A major challenge in developing quantum computing technologies is to accomplish high precision tasks by utilizing multiplex optimization approaches, on both the physical system and algorithm levels. Loss functions assessing the overall performance of quantum circuits can provide the foundation for many optimization techniques. In this Letter, we use the quadratic error loss and the final-state fidelity loss to characterize quantum circuits. We find that the distribution of computation error is approximately Gaussian, which in turn justifies the quadratic error loss. It is shown that these loss functions can be efficiently evaluated in a scalable way by sampling from Clifford-dominated circuits. We demonstrate the results by numerically simulating 10-qubit noisy quantum circuits with various error models as well as executing 4-qubit circuits with up to ten layers of 2-qubit gates on a superconducting quantum processor. Our results pave the way toward the optimization-based quantum device and algorithm design in the intermediate-scale quantum regime.

Quantum annealing (QA) and the quantum approximate optimization algorithm (QAOA) are two special cases of the following control problem: apply a combination of two Hamiltonians to minimize the energy of a quantum state. Which is more effective has remained unclear. Here we analytically apply the framework of optimal control theory to show that generically, given a fixed amount of time, the optimal procedure has the pulsed (or “bang-bang”) structure of QAOA at the beginning and end but can have a smooth annealing structure in between. This is in contrast to previous works which have suggested that bang-bang (i.e., QAOA) protocols are ideal. To support this theoretical work, we carry out simulations of various transverse field Ising models, demonstrating that bang-anneal-bang protocols are more common. The general features identified here provide guideposts for the nascent experimental implementations of quantum optimization algorithms.

Weakly interacting Fermi gases simulate spin lattices in energy space, offering a rich platform for investigating information spreading and spin coherence in a large many-body quantum system. We show that the collective spin vector can be determined as a function of energy from the measured spin density, enabling general energy-space resolved protocols. We measure an out-of-time-order correlation function in this system and observe the energy dependence of the many-body coherence.

We have recently shown how a polarized beam in Talbot-Lau interferometric imaging can be used to analyze strong magnetic fields through the spin dependent differential phase effect at field gradients. While in that case an adiabatic spin coupling with the sample field is required, here we investigate a nonadiabatic coupling causing a spatial splitting of the neutron spin states with respect to the external magnetic field. This subsequently leads to no phase contrast signal but a loss of interferometer visibility referred to as dark-field contrast. We demonstrate how the implementation of spin analysis to the Talbot-Lau interferometer setup enables one to recover the differential phase induced to a single spin state. Thus, we show that the dark-field contrast is a measure of the quantum mechanical spin split analogous to the Stern-Gerlach experiment without, however, spatial beam separation. In addition, the spin analyzed dark-field contrast imaging introduced here bears the potential to probe polarization dependent small-angle scattering and thus magnetic microstructures.

Detector backaction can be completely evaded when the state of a one-electron quantum cyclotron is detected, but it nonetheless significantly broadens the quantum-jump resonance line shapes from which the cyclotron frequency can be deduced. This limits the accuracy with which the electron magnetic moment can be determined to test the standard model’s most precise prediction. A steady-state solution to a master equation, the first quantum calculation for the open quantum cyclotron system, illustrates a method to circumvent the detection backaction upon the measured frequency.

The Heisenberg scaling, which scales as $N^{-1}$ in terms of the number of particles or $T^{-1}$ in terms of the evolution time, serves as a fundamental limit in quantum metrology. Better scalings, dubbed as “super-Heisenberg scaling,” however, can also arise when the generator of the parameter involves many-body interactions or when it is time dependent. All these different scalings can actually be seen as manifestations of the Heisenberg uncertainty relations. While there is only one best scaling in the single-parameter quantum metrology, different scalings can coexist for the estimation of multiple parameters, which can be characterized by multiple Heisenberg uncertainty relations. We demonstrate the coexistence of two different scalings via the simultaneous estimation of the magnitude and frequency of a field where the best precisions, characterized by two Heisenberg uncertainty relations, scale as $T^{-1}$ and $T^{-2}$, respectively (in terms of the standard deviation). We show that the simultaneous saturation of two Heisenberg uncertainty relations can be achieved by the optimal protocol, which prepares the optimal probe state, implements the optimal control, and performs the optimal measurement. The optimal protocol is experimentally implemented on an optical platform that demonstrates the saturation of the two Heisenberg uncertainty relations simultaneously, with up to five controls. As the first demonstration of simultaneously achieving two different Heisenberg scalings, our study deepens the understanding on the connection between the precision limit and the uncertainty relations, which has wide implications in practical applications of multiparameter quantum estimation.

The accurate computation of ground and excited states of many-fermion quantum systems is one of the most consequential, contemporary challenges in the physical and computational sciences whose solution stands to benefit significantly from the advent of quantum computing devices. Existing methodologies using phase estimation or variational algorithms have potential drawbacks such as deep circuits requiring substantial error correction or nontrivial high-dimensional classical optimization. Here, we introduce a quantum solver of contracted eigenvalue equations, the quantum analog of classical methods for the energies and reduced density matrices of ground and excited states. The solver does not require deep circuits or difficult classical optimization and achieves an exponential speed-up over its classical counterpart. We demonstrate the algorithm though computations on both a quantum simulator and two IBM quantum processing units.

We develop a coherent beam splitter for single electrons driven through two tunnel-coupled quantum wires by surface acoustic waves (SAWs). The output current through each wire oscillates with gate voltages to tune the tunnel coupling and potential difference between the wires. This oscillation is assigned to coherent electron tunneling motion that can be used to encode a flying qubit and is well reproduced by numerical calculations of time evolution of the SAW-driven single electrons. The oscillation visibility is currently limited to about 3%, but robust against decoherence, indicating that the SAW electron can serve as a novel platform for a solid-state flying qubit.

The ability to efficiently simulate random quantum circuits using a classical computer is increasingly important for developing noisy intermediate-scale quantum devices. Here, we present a tensor network states based algorithm specifically designed to compute amplitudes for random quantum circuits with arbitrary geometry. Singular value decomposition based compression together with a two-sided circuit evolution algorithm are used to further compress the resulting tensor network. To further accelerate the simulation, we also propose a heuristic algorithm to compute the optimal tensor contraction path. We demonstrate that our algorithm is up to 2 orders of magnitudes faster than the Schrödinger-Feynman algorithm for verifying random quantum circuits on the 53-qubit Sycamore processor, with circuit depths below 12. We also simulate larger random quantum circuits with up to 104 qubits, showing that this algorithm is an ideal tool to verify relatively shallow quantum circuits on near-term quantum computers.

We study the decay mechanism of the gapped lowest-lying axial excitation of a quasipure atomic Bose-Einstein condensate confined in a cylindrical box trap. Owing to the absence of accessible lower-energy modes, or direct coupling to an external bath, this excitation is protected against one-body (linear) decay, and the damping mechanism is exclusively nonlinear. We develop a universal theoretical model that explains this fundamentally nonlinear damping as a process whereby two quanta of the gapped lowest excitation mode couple to a higher-energy mode, which subsequently decays into a continuum. We find quantitative agreement between our experiments and the predictions of this model. Finally, by strongly driving the system below its (lowest) resonant frequency, we observe third-harmonic generation, a hallmark of nonlinear behavior.

The exact critical Casimir amplitude is derived for anisotropic systems within the $d=2$ Ising universality class by combining conformal field theory with anisotropic ${\phi }^4$ theory. Explicit results are presented for the general anisotropic scalar ${\phi }^4$ model and for the fully anisotropic triangular-lattice Ising model in finite rectangular and infinite strip geometries with periodic boundary conditions. These results demonstrate the validity of multiparameter universality for confined anisotropic systems and the nonuniversality of the critical Casimir amplitude. We find an unexpected complex form of self-similarity of the anisotropy effects near the instability where weak anisotropy breaks down. This can be traced back to the property of modular invariance of isotropic conformal field theory for $d=2$. More generally, for $d>2$ we predict the existence of self-similar structures of the finite-size scaling functions of $O(n)$-symmetric systems with planar anisotropies and periodic boundary conditions both in the critical region for $n\ge 1$ as well as in the Goldstone-dominated low-temperature region for $n\ge 2$.

A phase reference has been a standard requirement in continuous-variable quantum sensing and communication protocols. However, maintaining a phase reference is challenging due to environmental fluctuations, preventing quantum phenomena such as entanglement and coherence from being utilized in many scenarios. We show that quantum communication and entanglement-assisted communication without a phase reference are possible, when a short-time memory effect is present. The degradation in the communication rate of classical or quantum information transmission decreases inversely with the correlation time. Exact solutions of the quantum capacity and entanglement-assisted classical and quantum capacity for pure dephasing channels are derived, where non-Gaussian multipartite-entangled states show strict advantages over usual Gaussian sources. For thermal-loss dephasing channels, lower bounds of the capacities are derived. The lower bounds also extend to scenarios with fading effects in the channel. In addition, for entanglement-assisted communication, the lower bounds can be achieved by a simple phase-encoding scheme on two-mode squeezed vacuum sources, when the noise is large.

The laws of quantum mechanics forbid the perfect copying of an unknown quantum state, known as the no-cloning theorem. In spite of this, approximate cloning with imperfect fidelity is possible, which opens up the field of quantum cloning. In general, quantum cloning can be divided into discrete variable and continuous variable (CV) categories. In the CV regime, all-optical implementation of the optimal $N\to M$ quantum cloning has been proposed in two original parallel works, which involves a parametric amplifier and a set of beam splitters and thus avoids the optic-electro and electro-optic conversions in the current CV quantum cloning technologies. However, such original proposal of all-optical CV optimal $N\to M$ quantum cloning scheme has never been experimentally implemented. Here, we show that optimal $N\to M$ quantum cloning of coherent states can be realized by utilizing a parametric amplifier based on four-wave mixing process in a hot atomic vapor and a set of beam splitters. In particular, we realize $1\to M$, $2\to M$, and $4\to M$ quantum cloning. We find that the fidelity of $N\to M$ quantum cloning increases with the decrease of clone number $M$ and the increase of original replica number $N$. The best cloning fidelity achieved in our experiment is about 93.3% $\pm 1.0\%$ in the $4\to 5$ case. Our results may find potential applications in realizing all-optical high-fidelity quantum state transfer and all-optical high-compatibility eavesdropping attack in quantum communication networks.

An energy gap develops near quantum critical point of quantum phase transition in a finite many-body (MB) system, facilitating the ground state transformation by adiabatic parameter change. In real application scenarios, however, the efficacy for such a protocol is compromised by the need to balance finite system lifetime with adiabaticity, as exemplified in a recent experiment that prepares three-mode balanced Dicke state near deterministically [Y.-Q. Zou et al., Proc. Natl. Acad. Sci. U.S.A. 115, 6381 (2018)]. Instead of tracking the instantaneous ground state as unanimously required for most adiabatic crossing, this work reports a faster sweeping policy taking advantage of excited level dynamics. It is obtained based on deep reinforcement learning (DRL) from a multistep training scheme we develop. In the absence of loss, a fidelity $\ge 99\%$ between prepared and the target Dicke state is achieved over a small fraction of the adiabatically required time. When loss is included, training is carried out according to an operational benchmark, the interferometric sensitivity of the prepared state instead of fidelity, leading to better sensitivity in about half of the previously reported time. Implemented in a Bose-Einstein condensate of $\sim {10}^4$ ${}^{87}\mathrm{Rb}$ atoms, the balanced three-mode Dicke state exhibiting an improved number squeezing of $13.02\pm 0.20\mathrm{dB}$ is observed within 766 ms, highlighting the potential of DRL for quantum dynamics control and quantum state preparation in interacting MB systems.

Gain-dissipative platforms consisting of lasers, optical parametric oscillators and nonequilibrium condensates operating at the condensation or coherence threshold have been recently proposed as efficient analog simulators of the two-local spin Hamiltonians with continuous or discrete degrees of freedom. We show that nonequilibrium condensates above the threshold arranged in an interacting network may realize $k$-local Hamiltonians with $k>2$ and lead to nontrivial phase configurations. Similarly, many gain-dissipative systems that can be manipulated by optical means can bring about the ground state of the $k$-local Hamiltonians and solve higher-order binary optimization problems. We show how to facilitate the search for the global solution by invoking complex couplings in the system and demonstrate the efficiency of the method on the sets of complex problems. This approach offers a highly flexible new kind of computation based on gain-dissipative simulators with complex coupling switching.

Randomness expansion where one generates a longer sequence of random numbers from a short one is viable in quantum mechanics but not allowed classically. Device-independent quantum randomness expansion provides a randomness resource of the highest security level. Here, we report the first experimental realization of device-independent quantum randomness expansion secure against quantum side information established through quantum probability estimation. We generate $5.47\times {10}^8$ quantum-proof random bits while consuming $4.39\times {10}^8\mathrm{bits}$ of entropy, expanding our store of randomness by $1.08\times {10}^8\mathrm{bits}$ at a latency of about 13.1 h, with a total soundness error $4.6\times {10}^{-10}$. Device-independent quantum randomness expansion not only enriches our understanding of randomness but also sets a solid base to bring quantum-certifiable random bits into realistic applications.

We simulate a zero-temperature pure $Z_3$ lattice gauge theory in $2+1$ dimensions by using an iPEPS (infinite projected entangled-pair state) Ansatz for the ground state. Our results are therefore directly valid in the thermodynamic limit. They clearly show two distinct phases separated by a phase transition. We introduce an update strategy that enables plaquette terms and Gauss-law constraints to be applied as sequences of two-body operators. This allows the use of the most up-to-date iPEPS algorithms. From the calculation of spatial Wilson loops we are able to prove the existence of a confined phase. We show that with relatively low computational cost it is possible to reproduce crucial features of gauge theories. We expect that the strategy allows the extension of iPEPS studies to more general LGTs.

One of the main topological invariants that characterizes several topologically ordered phases is the many-body Chern number (MBCN). Paradigmatic examples include several fractional quantum Hall phases, which are expected to be realized in different atomic and photonic quantum platforms in the near future. Experimental measurement and numerical computation of this invariant are conventionally based on the linear-response techniques that require having access to a family of states, as a function of an external parameter, which is not suitable for many quantum simulators. Here, we propose an ancilla-free experimental scheme for the measurement of this invariant, without requiring any knowledge of the Hamiltonian. Specifically, we use the statistical correlations of randomized measurements to infer the MBCN of a wave function. Remarkably, our results apply to disklike geometries that are more amenable to current quantum simulator architectures.