Matrix quantum mechanics plays various important roles in theoretical physics, such as a holographic description of quantum black holes, and it underpins the only practical numerical approach to the study of complex high-dimensional supergravity theories. Understanding quantum black holes and the role of entanglement in a holographic setup is of paramount importance for the realization of a quantum theory of gravity. Moreover, a complete numerical understanding of the holographic duality and the emergence of geometric space-time features from microscopic degrees of freedom could pave the way for new discoveries in quantum information science. Euclidean lattice Monte Carlo simulations are the de facto numerical tool for understanding the spectrum of large matrix models and have been used to test the holographic duality. However, they are not tailored to extract dynamical properties or even the quantum wave function of the ground state of matrix models. Quantum computing and deep learning provide potentially useful approaches to study the dynamics of matrix quantum mechanics. If successful in the context of matrix models, these rapidly improving numerical techniques could become the new Swiss army knife of quantum gravity practitioners. In this paper, we perform the first systematic survey for quantum computing and deep-learning approaches to matrix quantum mechanics, comparing them to lattice Monte Carlo simulations. These provide baseline benchmarks before addressing more complicated problems. In particular, we test the performance of each method by calculating the low-energy spectrum.

Describing the thermodynamic properties of quantum systems far from equilibrium is challenging, in particular when the system is strongly coupled to its environment, or when memory effects cannot be neglected. Here, we address such regimes when the system-bath couplings are periodically modulated in time. We show that the couplings modulation, usually associated with a purely dissipative effect, can be suitably engineered to perform thermodynamic tasks. In particular, asymmetric couplings to two heat baths can be used to extract heat from the cold reservoir and to realize an ideal heat rectifier, where the heat current can be blocked either in the forward or in the reverse configuration by simply tuning the frequency of the couplings modulation. Interestingly, both effects take place in the low-temperature, quantum non-Markovian regime. Our work paves the way for the use of optimal control techniques for heat engines and refrigerators working in regimes beyond standard approaches.

Many advanced quantum techniques feature non-Gaussian dynamics, and the ability to manipulate the system in that domain is the next stage in many experiments. One example of meaningful non-Gaussian dynamics is that of a double-well potential. Here we study the dynamics of a levitated nanoparticle undergoing the transition from a harmonic potential to a double well in a realistic setting, subjected to both thermalization and localization. We characterize the dynamics of the nanoparticle from a thermodynamic point of view, investigating the dynamics with the Wehrl entropy production and its rates. Furthermore, we investigate coupling regimes where the the quantum effect and thermal effect are of the same magnitude, and look at suitable squeezing of the initial state that provides the maximum coherence. The effects and the competitions of the unitary and the dissipative parts onto the system are demonstrated. We quantify the requirements to relate our results to a bonafide experiment with the presence of the environment, and discuss the experimental interpretations of our results in the end.

When a quantum system couples strongly to multiple baths, then it is generally no longer possible to describe the resulting system dynamics by simply adding the individual effects of each bath. However, capturing such multibath system dynamics typically requires approximations that can obscure some of the nonadditive effects. Here we present a numerically exact and efficient technique for tackling this problem that builds on the time-evolving matrix product operator (TEMPO) representation. We test the method by applying it to a simple model system that exhibits nonadditive behavior: a two-level dipole coupled to both a vibrational and an optical bath. Although not directly coupled, there is an effective interaction between the baths mediated by the system that can lead to population inversion in the matter system when the vibrational coupling is strong. We benchmark and validate multibath TEMPO against two approximate methods—one based on a polaron transformation, the other on an identification of a reaction coordinate—before exploring the regime of simultaneously strong vibrational and optical coupling where the approximate techniques break down. Here we uncover a new regime where the quantum Zeno effect leads to a fully mixed state of the electronic system.

Quantum simulation on emerging quantum hardware is a topic of intense interest. While many studies focus on computing ground-state properties or simulating unitary dynamics of closed systems, open quantum systems are an interesting target of study owing to their ubiquity and rich physical behavior. However, their nonunitary dynamics are also not natural to simulate on digital quantum devices. Here, we report algorithms for the digital quantum simulation of the dynamics of open quantum systems governed by a Lindblad equation using adaptations of the quantum imaginary–time evolution algorithm. We demonstrate the algorithms on IBM Quantum’s hardware with simulations of the spontaneous emission of a two-level system and the dissipative transverse field Ising model. Our work advances efforts to simulate the dynamics of open quantum systems on quantum hardware.

A clock is, from an information-theoretic perspective, a system that emits information about time. One may therefore ask whether the theory of information imposes any constraints on the maximum precision of clocks. Here we show a quantum-over-classical advantage for clocks or, more precisely, the task of generating information about what time it is. The argument is based on information-theoretic considerations: we analyze how the accuracy of a clock scales with its size, measured in terms of the number of bits that could be stored in it. We find that a quantum clock can achieve a quadratically improved accuracy compared to a purely classical one of the same size.

Under suitable assumptions, the quantum-phase-estimation (QPE) algorithm is able to achieve Heisenberg-limited precision scaling in estimating the ground-state energy. However, QPE requires a large number of ancilla qubits and a large circuit depth, as well as the ability to perform inverse quantum Fourier transform, making it expensive to implement on an early fault-tolerant quantum computer. We propose an alternative method to estimate the ground-state energy of a Hamiltonian with Heisenberg-limited precision scaling, which employs a simple quantum circuit with one ancilla qubit, and a classical postprocessing procedure. Besides the ground-state energy, our algorithm also produces an approximate cumulative distribution function of the spectral measure, which can be used to compute other spectral properties of the Hamiltonian.

Authentication of quantum sources is a crucial task in building reliable and efficient protocols for quantum-information processing. Steady progress vis-à-vis verification of quantum devices in the scenario with fully characterized measurement devices has been observed in recent years. When it comes to the scenario with uncharacterized measurements, the so-called black-box scenario, practical verification methods are still rather scarce. Development of self-testing methods is an important step forward, but these results so far have been used for reliable verification only by considering the asymptotic behavior of large, identically and independently distributed (IID) samples of a quantum resource. Such strong assumptions deprive the verification procedure of its truly device-independent character. In this paper, we develop a systematic approach to device-independent verification of quantum states free of IID assumptions in the finite copy regime. Remarkably, we show that device-independent verification can be performed with optimal sample efficiency. Finally, for the case of independent copies, we develop a device-independent protocol for quantum state certification: a protocol in which a fragment of the resource copies is measured to warrant the rest of the copies to be close to some target state.

The interplay between matter particles and gauge fields in physical spaces with nontrivial geometries can lead to novel topological quantum matter. However, detailed microscopic mechanisms are often obscure, and unconventional spaces are generally challenging to construct in solids. Highly controllable atomic systems can quantum simulate such physics, even those inaccessible in other platforms. Here, we realize a Bose-Einstein condensate (BEC) on a synthetic cylindrical surface subject to a net radial synthetic magnetic flux. We observe a symmetry-protected topological band structure emerging on this Hall cylinder but disappearing in the planar counterpart. BEC’s transport observed as Bloch oscillations in the band structure is analogous to traveling on a Möbius strip in the momentum space, revealing topological band crossings protected by a nonsymmorphic symmetry. We demonstrate that breaking this symmetry induces a topological transition manifested as gap opening at band crossings, and further manipulate the band structure and BEC’s transport by controlling the axial synthetic magnetic flux. Our work opens the door for using atomic quantum simulators to explore intriguing topological phenomena intrinsic in unconventional spaces.

Fault-tolerant quantum error correction is essential for implementing quantum algorithms of significant practical importance. In this work, we propose a highly effective use of the surface Gottesman-Kitaev-Preskill (GKP) code, i.e., the surface code consisting of bosonic GKP qubits instead of bare two-level qubits. In our proposal, we use error-corrected two-qubit gates between GKP qubits and introduce a maximum-likelihood decoding strategy for correcting shift errors in the two-GKP-qubit gates. Our proposed decoding reduces the total cnot failure rate of the GKP qubits, e.g., from $0.87\mathrm{\%}$ to $0.36\mathrm{\%}$ at a GKP squeezing of 12 dB, compared to the case where the simple closest-integer decoding is used. Then, by concatenating the GKP code with the surface code, we find that the threshold GKP squeezing is given by $9.9$ dB under the the assumption that finite squeezing of the GKP states is the dominant noise source. More importantly, we show that a low logical failure rate $p_L<{10}^{-7}$ can be achieved with moderate hardware requirements, e.g., 291 modes and 97 qubits at a GKP squeezing of 12 dB as opposed to 1457 bare qubits for the standard rotated surface code at an equivalent noise level (i.e., $p=0.36\mathrm{\%}$). Such a low failure rate of our surface-GKP code is possible through the use of space-time correlated edges in the matching graphs of the surface-code decoder. Further, all edge weights in the matching graphs are computed dynamically based on analog information from the GKP error correction using the full history of all syndrome measurement rounds. We also show that a highly squeezed GKP state of GKP squeezing $\gtrsim 12$ dB can be experimentally realized by using a dissipative stabilization method, namely, the big-small-big method, with fairly conservative experimental parameters. Lastly, we introduce a three-level ancilla scheme to mitigate ancilla decay errors during a GKP state preparation.

When a resonant photon traverses a sample of absorbing atoms, how much time do atoms spend in the excited state? Does the answer depend on whether the photon is ultimately absorbed or transmitted? In particular, if it is not absorbed, does it cause atoms to spend any time in the excited state and if so, how much? To answer these questions, we perform an experiment with ultracold rubidium atoms in which we simultaneously record whether atoms are excited by incident (“signal”) photons and whether those photons are transmitted. We measure the time spent by atoms in the excited state by using a separate off-resonant “probe” laser to monitor the index of refraction of the sample—that is, we measure the nonlinear phase shift written by a signal pulse on this probe beam—and use direct detection to isolate the effect of single transmitted photons. For short pulses ($10$ ns, to be compared to the $26$-ns atomic lifetime) and an optically thick medium (peak optical depth equals 4, leading to 60% absorption given our broad bandwidth), we find that the average time atoms spend in the excited state due to one transmitted photon is not zero but, rather, $(77\pm 16)\mathrm{\%}$ of the time the average incident photon causes them to spend in the excited state. We attribute this observation of “excitation without loss” to coherent forward emission, which can arise when the instantaneous Rabi frequency (pulse envelope) picks up a ${180}^{\circ }$ phase flip—this happens naturally when a broadband pulse propagates through an optically thick medium with frequency-dependent absorption. These results unambiguously reveal for the first time the complex history of photons as they propagate through an absorbing medium and illustrate the power of utilizing postselection to experimentally investigate the past behavior of observed quantum systems.

The purpose of quantum technologies is to explore how quantum effects can improve on existing solutions for the treatment of information. Quantum photonics sensing holds great promise for reaching a more efficient trade-off between invasivity and quality of the measurement, when compared with the potential of classical means. This tutorial is dedicated to presenting how this advantage is brought about by nonclassical light, examining the basic principles of parameter estimation and reviewing the state of the art.

Parametrized quantum circuits serve as ansatze for solving variational problems and provide a flexible paradigm for the programming of near-term quantum computers. Ideally, such ansatze should be highly expressive, so that a close approximation of the desired solution can be accessed. On the other hand, the ansatz must also have sufficiently large gradients to allow for training. Here, we derive a fundamental relationship between these two essential properties: expressibility and trainability. This is done by extending the well-established barren plateau phenomenon, which holds for ansatze that form exact 2-designs, to arbitrary ansatze. Specifically, we calculate the variance in the cost gradient in terms of the expressibility of the ansatz, as measured by its distance from being a 2-design. Our resulting bounds indicate that highly expressive ansatze exhibit flatter cost landscapes and therefore will be harder to train. Furthermore, we provide numerics illustrating the effect of expressibility on gradient scalings and we discuss the implications for designing strategies to avoid barren plateaus.

Exploiting multiple modes in a quantum acoustic device could enable applications in quantum information in a hardware-efficient setup, including quantum simulation in a synthetic dimension and continuous-variable quantum computing with cluster states. We develop a multimode surface acoustic wave (SAW) resonator with a superconducting quantum interference device (SQUID) integrated in one of the Bragg reflectors. The interaction with the SQUID-shunted mirror gives rise to coupling between the more than 20 accessible resonator modes. We exploit this coupling to demonstrate two-mode squeezing of SAW phonons, as well as four-mode multipartite entanglement. Our results open avenues for continuous-variable quantum computing in a compact hybrid quantum system.

We propose a multimode modulation scheme for continuous-variable (CV) quantum communications, which we call quantum pattern encoding. In this setting, classical information can be encoded into multimode patterns of discretely modulated coherent states, which form instances of a communicable image space. Communicators can devise arbitrarily complex encoding schemes that are degenerate and highly nonuniform, such that communication is likened to the task of pattern recognition. We explore initial communication schemes that exploit these techniques and that lead to an increased encoding complexity. We discuss the impact that this has on the role of a near-term quantum eavesdropper; formulating new realistic classes of attacks and secure communication rates.

The color code is remarkable for its ability to perform fault-tolerant logic gates. This motivates the design of practical decoders that minimize the resource cost of color-code quantum computation. Here we propose a decoder for the planar color code with a triangular boundary where we match syndrome defects on a nontrivial manifold that has the topology of a Möbius strip. A basic implementation of our decoder used on the color code with hexagonal lattice geometry demonstrates a logical failure rate that is competitive with the optimal performance of the surface code. The logical failure rate scales approximately like $p^{\alpha \sqrt{n}}$, with $\alpha \approx 6/7\sqrt{3}\approx 0.5$, error rate $p$, and $n$ the code length. Furthermore, by exhaustively testing over five billion error configurations, we find that a modification of our decoder that manually compares inequivalent recovery operators can correct all errors of weight $\le (d-1)/2$ for codes with distance $d\le 13$. Our decoder is derived using relations among the stabilizers that preserve global conservation laws at the lattice boundary. We present generalizations of our method to depolarizing noise and fault-tolerant error correction, as well as to Majorana surface codes, higher-dimensional color codes, and single-shot error correction.

Quantum computers are promising for simulations of chemical and physical systems, but the limited capabilities of today’s quantum processors permit only small, and often approximate, simulations. Here we present a method, classical entanglement forging, that harnesses classical resources to capture quantum correlations and double the size of the system that can be simulated on quantum hardware. Shifting some of the computation to classical postprocessing allows us to represent ten spin orbitals of the water molecule on five qubits of an IBM Quantum processor in the most accurate variational simulation of the ${\mathrm{H}}_2\mathrm{O}$ ground-state energy using quantum hardware to date. We discuss conditions for applicability of classical entanglement forging and present a roadmap for scaling to larger problems.

Recent work has demonstrated the existence of universal Hamiltonians—simple spin-lattice models that can simulate any other quantum many-body system to any desired level of accuracy. Until now, proofs of universality have relied on explicit constructions, tailored to each specific family of universal Hamiltonians. In this work, we go beyond this approach and completely classify the simulation ability of quantum Hamiltonians by their complexity classes. We do this by deriving necessary and sufficient complexity-theoretic conditions characterizing universal quantum Hamiltonians. Although the result concerns the theory of analog Hamiltonian simulation—a promising application of near-term quantum technology—the proof relies on abstract complexity-theoretic concepts and the theory of quantum computation. As well as providing simplified proofs of previous Hamiltonian universality results and offering a route to new universal constructions, the results in this paper give insight into the origins of universality; for example, finally explaining the previously noted coincidences between families of universal Hamiltonian and classes of Hamiltonians appearing in complexity theory.