Geometric phases accompanying adiabatic quantum evolutions can be used to construct robust quantum control for quantum information processing due to their noise-resilient feature. A significant development along this line is to construct geometric gates using nonadiabatic quantum evolutions to reduce errors due to decoherence. However, it has been shown that nonadiabatic geometric gates are not necessarily more robust than dynamical ones, in contrast to an intuitive expectation. Here we experimentally investigate this issue for the case of nonadiabatic holonomic quantum computation (NHQC) and show that conventional NHQC schemes cannot guarantee the expected robustness due to a cross-coupling to the states outside the computational space. We implement a different set of constraints for gate construction in order to suppress such cross-coupling to achieve an enhanced robustness. Using a superconducting quantum circuit, we demonstrate high-fidelity holonomic gates whose infidelity against quasistatic transverse errors can be suppressed up to the fourth order, instead of the second order in conventional NHQC and dynamical gates. In addition, we explicitly measure the accumulated dynamical phase due to the abovementioned cross-coupling and verify that it is indeed much reduced in our NHQC scheme. We further demonstrate a protocol for constructing two-qubit NHQC gates also with an enhanced robustness.

We present the design and characterization of a three-Josephson-junction superconducting loop circuit with three large shunt capacitors. Used as a qubit, the circuit shows long energy-relaxation times, of the order of $40\mu \mathrm{s}$ and a spin-echo dephasing time of $9.4\mu \mathrm{s}$. The circuit has high anharmonicity, of $2\pi \times 3.69\mathrm{GHz}$. We extract the multilevel relaxation and dephasing rates of the circuit used as a qutrit and discuss the possible sources for the decoherence. The high anharmonicity allows for fast qubit control with nanosecond-range gate durations and a measured average gate fidelity of 99.92%, characterized by randomized benchmarking. These results demonstrate interesting potential use for fast nanosecond-time-scale two-qubit gates and multilevel quantum logic.

Scalable quantum information processing requires the ability to tune multiqubit interactions. This makes the precise manipulation of quantum states particularly difficult for multiqubit interactions because tunability unavoidably introduces sensitivity to fluctuations in the tuning parameters, leading to erroneous multiqubit gate operations. The performance of quantum algorithms may be severely compromised by coherent multiqubit errors. It is therefore imperative to understand how these fluctuations affect multiqubit interactions and, more importantly, to mitigate their influence. In this study, we demonstrate how to implement dynamical-decoupling techniques to suppress the two-qubit analogue of the dephasing on a superconducting quantum device featuring a compact tunable coupler, a trending technology that enables the fast manipulation of qubit-qubit interactions. The pure-dephasing time shows up to an approximate 14 times enhancement on average when using robust sequences. The results are in good agreement with the noise generated from room-temperature circuits. Our study further reveals the decohering processes associated with tunable couplers and establishes a framework to develop gates and sequences robust against two-qubit errors.

Fixed-frequency qubits can suffer from always-on interactions that inhibit independent control. Here, we address this issue by experimentally demonstrating a superconducting architecture using qubits that comprise of two capacitively shunted Josephson junctions connected in series. Historically known as tunable coupling qubits (TCQs), such two-junction qubits support two modes with distinct frequencies and spatial symmetries. By selectively coupling only one type of mode and using the other as our computational basis, we greatly suppress crosstalk between the data modes while permitting all-microwave two-qubit gates.

Classical simulations of time-dependent quantum systems are widely used in quantum control research. In particular, these simulations are commonly used to host iterative optimal control algorithms. This is convenient for algorithms that are too onerous to run in the loop with current-day quantum hardware, as well as for researchers without consistent access to hardware. However, if the model used to represent the system is not selected carefully, an optimized control protocol may be rendered futile when applied to hardware. We present a series of models, ordered in a hierarchy of progressive approximation, which appear in quantum control literature. The validity of each model is characterized experimentally by designing and benchmarking control protocols for an IBMQ cloud quantum device. This result demonstrates error amplification induced by the application of a first-order perturbative approximation. Furthermore, the emergence of errors that cannot be corrected by simple amplitude scaling of control pulses is demonstrated in simulation, due to an underlying mistreatment of noncomputational dynamics. Finally, an evaluation of simulated control dynamics reveals that despite the substantial variance in numerical predictions across the proposed models, the complexity of discovering local optimal control protocols appears invariant in the simple control scheme setting.

Scanning tunneling microscope lithography can be used to create nanoelectronic devices in which dopant atoms are precisely positioned in a $\mathrm{Si}$ lattice within approximately $1$ nm of a target position. This exquisite precision is promising for realizing various quantum technologies. However, a potentially impactful form of disorder is due to incorporation kinetics, in which the number of P atoms that incorporate into a single lithographic window is manifestly uncertain. We present experimental results indicating that the likelihood of incorporating into an ideally written three-dimer single-donor window is $63\pm 10\mathrm{\%}$ for room-temperature dosing, and corroborate these results with a model for the incorporation kinetics. Nevertheless, further analysis of this model suggests conditions that might raise the incorporation rate to near-deterministic levels. We simulate bias spectroscopy on a chain of comparable dimensions to the array in our yield study, indicating that such an experiment may help confirm the inferred incorporation rate.

Continuous-time quantum walks (CTQWs) have shown the capability to perform efficiently the spatial search of a marked site on many kinds of graphs. However, most of such graphs are hard to realize in an experimental setting. Here we study CTQW spatial search on a planar triangular lattice by means of both numerical simulations and experiments. The experiments are performed using two-dimensional waveguide arrays fabricated by femtosecond laser pulses, illuminated by coherent light. We show that the retrieval of the marked site by the quantum walker is accomplished with higher probability than the classical counterpart, in a convenient time window placed early in the evolution.

The preparation of a quantum Gibbs state is an essential part of quantum computation and has wide-ranging applications in various areas, including quantum simulation, quantum optimization, and quantum machine learning. In this paper, we propose variational hybrid quantum-classical algorithms for quantum Gibbs state preparation. We first utilize a truncated Taylor series to evaluate the free energy and choose the truncated free energy as the loss function. Our protocol then trains the parameterized quantum circuits to learn the desired quantum Gibbs state. Notably, this algorithm can be implemented on near-term quantum computers equipped with parameterized quantum circuits. By performing numerical experiments, we show that shallow parameterized circuits with only one additional qubit can be trained to prepare the Ising chain and spin chain Gibbs states with a fidelity higher than 95%. In particular, for the Ising chain model, we find that a simplified circuit ansatz with only one parameter and one additional qubit can be trained to realize a 99% fidelity in Gibbs state preparation at inverse temperatures larger than $2$.

Hole spins in semiconductor quantum dots represent a viable route for the implementation of electrically controlled qubits. In particular, the qubit implementation based on $\mathrm{Si}$ $p$-MOSFETs offers great potentialities in terms of integration with the control electronics and long-term scalability. Moreover, the future down scaling of these devices will possibly improve the performance of both the classical (control) and quantum components of such monolithically integrated circuits. Here, we use a multiscale approach to simulate a hole-spin qubit in a down-scaled $\mathrm{Si}$-channel $p$-MOSFET, the structure of which is based on a commercial 22-nm fully depleted silicon-on-insulator device. Our calculations show the formation of well-defined hole quantum dots within the $\mathrm{Si}$ channel and the possibility of a general electrical control, with Rabi frequencies of the order of $100\mathrm{MHz}$ for realistic field values. A crucial role of the channel aspect ratio is also demonstrated, as well as the presence of a favorable parameter range for the qubit manipulation.

Optimization is one of the key applications of quantum computing where a quantum speedup has been an eagerly anticipated outcome. A promising approach to optimization using quantum dynamics is to consider a linear combination $s(t)B+[1-s(t)]C$ of two noncommuting Hamiltonians $B$ and $C$, where $C$ encodes the solution to the optimization problem in its ground state, $B$ is a Hamiltonian whose ground state is easy to prepare, and $s(t)\in [0,1]$ is the bounded “switching schedule” or “path,” with $t\in [0,t_f]$. This approach encompasses two of the most widely studied quantum-optimization algorithms: quantum annealing [QA; continuous $s(t)$] and the quantum approximate optimization algorithm [QAOA; piecewise constant $s(t)$]. While it is notoriously difficult to prove a quantum advantage for either algorithm, it is possible to compare and contrast them by finding the optimal $s(t)$. Here we provide a rigorous analysis of this quantum optimal control problem, entirely within the geometric framework of Pontryagin’s maximum principle of optimal control theory. We extend earlier results, derived in a purely closed-system setting, to open systems. This is the natural setting for experimental realizations of QA and QAOA. In the closed-system setting it was shown that the optimal solution is a “bang-anneal-bang” schedule, with the bangs characterized by $s(t)=0$ and $s(t)=1$ in finite subintervals of $[0,t_f]$, in particular, $s(0)=0$ and $s(t_f)=1$, in contrast to the standard prescription $s(0)=1$ and $s(t_f)=0$ of QA. As an example, we prove that for a single spin-$1/2$, the optimal solution in the closed-system setting is the bang-bang schedule, switching midway from $s\equiv 0$ to $s\equiv 1$. For finite-dimensional environments and without any approximations we identify sufficient conditions ensuring that either the bang-anneal, anneal-bang, or bang-anneal-bang schedules are optimal, and recover the optimality of $s(0)=0$ and $s(t_f)=1$. However, for infinite-dimensional environments and a system described by an adiabatic Redfield master equation we do not recover the bang-type optimal solution. In fact we can only identify conditions under which $s(t_f)=1$, and even this result is not recovered in the fully Markovian limit, suggesting that the pure anneal-type schedule is optimal. Our open-system results have implications for the use of experimental quantum-information processors, which are by necessity noisy, and suggest that in this practical sense the optimal schedules for quantum optimization are likely to be continuous.

Networks of optical oscillators simulating coupled Ising spins have been recently proposed as a heuristic platform to solve hard optimization problems. These networks, called coherent Ising machines (CIMs), exploit the fact that the collective nonlinear dynamics of coupled oscillators can drive the system close to the global minimum of the classical Ising Hamiltonian, encoded in the coupling matrix of the network. To date, realizations of large-scale CIMs have been demonstrated using hybrid optical-electronic setups, where optical oscillators simulating different spins are subject to electronic feedback mechanisms emulating their mutual interaction. While the optical evolution ensures an ultrafast computation, the electronic coupling represents a bottleneck that causes the computational time to severely depend on the system size. Here, we propose an all-optical scalable CIM with fully programmable coupling. Our setup consists of an optical parametric amplifier with a spatial light modulator (SLM) within the parametric cavity. The spin variables are encoded in the binary phases of the optical wave front of the signal beam at different spatial points, defined by the pixels of the SLM. We first discuss how different coupling topologies can be achieved by different configurations of the SLM, and then benchmark our setup with a numerical simulation that mimics the dynamics of the proposed machine. In our proposal, both the spin dynamics and the coupling are fully performed in parallel, paving the way towards the realization of size-independent ultrafast optical hardware for large-scale computation purposes.

A multiple access channel (MAC) consists of multiple senders simultaneously transmitting their messages to a single receiver. For the classical-quantum case (CQ MAC), achievable rates are known assuming that all the messages are decoded, a common assumption in quantum network design. However, such a conventional design approach ignores the global network structure, i.e., the network topology. When a CQ MAC is given as a part of quantum network communication, this work shows that computation properties can be used to boost communication speeds with code design dependent on the network topology. We quantify achievable quantum communication rates of codes with the computation property for a two-sender CQ MAC. When the two-sender CQ MAC is a boson coherent channel with binary discrete modulation, we show that it achieves the maximum possible communication rate (the single-user capacity), which cannot be achieved with conventional design. Further, such a rate can be achieved by different detection methods: quantum (with and without quantum memory), on-off photon counting, and homodyne (each at different photon power). Finally, we describe two practical applications, one of which cryptographic.

High-fidelity two-qubit entangling gates are essential building blocks for fault-tolerant quantum computers. Over the past decade, tremendous efforts have been made to develop scalable high-fidelity two-qubit gates with superconducting quantum circuits. Recently, an easy-to-scale controlled-phase gate scheme that utilizes the tunable-coupling architecture with fixed-frequency qubits [Phys. Rev. Lett. 125, 240502 (2020); Phys. Rev. Lett. 125, 240503 (2020)] has been demonstrated with high fidelity and attracted broad interest. However, in-depth understanding of the underlying mechanism is still missing, preventing us from fully exploiting its potential. Here we present a comprehensive theoretical study, explaining the origin of the high-contrast $ZZ$ interaction. Based on improved understanding, we develop a general yet convenient method for shaping an adiabatic pulse in a multilevel system, and identify how to optimize the gate performance from design. Given state-of-the-art coherence properties, we expect the scheme to potentially achieve a two-qubit gate error rate near ${10}^{-5}$, which would drastically speed up the progress towards fault-tolerant quantum computation.

Nitrogen-vacancy color centers in diamond have attracted broad attention as quantum sensors for both static and dynamic magnetic, electrical, strain, and thermal fields and are particularly attractive for quantum sensing under pressure in diamond anvil cells. Optically based nuclear magnetic resonance may be possible at pressures greater than a few gigapascals and offers an attractive alternative to conventional Faraday-induction-based detection. Here, we present ac sensing results and demonstrate synchronized readout up to 6 GPa but find that the sensitivity is reduced due to inhomogeneities of the microwave field and pressure within the sample space. These experiments enable the possibility of all-optical high resolution magnetic resonance of nanoliter sample volumes at high pressures.