Impossibility of Classically Simulating One-Clean-Qubit Model with Multiplicative Error.

The one-clean-qubit model (or the deterministic quantum computation with one quantum bit model) is a restricted model of quantum computing where all but a single input qubits are maximally mixed. It is known that the probability distribution of measurement results on three output qubits of the one-clean-qubit model cannot be classically efficiently sampled within a constant multiplicative error unless the polynomial-time hierarchy collapses to the third level [T. Morimae, K. Fujii, and J. F. Fitzsimons, Phys. Rev. Lett. 112, 130502 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.130502]. It was open whether we can keep the no-go result while reducing the number of output qubits from three to one. Here, we solve the open problem affirmatively. We also show that the third-level collapse of the polynomial-time hierarchy can be strengthened to the second-level one. The strengthening of the collapse level from the third to the second also holds for other subuniversal models such as the instantaneous quantum polynomial model [M. Bremner, R. Jozsa, and D. J. Shepherd, Proc. R. Soc. A 467, 459 (2011)PRLAAZ1364-502110.1098/rspa.2010.0301] and the boson sampling model [S. Aaronson and A. Arkhipov, STOC 2011, p. 333]. We additionally study the classical simulatability of the one-clean-qubit model with further restrictions on the circuit depth or the gate types.

A coherent Ising machine for 2000-node optimization problems.

The analysis and optimization of complex systems can be reduced to mathematical problems collectively known as combinatorial optimization. Many such problems can be mapped onto ground-state search problems of the Ising model, and various artificial spin systems are now emerging as promising approaches. However, physical Ising machines have suffered from limited numbers of spin-spin couplings because of implementations based on localized spins, resulting in severe scalability problems. We report a 2000-spin network with all-to-all spin-spin couplings. Using a measurement and feedback scheme, we coupled time-multiplexed degenerate optical parametric oscillators to implement maximum cut problems on arbitrary graph topologies with up to 2000 nodes. Our coherent Ising machine outperformed simulated annealing in terms of accuracy and computation time for a 2000-node complete graph.

A fully programmable 100-spin coherent Ising machine with all-to-all connections.

Unconventional, special-purpose machines may aid in accelerating the solution of some of the hardest problems in computing, such as large-scale combinatorial optimizations, by exploiting different operating mechanisms than those of standard digital computers. We present a scalable optical processor with electronic feedback that can be realized at large scale with room-temperature technology. Our prototype machine is able to find exact solutions of, or sample good approximate solutions to, a variety of hard instances of Ising problems with up to 100 spins and 10,000 spin-spin connections.

A 16-bit Coherent Ising Machine for One-Dimensional Ring and Cubic Graph Problems.

Many tasks in our modern life, such as planning an efficient travel, image processing and optimizing integrated circuit design, are modeled as complex combinatorial optimization problems with binary variables. Such problems can be mapped to finding a ground state of the Ising Hamiltonian, thus various physical systems have been studied to emulate and solve this Ising problem. Recently, networks of mutually injected optical oscillators, called coherent Ising machines, have been developed as promising solvers for the problem, benefiting from programmability, scalability and room temperature operation. Here, we report a 16-bit coherent Ising machine based on a network of time-division-multiplexed femtosecond degenerate optical parametric oscillators. The system experimentally gives more than 99.6% of success rates for one-dimensional Ising ring and nondeterministic polynomial-time (NP) hard instances. The experimental and numerical results indicate that gradual pumping of the network combined with multiple spectral and temporal modes of the femtosecond pulses can improve the computational performance of the Ising machine, offering a new path for tackling larger and more complex instances.

Dysregulation of a potassium channel, THIK-1, targeted by caspase-8 accelerates cell shrinkage.

Activation of caspases is crucial for the execution of apoptosis. Although the caspase cascade associated with activation of the initiator caspase-8 (CASP8) has been investigated in molecular and biochemical detail, the physiological role of CASP8 is not fully understood. Here, we identified a two-pore domain potassium channel, tandem-pore domain halothane-inhibited K+ channel 1 (THIK-1), as a novel CASP8 substrate. The intracellular region of THIK-1 was cleaved by CASP8 in apoptotic cells. Overexpression of THIK-1, but not its mutant lacking the CASP8-target sequence in the intracellular portion, accelerated cell shrinkage in response to apoptotic stimuli. In contrast, knockdown of endogenous THIK-1 by RNA interference resulted in delayed shrinkage and potassium efflux. Furthermore, a truncated THIK-1 mutant lacking the intracellular region, which mimics the form cleaved by CASP8, led to a decrease of cell volume of cultured cells without apoptotic stimulation and excessively promoted irregular development of Xenopus embryos. Taken together, these results indicate that THIK-1 is involved in the acceleration of cell shrinkage. Thus, we have demonstrated a novel physiological role of CASP8: creating a cascade that advances the cell to the next stage in the apoptotic process.

Computational quantum-classical boundary of noisy commuting quantum circuits.

It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projected-entangled-pair-state picture and the Gottesman-Knill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a single-qubit complete-positive-trace-preserving noise, the computational quantum-classical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantum-classical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region.