The complexity of NISQ

The recent proliferation of NISQ devices has made it imperative to understand their power. In this work, we define and study the complexity class NISQ, which encapsulates problems that can be efficiently solved by a classical computer with access to noisy quantum circuits. We establish super-polynomial separations in the complexity among classical computation, NISQ, and fault-tolerant quantum computation to solve some problems based on modifications of Simon's problems. We then consider the power of NISQ for three well-studied problems. For unstructured search, we prove that NISQ cannot achieve a Grover-like quadratic speedup over classical computers. For the Bernstein-Vazirani problem, we show that NISQ only needs a number of queries logarithmic in what is required for classical computers. Finally, for a quantum state learning problem, we prove that NISQ is exponentially weaker than classical computers with access to noiseless constant-depth quantum circuits.

Quantum advantage in learning from experiments

Quantum technology promises to revolutionize how we learn about the physical world. An experiment that processes quantum data with a quantum computer could have substantial advantages over conventional experiments in which quantum states are measured and outcomes are processed with a classical computer. We proved that quantum machines could learn from exponentially fewer experiments than the number required by conventional experiments. This exponential advantage is shown for predicting properties of physical systems, performing quantum principal component analysis, and learning about physical dynamics. Furthermore, the quantum resources needed for achieving an exponential advantage are quite modest in some cases. Conducting experiments with 40 superconducting qubits and 1300 quantum gates, we demonstrated that a substantial quantum advantage is possible with today's quantum processors.

Quantum algorithmic measurement

There has been recent promising experimental and theoretical evidence that quantum computational tools might enhance the precision and efficiency of physical experiments. However, a systematic treatment and comprehensive framework are missing. Here we initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms and interactive protocols. We use the QUALM framework to study two important experimental problems in quantum many-body physics: determining whether a system’s Hamiltonian is time-independent or time-dependent, and determining the symmetry class of the dynamics of the system. We study abstractions of these problems and show for both cases that if the experimentalist can use her experimental samples coherently (in both space and time), a provable exponential speedup is achieved compared to the standard situation in which each experimental sample is accessed separately. Our work suggests that quantum computers can provide a new type of exponential advantage: exponential savings in resources in quantum experiments.

Applying the language of computational complexity to study real-world experiments requires a rigorous framework. Here, the authors provide such a framework and establish that there can be an exponential savings in resources if an experimentalist can entangle apparatuses with experimental samples.

Improved Spatial Resolution Achieved by Chromatic Intensity Interferometry

Interferometers are widely used in imaging technologies to achieve enhanced spatial resolution, but require that the incoming photons be indistinguishable. In previous work, we built and analyzed color erasure detectors, which expand the scope of intensity interferometry to accommodate sources of different colors. Here we demonstrate experimentally how color erasure detectors can achieve improved spatial resolution in an imaging task, well beyond the diffraction limit. Utilizing two 10.9-mm-aperture telescopes and a 0.8 m baseline, we measure the distance between a 1063.6 and a 1064.4 nm source separated by 4.2 mm at a distance of 1.43 km, which surpasses the diffraction limit of a single telescope by about 40 times. Moreover, chromatic intensity interferometry allows us to recover the phase of the Fourier transform of the imaged objects-a quantity that is, in the presence of modest noise, inaccessible to conventional intensity interferometry.

Chromatic interferometry with small frequency differences

By developing a 'two-crystal' method for color erasure, we can broaden the scope of chromatic interferometry to include optical photons whose frequency difference falls outside of the 400 nm to 4500 nm wavelength range, which is the passband of a PPLN crystal. We demonstrate this possibility experimentally, by observing interference patterns between sources at 1064.4 nm and 1063.6 nm, corresponding to a frequency difference of about 200 GHz.

Quantum Overlapping Tomography

It is now experimentally possible to entangle thousands of qubits, and efficiently measure each qubit in parallel in a distinct basis. To fully characterize an unknown entangled state of n qubits, one requires an exponential number of measurements in n, which is experimentally unfeasible even for modest system sizes. By leveraging (i) that single-qubit measurements can be made in parallel, and (ii) the theory of perfect hash families, we show that all k-qubit reduced density matrices of an n qubit state can be determined with at most e^{O(k)}log^{2}(n) rounds of parallel measurements. We provide concrete measurement protocols which realize this bound. As an example, we argue that with near-term experiments, every two-point correlator in a system of 1024 qubits could be measured and completely characterized in a few days. This corresponds to determining nearly 4.5 million correlators.

Color Erasure Detectors Enable Chromatic Interferometry

By engineering and manipulating quantum entanglement between incoming photons and experimental apparatus, we construct single-photon detectors which cannot distinguish between photons of very different wavelengths. These color-erasure detectors enable a new kind of intensity interferometry, with potential applications in microscopy and astronomy. We demonstrate chromatic interferometry experimentally, observing robust interference using both coherent and incoherent photon sources.

Mycotic Aneurysm and Aortic Graft Infection Presenting with Vertebral Body Destruction Requiring Debridement and Stabilization

Vertebral osteomyelitis may occur with mycotic aneurysms or infected aortic grafts. A high index of suspicion for these concurrent processes as well as appropriate preoperative evaluation and interspecialty communication is critical for appropriate diagnosis and treatment. Extraanatomic bypass, wide debridement of necrotic soft tissue and bony structures, and concurrent bony stabilization are important aspects of treatment.

The changing nature of admissions to a spinal cord injury center: violence on the rise

The purpose of this study was to analyze changing etiologies for admission to a spinal cord injury center. This study was designed to retrospectively analyze the etiology of admissions to a spinal cord injury center during a 15-year period, specifically gunshot versus nongunshot wound injuries. Gunshot wounds are a well-recognized cause of spinal cord injury. In some centers, up to 52% of admissions are due to this, and these trends are believed to be increasing. All patients with spinal cord injury admitted to our center between 1979 and 1993 were analyzed. Frequencies of specific etiologies were determined and then comparisons were made between gunshot wound and nongunshot wound groups. Factors analyzed included age, male/female ratio, ethnic make-up, marital status, employment status, level of injury, and neurologic status. One thousand eight hundred seventeen patients were included. Overall, gunshot wound spinal cord injuries compromised 16.9% of injuries. A clear trend of increasing numbers of admissions was seen between 1984 and 1993 because of this. Gunshot wounds and nongunshot wounds differed dramatically in terms of age, ethnic make-up, marital status, employment status, and neurologic status. Cost attributed to treating gunshot wound injuries at our center for 1993 was 5.4 million dollars. Gunshot wounds as a cause of spinal cord injury are increasing at an alarming rate. The demographics of the gunshot wounds and nongunshot wound spine cord injuries differ significantly.

A new method of management using the Kim-Ray Greenfield filter for deep venous thrombosis and pulmonary embolism in spinal cord injury

In this study, it is documented that the proper location of the Kim-Ray Greenfield filter offers excellent protection against PE in patients with SCI and DVT. The device has been associated with thrombosis of the IVC in two of 21 patients, and the thrombosis was well tolerated. The incidence of complications has been quite low. We believe that this is a most acceptable method of managing patients with SCI and DVT or PE when heparin is either inadequate or contraindicated.

Double contrast knee arthrography in the evaluation of osteochondritis dissecans

Double contrast knee arthrography is an invaluable adjunct in the evaluation of patients with osteochondritis dissecans. The cartilage overlying the osteochondritic defect can be evaluated and unsuspected meniscal pathology accurately diagnosed. In our series, there were three unsuspected medial meniscal tears, diagnosed by arthrography and confirmed at surgery. The location of the osteochondritic defect was atypical in all four of our female patients.