Chen-Fu Chiang

Quantum algorithm for approximating partition functions

We achieve a quantum speed-up of fully polynomial randomized approximation schemes (FPRAS) for estimating partition functions that combine simulated annealing with the Monte-Carlo Markov Chain method and use non-adaptive cooling schedules. The improvement in time complexity is twofold: a quadratic reduction with respect to the spectral gap of the underlying Markov chains and a quadratic reduction with respect to the parameter characterizing the desired accuracy of the estimate output by the FPRAS. Both reductions are intimately related and cannot be achieved separately. First, we use Grover’s fixed point search, quantum walks and phase estimation to efficiently prepare approximate coherent encodings of stationary distributions of the Markov chains. The speed-up we obtain in this way is due to the quadratic relation between the spectral and phase gaps of classical and quantum walks. Second, we generalize the method of quantum counting, showing how to estimate expected values of quantum observables. Using this method instead of classical sampling, we obtain the speed-up with respect to accuracy.

Characterizing the Performance Effect of Trials and Rotations in Applications that use Quantum Phase Estimation

Quantum Phase Estimation (QPE) is one of the key techniques used in quantum computation to design quantum algorithms which can be exponentially faster than classical algorithms. Intuitively, QPE allows quantum algorithms to find the hidden structure in certain kinds of problems. In particular, Shors well-known algorithm for factoring the product of two primes uses QPE. Simulation algorithms, such as Ground State Estimation (GSE) for quantum chemistry, also use QPE. Unfortunately, QPE can be computationally expensive, either requiring many trials of the computation (repetitions) or many small rotation operations on quantum bits. Selecting an efficient QPE approach requires detailed characterizations of the tradeoffs and overheads of these options. In this paper, we explore three different algorithms that trade off trials versus rotations. We perform a detailed characterization of their behavior on two important quantum algorithms (Shors and GSE). We also develop an analytical model that characterizes the behavior of a range of algorithms in this tradeoff space.

Hitting time of quantum walks with perturbation

The hitting time is the required minimum time for a Markov chain-based walk (classical or quantum) to reach a target state in the state space. We investigate the effect of the perturbation on the hitting time of a quantum walk. We obtain an upper bound for the perturbed quantum walk hitting time by applying Szegedy’s work and the perturbation bounds with Weyl’s perturbation theorem on classical matrix. Based on the definition of quantum hitting time given in MNRS algorithm, we further compute the delayed perturbed hitting time and delayed perturbed quantum hitting time (DPQHT). We show that the upper bound for DPQHT is bounded from above by the difference between the square root of the upper bound for a perturbed random walk and the square root of the lower bound for a random walk.

Selecting efficient phase estimation with constant-precision phase shift operators

We investigate the cost of three phase estimation procedures that require only constant-precision phase shift operators. The cost is in terms of the number of elementary gates, not just the number of measurements. Faster phase estimation requires the minimal number of measurements with a logarithmic factor of reduction when the required precision

Parameterized Pulsed Transaction Injection Computation Model And Performance Optimizer For IOTA-Tango

n

QUANTUM PHASE ESTIMATION WITH AN ARBITRARY NUMBER OF QUBITS

n is large. The arbitrary constant-precision approach (ACPA) requires the minimal number of elementary gates with a minimal factor of 14 of reduction in comparison with Kitaev’s approach. The reduction factor increases as the precision gets higher in ACPA. Kitaev’s approach is with a reduction factor of 14 in comparison with the faster phase estimation in terms of elementary gate counts.

Scaffold: Quantum Programming Language

Distributed ledger technologies have a central problem that involves the latency. When transactions are to be accepted in the ledger, latency is incurred due to transaction processing and verification. For efficient systems, high latency should be avoided for the governance of the ledger. To help reduce latency, we offer a distributed ledger architecture, Tango, that mimics the Iota-tangle design as articulated by Popov [1] in his seminal paper. We introduce a semi-synchronous transaction entry protocol layer to avoid asynchronism in the system since an asynchronous system has a high latency. We further model periodic pulsed injections into the evaluation layer from the entry layer to regulate the performance of the system.

Efficient circuits for quantum walks

To keep a cryptocurrency system at its optimal performance, it is necessary to utilize the resources and avoid latency in its network. To achieve this goal, dynamically and efficiently injecting the unverified transactions to enable synchronicity based on the current system configuration and the traffic of the network is crucial. To meet this need, we design the pulsed transaction injection parameterization (PTIP) protocol to provide a preliminary dynamic injection mechanism. To further assist the network to achieve its subgoals based on various house policies (such as maximal revenue to the network or maximum throughput of the system), we turn the house policy based optimization into a 0/1 knapsack problem. To efficiently solve these NP-hard problems, we adapt and improve a fully polynomial time approximation scheme (FPTAS) and dynamic programming as components in our approximate optimization algorithm.