Simulating Large Quantum Circuits on a Small Quantum Computer.

Limited quantum memory is one of the most important constraints for near-term quantum devices. Understanding whether a small quantum computer can simulate a larger quantum system, or execute an algorithm requiring more qubits than available, is both of theoretical and practical importance. In this Letter, we introduce cluster parameters K and d of a quantum circuit. The tensor network of such a circuit can be decomposed into clusters of size at most d with at most K qubits of inter-cluster quantum communication. We propose a cluster simulation scheme that can simulate any (K,d)-clustered quantum circuit on a d-qubit machine in time roughly 2^{O(K)}, with further speedups possible when taking more fine-grained circuit structure into account. We show how our scheme can be used to simulate clustered quantum systems-such as large molecules-that can be partitioned into multiple significantly smaller clusters with weak interactions among them. By using a suitable clustered ansatz, we also experimentally demonstrate that a quantum variational eigensolver can still achieve the desired performance for estimating the energy of the BeH_{2} molecule while running on a physical quantum device with half the number of required qubits.

Bound entangled states with a private key and their classical counterpart.

Entanglement is a fundamental resource for quantum information processing. In its pure form, it allows quantum teleportation and sharing classical secrets. Realistic quantum states are noisy and their usefulness is only partially understood. Bound-entangled states are central to this question--they have no distillable entanglement, yet sometimes still have a private classical key. We present a construction of bound-entangled states with a private key based on classical probability distributions. From this emerge states possessing a new classical analogue of bound entanglement, distinct from the long-sought bound information. We also find states of smaller dimensions and higher key rates than previously known. Our construction has implications for classical cryptography: we show that existing protocols are insufficient for extracting private key from our distributions due to their "bound-entangled" nature. We propose a simple extension of existing protocols that can extract a key from them.

Bilateral photoplethysmography studies of the leg arterial stenosis.

A newly developed portable multi-channel photoplethysmography (PPG) device has been used for comparative studies of 20 healthy control subjects and 45 patients with diagnosed arterial stenosis in a leg. The peripheral blood pulsations were detected simultaneously at four body sites-the same fingers and toes of both arms and legs. The PPG pulses recorded at the periphery of the stenotic leg, if compared with those of the healthy leg, were much weaker, with delayed arrival as a consequence of increased pulse wave transit time (PWTT) due to higher vascular resistance. The specific PWTT delays for the occluded legs were in the range of 20-80 ms, while in the case of healthy subjects the leg PPG signals arrived without delays or with smaller time-shifts not exceeding 14 ms. The reference bilateral PPG signals detected at the fingertips did not show any notable PWTT delays in both groups. Parallel measurements of local blood pressures by means of the oscillometry method with subsequent calculation of the ankle-brachial index were performed. Convincing correlation between the bilateral differences in the local blood pressure (a routine tool for diagnostics of leg stenosis) and in the corresponding PWTT delay (Pearson's coefficient r = 0.93), as well as between the PWTT delay and the ankle-brachial index (r = -0.96) has been established. From the point of view of PWTT delay, the average value of leg stenosis diagnostic threshold was established to be in the range of 23 +/- 9 ms, with full reliability above 32 ms. The obtained data may find further applications in alternative methodologies for detection and/or assessment of arterial occlusions in human extremities.

Unbounded number of channel uses may be required to detect quantum capacity.

Transmitting data reliably over noisy communication channels is one of the most important applications of information theory, and is well understood for channels modelled by classical physics. However, when quantum effects are involved, we do not know how to compute channel capacities. This is because the formula for the quantum capacity involves maximizing the coherent information over an unbounded number of channel uses. In fact, entanglement across channel uses can even increase the coherent information from zero to non-zero. Here we study the number of channel uses necessary to detect positive coherent information. In all previous known examples, two channel uses already sufficed. It might be that only a finite number of channel uses is always sufficient. We show that this is not the case: for any number of uses, there are channels for which the coherent information is zero, but which nonetheless have capacity.