v Abstract The coupled dynamics of a nanomechanical resonator and superconducting quantum circuits are studied in three experiments, in the context of studying the quantum limit for forc[r]

117 Read more

Researchers have spent decades refining and improving their methods for fabricating smaller, finer- tuned, higher-quality nanoscale optical elements with the goal of making more sensitive and accurate measurements of the world around them using optics. **Quantum** optics has been a well-established tool of choice in making these increasingly sensitive measurements which have repeatedly pushed the limits on the accuracy of measurement set forth by **quantum** mechanics. A recent develop- ment in **quantum** optics has been a creative integration of robust, high-quality, and well-established macroscopic experimental systems with highly-engineerable on-chip nanoscale oscillators fabricated in cleanrooms. However, merging large systems with nanoscale oscillators often require them to have extremely high aspect-ratios, which make them extremely delicate and difficult to fabricate with an “experimentally reasonable” repeatability, yield and high quality. In this work we give an overview of our research, which focused on microscopic oscillators which are **coupled** with macroscopic optical cavities towards the goal of cooling them to their motional ground state in room temperature envi- ronments. The quality factor of a mechanical **resonator** is an important figure of merit for various sensing applications and observing **quantum** behavior. We demonstrated a technique for pushing the quality factor of a micromechanical **resonator** beyond conventional material and fabrication limits by using an optical field to stiffen and trap a particular motional mode of a nanoscale oscillator. Optical forces increase the oscillation frequency by storing most of the mechanical energy in a nearly loss-less optical potential, thereby strongly diluting the effects of material dissipation. By placing a 130 nm thick SiO 2 pendulum in an optical standing wave, we achieve an increase in the pendulum

Show more
183 Read more

The **superconducting** setup that we are considering for this **quantum** simulation is com- posed of N transmon qubits **coupled** to a single **resonator**. In order to perform highly nonlocal interactions between two distant qubits, every qubit with label inside the inter- val spanned by them should interact with the same **resonator**. Coupling several qubits to just one **resonator** can be a diﬃcult task wherever the number of simulated sites is large enough. Therefore, we propose an optimized architecture for the simulation of Fermi- Hubbard model with up to next-nearest neighbours in D. As it is shown in Figure , we propose a setup with N **superconducting** **circuits** distributed in a square lattice []. Se- quentially coupling two rows by a single transmission line **resonator**, one can reduce the number of qubits **coupled** to a single **resonator**. Nevertheless, all the interactions needed for satisfying the Jordan-Wigner mapping can be simulated with this architecture. Fur- thermore, one can achieve a speedup of the protocol by performing interactions that in- volve diﬀerent qubits in a parallel way, e.g. the interaction between qubits and and the one between qubits and can be performed simultaneously using resonators and , respectively.

Show more
11 Read more

Hybrid **quantum** computation exploits the unique strengths of disparate **quantum** technologies, enabling realization of a scalable processor capable of both fast gates and long coher- ence times that has yet to be achieved using a single physi- cal qubit. **Superconducting** qubits **coupled** via microwave res- onators have been identified as promising candidates for such an interface offering both fast (∼ns) gate times and a scalabil- ity through fabrication of chip-based **superconducting** **circuits** [2–4], which have already been used to implement **quantum** algorithms [5], many-body Hamiltonians [6] and synthesis of arbitrary **quantum** states of the **resonator** mode [7]. However, a limiting factor is the coherence time of the qubits, typically around 60 µs [8, 9]. This makes coupling the **superconducting** **circuits** to external qubits for **quantum** memory advantageous. To date a number of systems have been explored for this pur- pose, including solid state spin-ensembles [10], color centers in diamond [11], nano-mechical resonators [12] and atoms.

Show more
155 Read more

A 4-channel multiplexer with a resonant junction is illustrated here. The specifications of the normalized passbands of the multiplexer channels are: channel 1: (−2.6 to −2.2), channel 2: (−1 to −0.6), channel 3: (0.6 to 1) and channel 4: (2.2 to 2.6). All the channels have 3rd order Chebyshev filtering function and a return loss of 20 dB. The topology of the multiplexer is depicted in Fig. 3 with two different arrangements of channels, where **resonator** 1 is the resonant junction. An unconstrained local optimization technique has been employed to synthesize the coupling matrix of the multiplexer for both arrangements of channels in Fig. 3(a) and Fig. 3(b).

Show more
We study the energetics of a **superconducting** double dot, by measuring both the **quantum** capacitance of the device and the response of a nearby charge sensor. We observe different behaviour for odd and even charge states and describe this with a model based on the competition between the charging energy and the superconduct- ing gap. We also find that, at finite temperatures, thermodynamic considerations have a significant effect on the charge stability diagram.

11 Read more

Sandwich structure of weakly **coupled** magnetic/nonmagnetic conducting layers can be used as a spin-ˇlter. Let the magnetic layers be narrow. The nonmagnetic layers can be considered as waveguides. The boundary conditions are determined by the number of free levels in magnetic layers with given spin orientation of the electron. If there are no free levels for the spin orientation, then one has the Dirichlet condition at the boundary. In other cases, we have another boundary conditions, for example, the Neumann one. Due to the difference in resonance position for different boundary conditions and the narrowness of the resonant peak there exist electron energies corresponding to the resonance for one spin orientation and the absence of the resonance for another one. Thus, the spin polarized beam of reected electrons appears, and the transmitted beam is partly polarized. The system of some coupling windows (which are placed at a distance to prevent an appearance of complex interference effects) gives us a strongly polarized beam. The same structure can be used for ˇnal measuring of resulting system state. Single-qubit operations can be accomplished as follows. We can use the applied electromagnetic ˇeld in some domains or ferromagnetic inclusions inserted in some parts of the semiconductor boundary.

Show more
Investigating the classical simulability of **quantum** **circuits** provides a promising av- enue towards understanding the computational power of **quantum** systems. Whether a class of **quantum** **circuits** can be efficiently simulated with a probabilistic classical computer, or is provably hard to simulate, depends quite critically on the precise no- tion of “classical simulation” and in particular on the required accuracy. We argue that a notion of classical simulation, which we call epsilon -simulation (or -simulation for short), captures the essence of possessing “equivalent computational power” as the **quantum** system it simulates: It is statistically impossible to distinguish an agent with access to an -simulator from one possessing the simulated **quantum** system. We relate -simulation to various alternative notions of simulation predominantly focusing on a simulator we call a poly-box. A poly-box outputs 1/poly precision additive estimates of Born probabilities and marginals. This notion of simulation has gained prominence through a number of recent simulability results. Accepting some plausible compu- tational theoretic assumptions, we show that -simulation is strictly stronger than a poly-box by showing that IQP **circuits** and unconditioned magic-state injected Clifford **circuits** are both hard to -simulate and yet admit a poly-box. In contrast, we also show that these two notions are equivalent under an additional assumption on the sparsity of the output distribution (poly-sparsity).

Show more
40 Read more

Nature readily gives us stable, discrete **quantum** systems - atoms. Atoms can be isolated by first ionizing them, then trapping them in an electromagnetic field within an ultra- high vacuum environment [40, 41, 42]. Historically, trapped ions were first used as highly stable clocks because the energy levels of the ions were highly stable and predictable [43, 44]. These properties also lend themselves to high fidelity single qubit manipulation. The qubit basis is formed using two of the ion’s energy levels, chosen based on a balance of stability and ease of manipulation and measurement. Single qubits can be controlled using microwaves [45, 46] or lasers [47]. The qubit state is measured by driving a tran- sition which causes the ion to fluoresce conditional on the qubit state [48]. Two qubit interactions are generally mediated by the Coulomb force between two ions, and high fidelity two qubit gates have been achieved by conditionally driving a vibrational mode between the two qubits [47].

Show more
242 Read more

where χ(r) is the susceptibility and p(r, t) is the small amplitude fluctuation of P(r, t) which we will use later in our analysis of noise. Generally speaking, in active struc- tures, the susceptibility is a function of time, since the carrier or population densities are modified by the optical field. We shall simplify the analysis to a quasi-static picture where the optical signal varies on a much longer time scale than the carrier **dynamics**, so the gain and loss can be taken as constants. Furthermore, in the regime of small values of gain, we can neglect nonlinearities due to saturation so χ(r) is linear and can be expressed as χ(r) = ²(r) + iσ(r). ²(r) is the dielectric profile of the structure and σ(r) accounts for the gain or loss depending on its sign (positive for gain and negative for loss). ²(r) and σ(r) are dimensionless. Substituting the polarization density into Maxwell’s equations, we arrive at

Show more
188 Read more

HE hybrid superconductor-semiconductor-superconductor (S-Sm-S) structures have been proposed to be the building blocks of the next generation of **quantum** computers, after the purported detection of exotic Majorana particles with zero electrical charges at the interface of S-Sm junctions [1-3]. However, there still is a fundamental technological problem in the (i) fabrication of highly transparent interfaces between superconductors and semiconductors and (ii) scaling the number of junctions up in a single chip to realize a **quantum** device applicable for **quantum** technology [4-7]. In this regard, we have recently demonstrated hybrid Josephson junctions with highly transparent interfaces between the **superconducting** Niobium (Nb) and semiconducting In 0.75 Ga 0.25 As two-dimensional electron gas (2DEG) contacts.

Show more
archical, quantitative simulations will be required which are capable of accurately and reliably predicting the be- haviour of the system-under-development at different lev- els of abstraction. The ultimate ambition of this ap- proach being to achieve a level of realism that would en- able the sort of zero-prototyping that occurs in the design of Very Large Scale Integrated (VLSI) microelectronics and which is also now becoming an aim of the automo- tive and other industries. Given the intractability by classical means of modelling complex **quantum** systems, it is an open question as to how well and how far this design paradigm can be translated to the engineering of **quantum** technologies. Consequently, there is a need to investigate the extent to which it is possible to develop a hierarchy of system models that is able to provide, from a design perspective, usefully accurate modelling, simu- lation and figures of merit at the component, device and system level.

Show more
12 Read more

The product of computer size and time is typically called “area-time product” or “AT ” in the literature on non-**quantum** computation; “volume” in the liter- ature on **quantum** computation; and “price-performance ratio” in the literature on economics. The cost of **quantum** error correction is not the only argument for viewing this product as the true cost of computation: there is a more fundamen- tal argument stating that the total cost assigned to two separate computations should not depend on whether the computations are carried out in serial (using hardware for twice as much time) or in parallel (using twice as much hardware). From this perspective, it is much better to use parallel algorithms for integer addition that finish in time Θ(log n). This still means Θ(n log n) error-correction steps, so the cost is larger by a factor Θ(log n) than the number of bit operations. At a higher level, the CSIDH computation involves various layers for which highly parallel algorithms are not known. For example, modular exponentiation is notoriously difficult to parallelize. A conventional computation of x mod n, x 2 mod n, x 4 mod n, x 8 mod n, etc. can store each intermediate result on top of the previous result, but Bennett’s conversion produces a reversible computation that uses much more storage, and the resulting **quantum** computation requires continual error correction for all of the stored qubits. Shor’s algorithm avoids this issue because it computes a superposition of powers of a constant x; this is not helpful in the CSIDH context.

Show more
56 Read more

We apply dynamical system methods and Melnikov theory to study small amplitude perturbation of some **coupled** implicit diﬀerential equations. In particular we show the persistence of such orbits connecting singularities in ﬁnite time provided a Melnikov like condition holds. Application is given to **coupled** nonlinear RLC system. MSC: Primary 34A09; secondary 34C23; 37G99

27 Read more

Yu, Pérez-Delgado and Fitzsimons [58] showed that perfectly information-theoretically secure QFHE is not possible for arbitrary unitary transformations, unless the size of the encryption grows exponentially in the input size. Thus, any scheme that attempts to achieve information-theoretically secure QFHE has to leak some proportion of the input to the server [5, 48] or can only be used to evaluate a subset of all unitary transformations on the input [48, 40, 54]. Information-theoretically secure QFHE is not known to be achievable for the subset of our interest, that of all unitary transformations for which efficient **quantum** **circuits** exist. Like the multiplication operation is hard in the classical case, the hurdle in the **quantum** case seems to be the evaluation of non-Clifford gates. A recent result by Ouyang, Tan and Fitzsimons provides information-theoretic security for **circuits** with at most a constant number of non-Clifford operations [44]. Broadbent and Jeffery [16] proposed two schemes that achieve homomorphic encryption for nontrivial sets of **quantum** **circuits**. Instead of trying to achieve information-theoretic security, they built their schemes based on a classical FHE scheme and hence any computational assumptions on the classical scheme are also required for the **quantum** schemes. Computational assumptions allow bypassing the impossibility result from [58] and work toward a (**quantum**) fully homomorphic encryption scheme.

Show more
45 Read more

or different formalisms were carried out to determine theoretical properties of such networks [4,5,6,7,8,9,10,11,12,13,14,15,16]. One of the main motivations of many of them was to better understand those emergent dynamical behaviours that networks display and that cannot be explained or predicted by a simple analysis of the local interactions existing between the components of the net- works. In particular, later works by [17] and [18] yielded conjectures and gave rise to problematics that are still relevant in the field of regulation networks be- yond the particular definition of the models one may choose to use. For instance, Thomas highlighted the importance of specific patterns, namely **circuits**, on the **dynamics** of discrete regulation networks and Kauffman gave an approximation of the number of different possible asymptotic behaviours of Boolean networks. Thus, from the point of view of theoretical biology but also from that of discrete mathematics and theoretical computer science, it is relevant to ad- dress the question of the number of attractors in the **dynamics** of a network. Close to the 16th Hilbert problem concerning the number of limit cycles of dy- namical systems [19], this question has already been considered in some works [20,21,22,15,16]. Driven by a similar will to understand the dynamical proper- ties of (regulation) networks modeled by Boolean automata networks, we have decided to first focus our attention on a simple instance of Boolean automata networks, that is, Boolean automata **circuits** (which also happen to be a sim- ple instance of threshold Boolean automata networks [1]). The reason for this choice is that **circuits** are known to play an important part in the **dynamics** of a network that contains them. One way to see this is to note that a network whose underlying interaction graph has no **circuits** can only eventually end up in a configuration that will never change over time. A network with retroactive loops, on the contrary, will exhibit more diverse dynamical behaviour patterns. [17] noted the importance of underlying **circuits** in networks and formulated con- jectures concerning the role of positive (i.e., with an even number of inhibitions) and negative (i.e., with an odd number of inhibitions) **circuits** in the **dynamics** of regulation networks. Besides the fact that they are known to be decisive pat- terns for the **dynamics** of arbitrary biological networks, **circuits** are also relevant because they may be regarded specifically as internal layers of feedforward net- works 5 . Identifying the **dynamics** of **circuits** is thus a first step in the process of

Show more
31 Read more

Low loss rates provided by **superconducting** coplanar waveguides (CPW) and CPW res- onators are relevant for microwave applications which require **quantum**-scale noise levels and high sensitivity, such as mutual kinetic inductance detectors [1], parametric ampliﬁers [2], and qubit devices based on Josephson junctions [3], electron spins in **quantum** dots [4], and NV-centers [5]. Transmission line (TL) coupling allows for implementing rela- tively weak **resonator**-feedline coupling strengths without signiﬁcant oﬀ-resonant pertur- bations to the propagating modes in the feedline CPW. Owing to this property and ben- eﬁting from their simplicity, notch-port couplers are extensively used in frequency mul- tiplexing schemes [6], where a large number of CPW resonators of diﬀerent frequencies are **coupled** to a single feedline. The geometric design of such resonators determines the resonant frequencies of their modes, loss rates and coupling coeﬃcients of these modes to other elements of the circuit. 3D electromagnetic simulation software provides excellent means for complete characterization of such structures by ﬁnite element analysis. How- ever, in the case of simple structures, analytical formulas can be devised that are invaluable for engineering of large multi-pixel **resonator** arrays.

Show more
16 Read more

Engineering, Universiti Sains Malaysia, Penang 14300, Malaysia Abstract—A 1 × 3 element linear array using cylindrical dielectric **resonator** antennas (CDRAs) is designed and presented for 802.11a WLAN system applications. The top and bottom elements of CDRA array are excited through the rectangular coupling slots etched on the ground plane, while the slots themselves are excited through the microstrip transmission line. The third element (i.e., central CDRA) is excited through the mutual coupling of two radiating elements by its sides. This mechanism enhances the bandwidth (96.1%) and gain (14.3%) as compared to aperture **coupled** technique. It is also observed that the side lobe levels are reduced over the designed frequency band. Using CST microwave studio, directivity of 10.5 dBi has been achieved for operating frequency of 5.6 GHz. Designed antenna array is fabricated and tested. Simulated and measured results are in good agreement. The equivalent lumped element circuit is also designed and presented using Advanced design system (ADS) for this proposed array.

Show more
11 Read more