativistic flying qubit and the impurity spin as a static qubit. The interaction between spins is described by a Heisenberg - like operator. The interaction by electron scattering shows the advantage of a low control in the interaction, and the operation success can be measured by means the electron transmition probability. We show that is possible to implement quantum logic gates of the type SWAP, and partial SWAP with a physicaly feasible coupling strenght between spins. We also present the condition to generate states of maximum entanglement. The possible use of the graphene pseudospin as an additional degree of freedom is discussed.   

Long-lived qubit constructed from three identical atoms

In this talk, I will present a scheme for constructing logical qubits from clusters of three identical atoms that are long-lived against decoherence from fluctuating magnetic fields, a limiting source of noise in many experiments. Each qubit is stored in a rotationally invariant subsystem of the total angular momentum states of the three atoms, and can persist with high fidelity for time-scales on the order of hours. This is to be compared with a fraction of a millisecond for an unprotected atomic qubit. I will first present the scheme of rotationally invariant subsystems in atomic systems and show that the information stored in the system is robust against decoherence. Then I will move on to discuss a proposal for an experiment to demonstrate the feasibility of the scheme. In our proposal, the state preparation is done with the help of Rydberg blockade for three atoms, where the atoms are localized in space and addressed by a sequence of laser pulses simultaneously. By carefully selecting the atomic levels addressed and tuning the parameters of the applied lasers, an arbitrary logical qubit state can be prepared. Lastly, the fidelity of state preparation will be discussed. Ref: R. Han, N. L\"{o}rch, J. Suzuki and B. G. Englert, Phys. Rev. A 84, 012322 (2011)   

Deterministic and Cascadable Conditional Phase Gate for Photonic Qubits

Cross-phase modulation (XPM) at the single-photon level, if strong enough, would enable a simple conditional $\pi$-phase gate for photonic qubits. Together with easily realized single-qubit rotations for such qubits, this would provide a universal gate set for quantum computation. However, previous analyses of photonic conditional $\phi$-phase gates that treat XPM in a causal, multimode, quantum field setting suggest that a large ($\sim$$\pi$\,rad) nonlinear phase shift is always accompanied by fidelity-degrading noise. We present a conditional phase gate that, for sufficiently small nonzero $\phi$, has high fidelity. Moreover, our gate is cascadable, in that it preserves the structure of the principal modes used to encode qubit information, and can therefore be cascaded to realize a high-fidelity conditional $\pi$-phase gate. The key components of our gate are: (1) an atomic $\vee$-system to create XPM; (2) a principal-mode restorer that compensates the evolution a principal-mode incurs when the $\vee$-system is driven by a single photon; and (3) a principal-mode projector that exploits the quantum Zeno effect to preclude the accumulation of fidelity-degrading departures from the principal-mode Hilbert space when both control and target photons illuminate the gate.   

Dynamic Phases and Robust Quantum Gates

We are interested in composite pulses widely employed in Nuclear Magnetic Resonance (NMR) and geometric phase gates (GQGs) with vanishing dynamic phases in Quantum Information Processing (QIP). A composite pulse in NMR is constructed with poor quality pulses but becomes more reliable than its components. We found: a composite pulse robust against pulse length error in NMR is always a GQG [1]. We then extended this observation to two-qubit operations. Let us consider the interaction $e^{-i \theta \sigma_z \otimes \sigma_z}$ and assume that there is a systematic error in $\theta$. When we construct a ``composite pulse'' robust against this error, we obtain a two-qubit GQG [2]. We clarified that geometric phase gates are really useful in QIT. \\[4pt] [1]Y.\ Kondo \& M.\ Bando, {\it J. Phys. Soc. Jpn.} {\bf 80}, 054002.\\[0pt] [2] T.\ Ichikawa, M.\ Bando, Y.\ Kondo \& M.\ Nakahara, submitted to {\it philosophical transaction} A.   

Non-Adiabatic Holonomic Quantum Gates in an atomic system

Quantum computation is essentially the implementation of a universal set of quantum gate operations on a set of qubits, which is reliable in the presence of noise. We propose a scheme to perform robust gates in an atomic four-level system using the idea of non-adiabatic holonomic quantum computation proposed in [1]. The gates are realized by applying sequences of short laser pulses that drive transitions between the four energy levels in such a way that the dynamical phases vanish. \\[4pt] [1] E. Sjoqvist, D.M. Tong, B. Hessmo, M. Johansson, K. Singh, arXiv:1107.5127v2 [quant-ph]   

Single-qubit gates by graph scattering

Continuous-time quantum walkers with tightly peaked momenta can simulate quantum computations by scattering off finite graphs. We enumerate all single-qubit gates that can be enacted by scattering off a single graph on up to $n=9$ vertices at certain momentum values, and provide numerical evidence that the number of such gates grows exponentially with $n$. The single-qubit rotations are about axes distributed roughly uniformly on the Bloch sphere, and rotations by both rational and irrational multiples of $\pi$ are found.   

Recent Results in Photonic Quantum Computations, Simulations and Quantum Networks

The applications of photonic entanglement manifold and reach from quantum communication [1] to quantum metrology [2] and optical quantum computing [3]. The advantage of the photon's mobility makes optical quantum computing unprecedented in speed, including feed-forward operations with high fidelity [4]. During the last few years the degree of control over photonic multi-particle entanglement has improved substantially and allows for not only overcoming the random nature of spontaneous emission sources [5], but also for the quantum simulation of other quantum systems. Here, I will also present the simulation of four spin-1/2 particles interacting via any Heisenberg-type Hamiltonian [6]. Moreover, recent experimental and theoretical progress, using the concepts of measurement-based quantum computation, indicates that photons are best suited for quantum networks. I will also present present results for the realization for such a client-server environment, where quantum information is communicated and computed using the same physical system [7]. References: [1] PRL 103, 020503 (2009); [2] Nature 429, 158 (2004); [3] Nature 434, 169 (2005); [4] Nature 445, 65 (2007); [5] Nature Photon 4, 553 (2010); [6] Nature Physics 7, 399 (2011); [7] in press.   

Physics of an isolated electron puddle revealed via dephasing in thermal equilibrium

Low dimensional electron systems serve as a good setup for studying interactions among quantum systems. In our study, we examined a system comprised of an electron puddle, confined in a quantum dot, coupled to an electronic Mach-Zehnder interferometer via Coulomb interactions. Surprisingly, even when the electron puddle was in thermal equilibrium and nearly isolated, it induced full and robust dephasing in the nearby interferometer when the average puddle's occupation was N+1/2. We attribute this unexpected behavior to a unique manifestation of the Friedel Sum Rule, which connects the occupation of a system with its scattering phase. Furthermore, this phenomena allowed accessing various properties of the isolated electron puddle, such as its average occupation, in thermal equilibrium and under bias, and decoherence rate of the confined electrons.   

Quantum trajectories for systems probed by fields in multimode Fock and Schrodinger cat states

Using Gardiner and Collet's input-output theory we derive system and output field master equations for an arbitrary quantum system probed by a field in a non-classical state of light. Specifically the field states we study are arbitrary combinations (superpositions and / or mixtures) of continuous-mode Fock states or continuous mode-coherent states. We also unravel the master equations for the system state to get the conditional evolution (the stochastic master equation) for homodyne and photon counting measurements.   

Optimal Experimental Detection and Characterization of SU(2) Decoherence

Quantum metrology is the art of measuring tiny forces by preparing quantum states, then measuring how much they get displaced by the force. The resulting precision often exceeds classical limits. The best state depends on what we want to detect. N00N states [1] are optimal for U(1) phase shifts. Measuring arbitrary dynamical shifts requires quantum process tomography (QPT)[3], in which the process is applied to a complete set of input states. In this work, we experimentally study the important intermediate case of SU(2) decoherence (SD), fluctuating SU(2) rotations, by probing it with biphotons [2]. We show that N00N states are optimal for detecting SD. Then, we turn to QPT, and examine how accurately SU(2)-covariant sets of states can identify SD. The set of spin-coherent states (generated by SU(2)-displacements of a ``highest-weight'' state) are sufficient for QPT [4], but exponentially insensitive to some parameters. We show that N00N states (though optimal at detecting SD) generate even less effective input sets, with zero sensitivity to some parameters. Finally, we show evidence that optimal input sets are 2-designs, which can be generated from a fiducial state and SU(2) rotations.\\[4pt] [1] PRL 85,2733(2000) [2] Nature 457,67(2009) [3] PRL 91,120402(2003) [4] Science 322,563(2008)   

Complete characterization of linear amplifiers including the quantum limits for nongaussian noise

We characterize the quantum limitations on the entire probability distribution of added noise in a phase-preserving linear amplifier. Previously the quantum limits on amplifiers have been given entirely in terms of second moments, i.e., noise power or noise temperature [1]. As Josephson parametric amplifiers approach fundamental quantum limits on noise temperature [2,3,4], it becomes important to investigate the limits on higher moments of the amplifier noise. We prove that all phase-preserving linear amplifiers with arbitrary noise are formally equivalent to a parametric amplifier: $\rho_{out}= {\rm tr}[S(r) \,\rho_{in}\otimes \sigma\, S^{\dag}(r)]$, where the gain is $g^{2}= \cosh^{2}(r)$, $S$ is a two-mode squeeze operator, and $\sigma$ is a physical state of an ancillary mode whose quantum noise determines the noise properties of the amplifier. We discuss generalization of these limits to the nondeterministic linear amplifiers proposed by Ralph and Lund [5]. [1] C. M. Caves, Phys. Rev. D {\bf 26}, 1817 (1982). [2] A. A. Clerk et al., Rev. Mod. Phys. {\bf 82}, 1155-1208 (2010). [3] N. Bergeal et al., Nature 465, 64--68 (2010). [4] D. Kinion and John Clarke Appl. Phys. Lett. 98, 202503 (2011). [5] T. C. Ralph and A. P. Lund, in QCMC Vol.~1110 of AIP Conf. Proc. (2009).   

Playing the Aharon-Vaidman quantum game with a Young type photonic qutrit

The Aharon-Vaidman (AV) game exemplifies the advantage of using simple quantum systems to outperform classical strategies. We present an experimental test of this quantum advantage by using a three-state quantum system (qutrit) encoded in a spatial mode of a single photon passing through a system of three slits. The preparation of a particular state is controlled as the photon propagates through the slits by varying the number of open slits and their respective phases. The measurements are achieved by placing detectors in the specific positions in the near and far-field after the slits. This set of tools allowed us to perform tomographic reconstructions of generalized qutrit states, and implement the quantum version of the AV game with compelling evidence of the quantum advantage.