scholarly journals Energy-participation quantization of Josephson circuits

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Zlatko K. Minev ◽  
Zaki Leghtas ◽  
Shantanu O. Mundhada ◽  
Lysander Christakis ◽  
Ioan M. Pop ◽  
...  
Keyword(s):  
Circuit Complexity ◽  
Quantum Circuits ◽  
Nonlinear Interactions ◽  
Electromagnetic Mode ◽  
System Quantum ◽  
Josephson Circuits ◽  
Nonlinear Devices ◽  
Hamiltonian Parameters ◽  
Mode Energy ◽  
Multi Mode

AbstractSuperconducting microwave circuits incorporating nonlinear devices, such as Josephson junctions, are a leading platform for emerging quantum technologies. Increasing circuit complexity further requires efficient methods for the calculation and optimization of the spectrum, nonlinear interactions, and dissipation in multi-mode distributed quantum circuits. Here we present a method based on the energy-participation ratio (EPR) of a dissipative or nonlinear element in an electromagnetic mode. The EPR, a number between zero and one, quantifies how much of the mode energy is stored in each element. The EPRs obey universal constraints and are calculated from one electromagnetic-eigenmode simulation. They lead directly to the system quantum Hamiltonian and dissipative parameters. The method provides an intuitive and simple-to-use tool to quantize multi-junction circuits. We experimentally tested this method on a variety of Josephson circuits and demonstrated agreement within several percents for nonlinear couplings and modal Hamiltonian parameters, spanning five orders of magnitude in energy, across a dozen samples.

scholarly journals QUANTUM ORACLES IN TERMS OF UNIVERSAL GATE SET

2011 ◽  
Vol 09 (06) ◽  
pp. 1363-1381 ◽  
Author(s):  
YUJI TANAKA ◽  
TSUBASA ICHIKAWA ◽  
MASAHITO TADA-UMEZAKI ◽  
YUKIHIRO OTA ◽  
MIKIO NAKAHARA
Keyword(s):  
Arbitrary Number ◽  
Search Algorithm ◽  
Circuit Complexity ◽  
Database Search ◽  
Quantum Circuits ◽  
Systematic Construction ◽  
Universal Gate

We present a systematic construction of quantum circuits implementing Grover's database search algorithm for arbitrary number of targets. We introduce a new operator which flips the sign of the targets and evaluate its circuit complexity. We find the condition under which the circuit complexity of the database search algorithm based on this operator is less than that of the conventional one.

scholarly journals Revisiting the simulation of quantum Turing machines by quantum circuits

2019 ◽  
Vol 475 (2226) ◽  
pp. 20180767 ◽  
Author(s):  
Abel Molina ◽  
John Watrous
Keyword(s):  
Turing Machine ◽  
Polynomial Time ◽  
Computational Models ◽  
Circuit Complexity ◽  
Simulation Method ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Turing Machines ◽  
Generated Family ◽  
Quantum Turing Machine

Yao's 1995 publication ‘Quantum circuit complexity’ in Proceedings of the 34th Annual IEEE Symposium on Foundations of Computer Science , pp. 352–361, proved that quantum Turing machines and quantum circuits are polynomially equivalent computational models: t ≥ n steps of a quantum Turing machine running on an input of length n can be simulated by a uniformly generated family of quantum circuits with size quadratic in t , and a polynomial-time uniformly generated family of quantum circuits can be simulated by a quantum Turing machine running in polynomial time. We revisit the simulation of quantum Turing machines with uniformly generated quantum circuits, which is the more challenging of the two simulation tasks, and present a variation on the simulation method employed by Yao together with an analysis of it. This analysis reveals that the simulation of quantum Turing machines can be performed by quantum circuits having depth linear in t , rather than quadratic depth, and can be extended to variants of quantum Turing machines, such as ones having multi-dimensional tapes. Our analysis is based on an extension of method described by Arright, Nesme and Werner in 2011 in Journal of Computer and System Sciences 77 , 372–378. ( doi:10.1016/j.jcss.2010.05.004 ), that allows for the localization of causal unitary evolutions.

scholarly journals Circuit optimization of Hamiltonian simulation by simultaneous diagonalization of Pauli clusters

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 322
Author(s):  
Ewout van den Berg ◽  
Kristan Temme
Keyword(s):  
Quantum Chemistry ◽  
Time Evolution ◽  
Circuit Complexity ◽  
Practical Interest ◽  
Quantum Circuits ◽  
Circuit Optimization ◽  
Simultaneous Diagonalization ◽  
Hamiltonian Simulation ◽  
Practical Algorithm ◽  
Circuit Depth

Many applications of practical interest rely on time evolution of Hamiltonians that are given by a sum of Pauli operators. Quantum circuits for exact time evolution of single Pauli operators are well known, and can be extended trivially to sums of commuting Paulis by concatenating the circuits of individual terms. In this paper we reduce the circuit complexity of Hamiltonian simulation by partitioning the Pauli operators into mutually commuting clusters and exponentiating the elements within each cluster after applying simultaneous diagonalization. We provide a practical algorithm for partitioning sets of Paulis into commuting subsets, and show that the proposed approach can help to significantly reduce both the number of CNOT operations and circuit depth for Hamiltonians arising in quantum chemistry. The algorithms for simultaneous diagonalization are also applicable in the context of stabilizer states; in particular we provide novel four- and five-stage representations, each containing only a single stage of conditional gates.

scholarly journals Complexity from the reduced density matrix: a new diagnostic for chaos

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Arpan Bhattacharyya ◽  
S. Shajidul Haque ◽  
Eugene H. Kim
Keyword(s):  
Density Matrix ◽  
Quantum Chaos ◽  
Open Quantum Systems ◽  
Circuit Complexity ◽  
Quantum Systems ◽  
Harmonic Oscillators ◽  
Quantum Circuits ◽  
Reduced Density Matrix ◽  
Evolution Of Complexity ◽  
Reduced Density

Abstract We investigate circuit complexity to characterize chaos in multiparticle quantum systems. In the process, we take a stride to analyze open quantum systems by using complexity. We propose a new diagnostic of quantum chaos from complexity based on the reduced density matrix by exploring different types of quantum circuits. Through explicit calculations on a toy model of two coupled harmonic oscillators, where one or both of the oscillators are inverted, we demonstrate that the evolution of complexity is a possible diagnostic of chaos.

A novel underwater AUV charging platform and its multi-mode energy coordinated control strategy

2021 ◽  
Author(s):  
Zhijie Zhang ◽  
Yuming Liu ◽  
Kefan Liu ◽  
Zongju Cai ◽  
Chuanxin Ye ◽  
...  
Keyword(s):  
Control Strategy ◽  
Coordinated Control ◽  
Mode Energy ◽  
Multi Mode
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