Time-crystalline eigenstate order on a quantum processor.

Quantum many-body systems display rich phase structure in their low-temperature equilibrium states1. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases2-8 that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC)7,9-15. Concretely, dynamical phases can be defined in periodically driven many-body-localized (MBL) systems via the concept of eigenstate order7,16,17. In eigenstate-ordered MBL phases, the entire many-body spectrum exhibits quantum correlations and long-range order, with characteristic signatures in late-time dynamics from all initial states. It is, however, challenging to experimentally distinguish such stable phases from transient phenomena, or from regimes in which the dynamics of a few select states can mask typical behaviour. Here we implement tunable controlled-phase (CPHASE) gates on an array of superconducting qubits to experimentally observe an MBL-DTC and demonstrate its characteristic spatiotemporal response for generic initial states7,9,10. Our work employs a time-reversal protocol to quantify the impact of external decoherence, and leverages quantum typicality to circumvent the exponential cost of densely sampling the eigenspectrum. Furthermore, we locate the phase transition out of the DTC with an experimental finite-size analysis. These results establish a scalable approach to studying non-equilibrium phases of matter on quantum processors.

Information scrambling in quantum circuits.

Interactions in quantum systems can spread initially localized quantum information into the exponentially many degrees of freedom of the entire system. Understanding this process, known as quantum scrambling, is key to resolving several open questions in physics. Here, by measuring the time-dependent evolution and fluctuation of out-of-time-order correlators, we experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We engineer quantum circuits that distinguish operator spreading and operator entanglement and experimentally observe their respective signatures. We show that whereas operator spreading is captured by an efficient classical model, operator entanglement in idealized circuits requires exponentially scaled computational resources to simulate. These results open the path to studying complex and practically relevant physical observables with near-term quantum processors.

Quantum supremacy using a programmable superconducting processor.

The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor1. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits2-7 to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 253 (about 1016). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times-our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy8-14 for this specific computational task, heralding a much-anticipated computing paradigm.

Fast accurate state measurement with superconducting qubits.

Faster and more accurate state measurement is required for progress in superconducting qubit experiments with greater numbers of qubits and advanced techniques such as feedback. We have designed a multiplexed measurement system with a bandpass filter that allows fast measurement without increasing environmental damping of the qubits. We use this to demonstrate simultaneous measurement of four qubits on a single superconducting integrated circuit, the fastest of which can be measured to 99.8% accuracy in 140 ns. This accuracy and speed is suitable for advanced multiqubit experiments including surface-code error correction.

Optomechanical superpositions via nested interferometry.

We present a scheme for achieving macroscopic quantum superpositions in optomechanical systems by using single photon postselection and detecting them with nested interferometers. This method relieves many of the challenges associated with previous optical schemes for measuring macroscopic superpositions and only requires the devices to be in the weak coupling regime. It requires only small improvements on currently achievable device parameters and allows the observation of decoherence on a time scale unconstrained by the system's optical decay time. Prospects for observing novel decoherence mechanisms are discussed.

Optomechanical trampoline resonators.

We report on the development of optomechanical "trampoline" resonators composed of a tiny SiO(2)/Ta(2)O(5) dielectric mirror on a silicon nitride micro-resonator. We observe optical finesses of up to 4 × 10(4) and mechanical quality factors as high as 9 × 10(5) in relatively massive (~100 ng) and low frequency (10-200 kHz) devices. This results in a photon-phonon coupling efficiency considerably higher than previous Fabry-Perot-type optomechanical systems. These devices are well suited to ultra-sensitive force detection, ground-state optical cooling experiments, and demonstrations of quantum dynamics for such systems.

Analysis of wrist motion following vascularized bone graft to the proximal scaphoid.

PURPOSE: To determine whether there is any motion loss associated with the 1,2 intracompartmental supraretinacular artery (ICSRA) bone graft to the dorsal scaphoid. The null hypothesis is that placement of a vascularized bone graft in the dorsal scaphoid does not lead to a significant change in range of motion. METHODS: Seven fresh-frozen cadaveric upper extremities were examined. Simulated 1,2 ICSRA bone grafts were harvested and placed into a dorsal trough made in the proximal scaphoid. Wrist motion measurements were performed before and after 1,2 ICSRA bone graft implantation. RESULTS: There were no significant changes in wrist motion following 1,2 ICSRA bone graft implantation. CONCLUSIONS: Properly placed 1,2 ICSRA vascularized bone grafts for treatment of proximal scaphoid nonunions do not by themselves cause loss of wrist motion. CLINICAL RELEVANCE: Loss of motion following the treatment of proximal scaphoid nonunions with properly placed 1,2 ICSRA vascularized bone grafts are due to factors other than the bone graft itself.

Entangled photon polarimetry.

We construct an entangled photon polarimeter capable of monitoring a two-qubit quantum state in real time. Using this polarimeter, we record a nine frames-per-second video of a two-photon state's transition from separability to entanglement.

Optical implementation of quantum orienteering.

We present results from an optical implementation of quantum orienteering, a protocol for communicating directions in space using quantum bits. We show how different types of measurements and encodings can be used to increase the communication efficiency. In particular, if Alice and Bob use two spin- particles for communication and employ joint measurements, they do better than is possible with local operations and classical communication. Furthermore, by using oppositely oriented spins, the achievable communication efficiency is further increased. Finally, we discuss the limitations of an optical approach: our results highlight the usually overlooked nonequivalence of different physical encodings of quantum bits.

Maximally entangled mixed states: creation and concentration.

Using correlated photons from parametric down-conversion, we extend the boundaries of experimentally accessible two-qubit Hilbert space. Specifically, we have created and characterized maximally entangled mixed states that lie above the Werner boundary in the linear entropy-tangle plane. In addition, we demonstrate that such states can be efficiently concentrated, simultaneously increasing both the purity and the degree of entanglement. We investigate a previously unsuspected sensitivity imbalance in common state measures, i.e., the tangle, linear entropy, and fidelity.