High-fidelity Operations Research Articles

Fast two-qubit logic with holes in germanium.

Universal quantum information processing requires the execution of single-qubit and two-qubit logic. Across all qubit realizations1, spin qubits in quantum dots have great promise to become the central building block for quantum computation2. Excellent quantum dot control can be achieved in gallium arsenide3-5, and high-fidelity qubit rotations and two-qubit logic have been demonstrated in silicon6-9, but universal quantum logic implemented with local control has yet to be demonstrated. Here we make this step by combining all of these desirable aspects using hole quantum dots in germanium. Good control over tunnel coupling and detuning is obtained by exploiting quantum wells with very low disorder, enabling operation at the charge symmetry point for increased qubit performance. Spin-orbit coupling obviates the need for microscopic elements close to each qubit and enables rapid qubit control with driving frequencies exceeding 100 MHz. We demonstrate a fast universal quantum gate set composed of single-qubit gates with a fidelity of 99.3 per cent and a gate time of20nanoseconds, and two-qubit logic operations executed within 75nanoseconds. Planar germanium has thus matured within a year from a material that can host quantum dots to a platform enabling two-qubit logic, positioning itself as an excellent material for use in quantum information applications.

Calibration of a Cross-Resonance Two-Qubit Gate Between Directly Coupled Transmons

Implementing high-fidelity entangling operations between qubits is a key challenge in quantum computing. Multiple sources of error and a large parameter space make optimization of control schemes for high-fidelity operations a complex technical challenge. This study presents a complete recipe for calibrating a high-fidelity cross-resonance gate implemented between two dispersively coupled transmon qubits, showing that even large amounts of crosstalk can be effectively canceled. This approach should be useful as a general tool for those working on experiments with coupled quantum systems, in particular for computing.

Adaptive Bayesian phase estimation for quantum error correcting codes

Realisation of experiments even on small and medium-scale quantum computers requires an optimisation of several parameters to achieve high-fidelity operations. As the size of the quantum register increases, the characterisation of quantum states becomes more difficult since the number of parameters to be measured grows as well and finding efficient observables in order to estimate the parameters of the model becomes a crucial task. Here we propose a method relying on application of Bayesian inference that can be used to determine systematic, unknown phase shifts of multi-qubit states. This method offers important advantages as compared to Ramsey-type protocols. First, application of Bayesian inference allows the selection of an adaptive basis for the measurements which yields the optimal amount of information about the phase shifts of the state. Secondly, this method can process the outcomes of different observables at the same time. This leads to a substantial decrease in the resources needed for the estimation of phases, speeding up the state characterisation and optimisation in experimental implementations. The proposed Bayesian inference method can be applied in various physical platforms that are currently used as quantum processors.

Coherent transfer of quantum information in a silicon double quantum dot using resonant SWAP gates

Spin-based quantum processors in silicon quantum dots offer high-fidelity single and two-qubit operation. Recently multi-qubit devices have been realized; however, many-qubit demonstrations remain elusive, partly due to the limited qubit-to-qubit connectivity. These problems can be overcome by using SWAP gates, which are challenging to implement in devices having large magnetic field gradients. Here we use a primitive SWAP gate to transfer spin eigenstates in 100 ns with a fidelity of {bar{F}}_{{rm{SWAP}}}^{{rm{(p)}}}=98 %. By swapping eigenstates we are able to demonstrate a technique for reading out and initializing the state of a double quantum dot without shuttling charges through the quantum dot. We then show that the SWAP gate can transfer arbitrary two-qubit product states in 300 ns with a fidelity of {bar{F}}_{{rm{SWAP}}}^{{rm{(c)}}}=84 %. This work sets the stage for many-qubit experiments in silicon quantum dots.

Synthesizing multi-phonon quantum superposition states using flux-mediated three-body interactions with superconducting qubits

Massive mechanical resonators operating at the quantum scale can enable a large variety of applications in quantum technologies as well as fundamental tests of quantum theory. Of crucial importance in that direction is both their integrability into state-of-the-art quantum platforms as well as the ability to prepare them in generic quantum states using well-controlled high-fidelity operations. Here, we propose a scheme for controlling a radio-frequency mechanical resonator at the quantum scale using two superconducting transmon qubits that can be integrated on the same chip. Specifically, we consider two qubits coupled via a capacitor in parallel to a superconducting quantum interference device (SQUID), which has a suspended mechanical beam embedded in one of its arms. Following a theoretical analysis of the quantum system, we find that this configuration, in combination with an in-plane magnetic field, can give rise to a tuneable three-body interaction in the single-photon strong-coupling regime, while enabling suppression of the stray qubit-qubit coupling. Using state-of-the-art parameters and qubit operations at single-excitation levels, we numerically demonstrate the possibility of ground-state cooling as well as high-fidelity preparation of mechanical quantum states and qubit-phonon entanglement, i.e. states having negative Wigner functions and obeying non-classical correlations. Our work significantly extends the quantum control toolbox of radio-frequency mechanical resonators and may serve as a promising architecture for integrating such mechanical elements with transmon-based quantum processors.

Validating quantum computers using randomized model circuits

We introduce a single-number metric, quantum volume, that can be measured using a concrete protocol on near-term quantum computers of modest size ($n\lesssim 50$), and measure it on several state-of-the-art transmon devices, finding values as high as 16. The quantum volume is linked to system error rates, and is empirically reduced by uncontrolled interactions within the system. It quantifies the largest random circuit of equal width and depth that the computer successfully implements. Quantum computing systems with high-fidelity operations, high connectivity, large calibrated gate sets, and circuit rewriting toolchains are expected to have higher quantum volumes. The quantum volume is a pragmatic way to measure and compare progress toward improved system-wide gate error rates for near-term quantum computation and error-correction experiments.

A Ten-Qubit Solid-State Spin Register with Quantum Memory up to One Minute

Spins associated to single defects in solids provide promising qubits for quantum information processing and quantum networks. Recent experiments have demonstrated long coherence times, high-fidelity operations and long-range entanglement. However, control has so far been limited to a few qubits, with entangled states of three spins demonstrated. Realizing larger multi-qubit registers is challenging due to the need for quantum gates that avoid crosstalk and protect the coherence of the complete register. In this paper, we present novel decoherence-protected gates that combine dynamical decoupling of an electron spin with selective phase-controlled driving of nuclear spins. We use these gates to realize a 10-qubit quantum register consisting of the electron spin of a nitrogen-vacancy center and 9 nuclear spins in diamond. We show that the register is fully connected by generating entanglement between all 45 possible qubit pairs, and realize genuine multipartite entangled states with up to 7 qubits. Finally, we investigate the register as a multi-qubit memory. We show coherence times up to 63(2) seconds - the longest reported for a single solid-state qubit - and demonstrate that two-qubit entangled states can be stored for over 10 seconds. Our results enable the control of large quantum registers with long coherence times and therefore open the door to advanced quantum algorithms and quantum networks with solid-state spin qubits.

(Invited) Silicon Coupled Quantum Dots for Spin-Based Quantum Bits

Recently quantum computation devices have been intensively studied in various systems. Spins in silicon quantum dots (Si QDs) are one of the promising candidates for implementing quantum bits (qubits). Since only 4.7% of Si atoms are isotopes with nuclear spins, long coherence times of electron spins reflecting small hyperfine interactions were demonstrated [1-3]. Moreover, using isotopically-engineered Si [4], qubits with extended coherence time and gate operation with high fidelity were demonstrated [5-7]. Si qubit research has accelerated following the demonstration of these high fidelity single qubit operations and two-qubit logic gates [8]. The major remaining issue is large scale integration of qubits. The advantage of Si qubits is that matured CMOS technologies can be applied for integration of qubits. At Tokyo Tech, we have studied physically-defined coupled QDs in MOS structures prepared on Si-on-insulator (SOI) substrates [9-20], which are promising for high density integration. The physically-defined devices do not require gates to create confinement potentials for the QDs. These devices thus represent a technological simplification owing to the reduced number of gates. Common fabrication processes normally used to produce Si MOS was applied to make the physically-defined Si QDs. We have developed various device structures of physically-defined Si QDs. By measuring double QD devices, we succeeded in charge sensing of few-electron regime [11, 15, 16] and observation of Pauli-spin blockade [12]. In triple QDs arranged in an equilateral triangle, we demonstrated for the first time in the world a silicon-based two-dimensional arrayed QD structure [20]. We also fabricated and characterized Si double QDs in p-channel MOS and few-hole regime and Pauli-spin blockade were observed [14, 18, 19]. Furthermore, we formed Si single QDs on ultrathin (~6 nm) SOI and obtained comparatively large charging energy (~ 20 meV). We performed three-dimensional calculations of capacitance matrix and transport properties through the QD and found a good quantitative agreement with experiment [17]. These achievements are the important steps for realizing quantum computation devices. We have also studied gate-defined QDs in Si/SiGe heterostructures to demonstrate high-fidelity gate operation through joint research with the University of Tokyo [3,6,7]. The fusion of Si devices and established GaAs qubit technology was advanced. Manipulation of spin states in Si QDs and single-shot readout using a measurement system constructed through development of GaAs qubits, demonstrating that the coherence time is about 100 times longer than that of GaAs systems [3]. The fidelity of single-qubit gate operation has been demonstrated to be 99.6% for native Si QDs [3] and 99.93% for isotopically-engineered Si QDs [6]. Both fidelity values are above the quantum error correction threshold of 99%. This work was financially supported by Q-LEAP of the Ministry of Education, Culture, Sports, Science and Technology (MEXT) and CREST (JPMJCR1675) of Japan Science and Technology Agency (JST) in Japan. B.M. Maune, et al., Nature 481, 344 (2012).E. Kawakami, et al., Nature Nanotech. 9, 666 (2014).K. Takeda, TK, et al., Sci. Adv., 2, 8, e1600694 (2016)K.M. Itoh and H. Watanabe, Mater. Res. Soc. Commun. 4, 143 (2014).M. Veldhorst, et al., Nature Nanotech. 9, 981 (2014).J. Yoneda, TK, et al., Nature Nanotech., 13, 102 (2018)K. Takeda, TK, et al., npj Quantum Information 4, 54 (2018)M. Veldhorst, et al., Nature 526, 410 (2015).A. Sulthoni, TK, et al., J. Appl. Phys., 110, 054511 (2011).A. Rossi, TK, et al., Appl. Phys. Lett. 98, 133506 (2011). K. Horibe, TK, et al., J. Appl. Phys. 111, 093715 (2012).G. Yamahata, TK, et al., Phys. Rev. B 86, 115322 (2012).T. Ferrus, TK, et al., New J. Phys. 16, 1, 013016 (2014).K. Yamada, TK, et al., Appl. Phys. Lett. 105, 113110 (2014).K. Horibe, TK, et al., Appl. Phys. Lett. 106, 083111 (2015).K. Horibe, TK, et al., Appl. Phys. Lett. 106, 053119 (2015).S. Ihara, TK, et al., Appl. Phys. Lett. 107, 013102 (2015)Y. Yamaoka, TK, et al., Jpn. J. Appl. Phys. 56, 04CK07 (2017)S. Mizoguchi, TK, et al., Jpn. J. Appl. Phys. 57, 04FK03 (2018)R. Mizokuchi, TK, et al., Appl. Phys. Lett. 114, 073104 (2019)

Two-qubit entangling gates within arbitrarily long chains of trapped ions

Ion trap systems are a leading platform for large scale quantum computers. Trapped ion qubit crystals are fully-connected and reconfigurable, owing to their long range Coulomb interaction that can be modulated with external optical forces. However, the spectral crowding of collective motional modes could pose a challenge to the control of such interactions for large numbers of qubits. Here, we show that high-fidelity quantum gate operations are still possible with very large trapped ion crystals, simplifying the scaling of ion trap quantum computers. To this end, we present analytical work that determines how parallel entangling gates produce a crosstalk error that falls off as the inverse cube of the distance between the pairs. We also show experimental work demonstrating entangling gates on a fully-connected chain of seventeen $^{171}{\rm{Yb}}^{+}$ ions with fidelities as high as $97(1)\%$.

Quantifying error and leakage in an encoded Si/SiGe triple-dot qubit.

Quantum computation requires qubits that satisfy often-conflicting criteria, which include long-lasting coherence and scalable control1. One approach to creating a suitable qubit is to operate in an encoded subspace of several physical qubits. Although such encoded qubits may be particularly susceptible to leakage out of their computational subspace, they can be insensitive to certain noise processes2,3 and can also allow logical control with a single type of entangling interaction4 while maintaining favourable features of the underlying physical system. Here we demonstrate high-fidelity operation of an exchange-only qubit encoded in a subsystem of three coupled electron spins5 confined in gated, isotopically enhanced silicon quantum dots6. This encoding requires neither high-frequency electric nor magnetic fields for control, and instead relies exclusively on the exchange interaction4,5, which is highly local and can be modulated with a large on-off ratio using only fast voltage pulses. It is also compatible with very low and gradient-free magnetic field environments, which simplifies integration with superconducting materials. We developed and employed a modified blind randomized benchmarking protocol that determines both computational and leakage errors7,8, and found that unitary operations have an average total error of 0.35%, with half of that, 0.17%, coming from leakage driven by interactions with substrate nuclear spins. The combination of this proven performance with complete control via gate voltages makes the exchange-only qubit especially attractive for use in many-qubit systems.

Experimental multiphase estimation on a chip

Multiparameter estimation is a general problem that aims at measuring unknown physical quantities, obtaining high precision in the process. In this context, the adoption of quantum resources promises a substantial boost in the achievable performances with respect to the classical case. However, several open problems remain to be addressed in the multiparameter scenario. A crucial requirement is the identification of suitable platforms to develop and experimentally test novel efficient methodologies that can be employed in this general framework. We report the experimental implementation of a reconfigurable integrated multimode interferometer designed for the simultaneous estimation of two optical phases. We verify the high-fidelity operation of the implemented device, and demonstrate quantum-enhanced performances in two-phase estimation with respect to the best classical case, post-selected to the number of detected coincidences. This device can be employed to test general adaptive multiphase protocols due to its high reconfigurability level, and represents a powerful platform to investigate the multiparameter estimation scenario.

Chip-Integrated Voltage Sources for Control of Trapped Ions

Trapped-ion quantum information processors offer many advantages for achieving high-fidelity operations on a large number of qubits, but current experiments require bulky external equipment for classical and quantum control of many ions. We demonstrate the cryogenic operation of an ion-trap that incorporates monolithically-integrated high-voltage CMOS electronics ($\pm 8\mathrm{V}$ full swing) to generate surface-electrode control potentials without the need for external, analog voltage sources. A serial bus programs an array of 16 digital-to-analog converters (DACs) within a single chip that apply voltages to segmented electrodes on the chip to control ion motion. Additionally, we present the incorporation of an integrated circuit that uses an analog switch to reduce voltage noise on trap electrodes due to the integrated amplifiers by over $50\mathrm{dB}$. We verify the function of our integrated electronics by performing diagnostics with trapped ions and find noise and speed performance similar to those we observe using external control elements.

Digital Coherent Control of a Superconducting Qubit

High-fidelity gate operations are essential to the realization of a fault-tolerant quantum computer. In addition, the physical resources required to implement gates must scale efficiently with system size. A longstanding goal of the superconducting qubit community is the tight integration of a superconducting quantum circuit with a proximal classical cryogenic control system. Here we implement coherent control of a superconducting transmon qubit using a Single Flux Quantum (SFQ) pulse driver cofabricated on the qubit chip. The pulse driver delivers trains of quantized flux pulses to the qubit through a weak capacitive coupling; coherent rotations of the qubit state are realized when the pulse-to-pulse timing is matched to a multiple of the qubit oscillation period. We measure the fidelity of SFQ-based gates to be ~95% using interleaved randomized benchmarking. Gate fidelities are limited by quasiparticle generation in the dissipative SFQ driver. We characterize the dissipative and dispersive contributions of the quasiparticle admittance and discuss mitigation strategies to suppress quasiparticle poisoning. These results open the door to integration of large-scale superconducting qubit arrays with SFQ control elements for low-latency feedback and stabilization.

Nonadiabatic holonomic quantum computation on coupled transmons with ancillaries

The physical implementation of holonomic quantum computation is challenging due to the needed complex controllable interactions in multilevel quantum systems. Here we propose to implement nonadiabatic holonomic quantum computation with conventional capacitive coupled superconducting transmon qubits. A universal set of holonomic gates is constructed with the help of the interaction with an auxiliary qubit rather than relying on delicate control over an auxiliary level of multilevel quantum systems. Explicitly, these quantum gates are realized by tunable interactions in an all-resonant way, which leads to high-fidelity gate operations. In this way, the distinct merit of our scheme is that we use only the lowest two levels of a transmon to form the qubit states. In addition, the auxiliary qubits are in their ground states before and after every gate operation, so that the holonomic gates can be constructed successively. Therefore, our scheme provides a promising method towards the practical realization of high-fidelity nonadiabatic holonomic quantum computation.

Joint Quantum-State and Measurement Tomography with Incomplete Measurements.

Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by imperfect knowledge of the system. We present a procedure to simultaneously characterize quantum states and measurements that mitigates systematic errors by use of a single high-fidelity state preparation and a limited set of high-fidelity unitary operations. Such states and operations are typical of many state-of-the-art systems. For this situation we design a set of experiments and an optimization algorithm that alternates between maximizing the likelihood with respect to the states and measurements to produce estimates of each. In some cases, the procedure does not enable unique estimation of the states. For these cases, we show how one may identify a set of density matrices compatible with the measurements and use a semi-definite program to place bounds on the state's expectation values. We demonstrate the procedure on data from a simulated experiment with two trapped ions.

Universal, high-fidelity quantum gates based on superadiabatic, geometric phases on a solid-state spin-qubit at room temperature

Geometric phases and holonomies are a promising resource for the realization of high-fidelity quantum operations in noisy devices, due to their intrinsic fault-tolerance against parametric noise. However, for a long time their practical use in quantum computing was limited to proof of principle demonstrations. This was partly due to the need for adiabatic time evolution or the requirement of complex, high-dimensional state spaces and a large number of driving field parameters to achieve universal quantum gates employing holonomies. In 2016 Liang et al. proposed universal, superadiabatic, geometric quantum gates exploiting transitionless quantum driving, thereby offering fast and universal quantum gate performance on a simple two-level system. Here, we report on the experimental implementation of a set of non-commuting single-qubit superadiabatic, geometric quantum gates on the electron spin of the nitrogen-vacancy center in diamond under ambient conditions. This provides a promising and powerful tool for large-scale quantum computing under realistic, noisy experimental conditions.

Review of directional sensors for low frequency underwater acoustic applications

In this review, we present some of the more common embodiments directional sensors take on for use in low-frequency underwater acoustic applications. Sensors that fit within this paradigm are typically substantially smaller than an acoustic wavelength and can form first- or second-order cardioid beams at frequencies well below 10 kHz. A mathematical treatment of scalar, vector, and dyadic acoustic fields is presented as it pertains to understanding the phenomenology the sensors are required to measure. Cardioid beam-forming and directivity index are explained to provide context of using directional sensors in aperture constrained situations. The electro-acoustic performance of various sensor concepts is presented using lumped parameter models. Packaging concepts for high-fidelity operation, low self-noise, and low electronic noise in the seawater environment are shown. Special problems such as using directional sensors in deep water or near impedance boundaries is also covered.

P-GaAs Nanowire Metal–Semiconductor Field-Effect Transistors with Near-Thermal Limit Gating

Difficulties in obtaining high-performance p-type transistors and gate insulator charge-trapping effects present two major challenges for III-V complementary metal-oxide semiconductor (CMOS) electronics. We report a p-GaAs nanowire metal-semiconductor field-effect transistor (MESFET) that eliminates the need for a gate insulator by exploiting the Schottky barrier at the metal-GaAs interface. Our device beats the best-performing p-GaSb nanowire metal-oxide-semiconductor field effect transistor (MOSFET), giving a typical subthreshold swing of 62 mV/dec, within 4% of the thermal limit, on-off ratio ∼105, on-resistance ∼700 kΩ, contact resistance ∼30 kΩ, peak transconductance 1.2 μS/μm, and high-fidelity ac operation at frequencies up to 10 kHz. The device consists of a GaAs nanowire with an undoped core and heavily Be-doped shell. We carefully etch back the nanowire at the gate locations to obtain Schottky-barrier insulated gates while leaving the doped shell intact at the contacts to obtain low contact resistance. Our device opens a path to all-GaAs nanowire MESFET complementary circuits with simplified fabrication and improved performance.

A crossbar network for silicon quantum dot qubits.

The spin states of single electrons in gate-defined quantum dots satisfy crucial requirements for a practical quantum computer. These include extremely long coherence times, high-fidelity quantum operation, and the ability to shuttle electrons as a mechanism for on-chip flying qubits. To increase the number of qubits to the thousands or millions of qubits needed for practical quantum information, we present an architecture based on shared control and a scalable number of lines. Crucially, the control lines define the qubit grid, such that no local components are required. Our design enables qubit coupling beyond nearest neighbors, providing prospects for nonplanar quantum error correction protocols. Fabrication is based on a three-layer design to define qubit and tunnel barrier gates. We show that a double stripline on top of the structure can drive high-fidelity single-qubit rotations. Self-aligned inhomogeneous magnetic fields induced by direct currents through superconducting gates enable qubit addressability and readout. Qubit coupling is based on the exchange interaction, and we show that parallel two-qubit gates can be performed at the detuning-noise insensitive point. While the architecture requires a high level of uniformity in the materials and critical dimensions to enable shared control, it stands out for its simplicity and provides prospects for large-scale quantum computation in the near future.

Thinking in PolAR Pictures: Using Rotation-Friendly Mental Images to Solve Leiter-R Form Completion

The Leiter International Performance Scale-Revised (Leiter-R) is a standardized cognitive test that seeks to "provide a nonverbal measure of general intelligence by sampling a wide variety of functions from memory to nonverbal reasoning." Understanding the computational building blocks of nonverbal cognition, as measured by the Leiter-R, is an important step towards understanding human nonverbal cognition, especially with respect to typical and atypical trajectories of child development. One subtest of the Leiter-R, Form Completion, involves synthesizing and localizing a visual figure from its constituent slices. Form Completion poses an interesting nonverbal problem that seems to combine several aspects of visual memory, mental rotation, and visual search. We describe a new computational cognitive model that addresses Form Completion using a novel, mental-rotation-friendly image representation that we call the Polar Augmented Resolution (PolAR) Picture, which enables high-fidelity mental rotation operations. We present preliminary results using actual Leiter-R test items and discuss directions for future work.