Circuit Decomposition Research Articles

Classification and transformations of quantum circuit decompositions for permutation operations

Classification and transformations of quantum circuit decompositions for permutation operations

Low depth virtual distillation of quantum circuits by deterministic circuit decomposition

Virtual distillation using measurements of multiple copies of a quantum circuit have recently been proposed as a method of noise mitigation of expectation values. Circuit decompositions known as B gates were found only for 1-local Hamiltonians, however practical problems for chemistry require n-local Hamiltonians, which cannot be corrected with B gates. We discover low depth circuit decompositions for expectation values for n-local Pauli strings by combining multiple projections to recover the correct measurement statistics or expectation values. Our method adds linear entangling gates with the number of qubits, but it requires extra measurements. Furthermore, in applications to find ground states such as the variational quantum eigensolver (VQE) algorithm, the variational principle is required which states that the energy cannot go below the ground-state energy. We find that the variational principle is violated when using B gates and is preserved if we use our low depth decomposition on all expectation values. We perform a demonstration on real devices, and we show that our decomposition can mitigate real experimental noise in VQE for the H2 molecule with a two-qubit tapered mapping, H3 with three qubits, and H2 with four qubits. Our decomposition provides a way to perform duplicate circuit virtual distillation on real devices at significantly lower depth and for arbitrary observables. Published by the American Physical Society 2024

A Power Optimization Approach for Large-scale RM-TB Dual Logic Circuits Based on an Adaptive Multi-Task Intelligent Algorithm

Logic synthesis is a crucial step in integrated circuit design, and power optimization is an indispensable part of this process. However, power optimization for large-scale Mixed Polarity Reed-Muller (MPRM) logic circuits is an NP-hard problem. In this article, we divide Boolean circuits into small-scale circuits based on the idea of divide and conquer using the proposed Dynamic Adaptive Grouping Strategy (DAGS) and the proposed circuit decomposition model (CDM). Each small-scale Boolean circuit is transformed into an MPRM logic circuit by a polarity transformation algorithm. Based on the gate-level integration, we integrate small-scale circuits into an MPRM and Boolean Dual Logic (RBDL) circuit. Furthermore, the power optimization problem of RBDL circuits is a multi-task, multi-extremal, high-dimensional combinatorial optimization problem, for which we propose an Adaptive Multi-task Intelligent Algorithm (AMIA), which includes global task optimization, population reproduction, valuable knowledge transfer (VKT), and local exploration to search for the lowest power for RBDL circuits. Moreover, based on the proposed Fast Power Decomposition Algorithm (FPDA), we proposed a Power Optimization Approach (POA) for an RBDL circuit with the lowest power using the AMIA. Experimental results based on Microelectronics Center of North Carolina (MCNC) Benchmark test circuits demonstrate the effectiveness and superiority of the POA compared to state-of-the-art POAes.

Circuit Decompositions of Binary Matroids

Circuit Decompositions of Binary Matroids

An Efficiency Improvement Strategy for Triple-Active-Bridge-Based DC Energy Routers in DC Microgrids

A triple-active bridge (TAB) can be used as a power conversion unit in a three-port DC energy router (DCER) such as a triple-active bridge-based DC energy router (TAB-DCER). The operational loss of a TAB can be seen as a key factor affecting the efficiency of a TAB-DCER. However, the RMS value of the inductor current of the TAB-DCER increases under single-phase shift (SPS) control, and this greatly increases the system operating losses. The use of phase-shifted plus PWM (PS-PWM) control can reduce the RMS value of the inductor current, but its mathematical model is complex, and involves difficult calculations. To address this problem, in the study reported here, we developed an optimal control strategy for the RMS value of the inductor current based on TAB-DCER. First, the working principle of a TAB-DCER under PS-PWM control was analyzed, and a circuit decomposition model was established. Second, the operating modes under PS-PWM control were analyzed, and corresponding expressions of port power and the RMS value of the inductor current were obtained. Third, an optimized mathematical model of the sum of squares of the RMS value of the inductor current of the TAB-DCER was constructed. Finally, a genetic algorithm was used to solve the mathematical model and derive the optimal phase shift angle; this resulted in a lower RMS value of the inductor current in the TAB-DCER and reduced the system operating losses. The simulation and experimental results show that the TAB-DCER used in the present study can reduce operating losses, improve system efficiency, and deliver coordinated power control.

Circuit Decomposition of Multicontrolled Special Unitary Single-Qubit Gates

Circuit Decomposition of Multicontrolled Special Unitary Single-Qubit Gates

A better SPQR‐tree decomposition of electrical circuits containing multiports and its application to wave digital emulation

SummaryWe report on a systematic method for the port‐wise decomposition of electrical networks. Our method exploits the SPQR‐tree decomposition as an algorithmic way for decomposing a given circuit into a maximal set of one‐port and multiports. We provide a solution for representing multiports by suitable replacement graphs, such that they are encapsulated not decomposed or processed by the SPQR‐algorithm. Contrary to current methods, our replacement graphs are not sophisticated but rather simple, which, in general, enhances the performance of the algorithm, when it comes to decomposing large electrical networks containing multiports. Some electrical devices, such as transistors or op‐amps, are commonly described in terms of their terminals rather than their ports. Thus, we cover the application of the template‐based approach to three‐terminal devices. Lastly, we make use of the new decomposition method for the emulation of a wave digital filter.

Fermionic quantum processing with programmable neutral atom arrays

Simulating the properties of many-body fermionic systems is an outstanding computational challenge relevant to material science, quantum chemistry, and particle physics.-5.4pc]Please note that the spelling of the following author names in the manuscript differs from the spelling provided in the article metadata: D. González-Cuadra, D. Bluvstein, M. Kalinowski, R. Kaubruegger, N. Maskara, P. Naldesi, T. V. Zache, A. M. Kaufman, M. D. Lukin, H. Pichler, B. Vermersch, Jun Ye, and P. Zoller. The spelling provided in the manuscript has been retained; please confirm. Although qubit-based quantum computers can potentially tackle this problem more efficiently than classical devices, encoding nonlocal fermionic statistics introduces an overhead in the required resources, limiting their applicability on near-term architectures. In this work, we present a fermionic quantum processor, where fermionic models are locally encoded in a fermionic register and simulated in a hardware-efficient manner using fermionic gates. We consider in particular fermionic atoms in programmable tweezer arrays and develop different protocols to implement nonlocal gates, guaranteeing Fermi statistics at the hardware level. We use this gate set, together with Rydberg-mediated interaction gates, to find efficient circuit decompositions for digital and variational quantum simulation algorithms, illustrated here for molecular energy estimation. Finally, we consider a combined fermion-qubit architecture, where both the motional and internal degrees of freedom of the atoms are harnessed to efficiently implement quantum phase estimation as well as to simulate lattice gauge theory dynamics.

Using Sequential Decomposition Algorithms on Electronic Circuits

The subject of consideration in this paper is the decomposition of electronic circuits. Their structure is represented by graph models. Sequential algorithms are used for partitioning. Functionally separated modules are obtained. Conclusions are made for the using of the decomposition algorithms.

Modeling Common-Mode Current Due to Asymmetric Aging of Machine Winding Insulation

Machine stator winding insulation degradation is one of the main results of machine aging. It is non-negligible once this degradation process becomes asymmetric between phases. The traditional way to determine the insulation state of health is a partial discharge test. However, this method requires the system offline, which causes production loss and extra administrative burden. This paper presents an idea for better characterizing the insulation machine's state of health using common-mode (CM) behavior in the machine-drive system. With the help of circuit decomposition methods and modeling tools, the CM quantities due to asymmetric aging show a unique characteristic that distinguishes itself from other differential-mode (DM) quantities in the equivalent circuit. It is shown effective to represent the asymmetric aging effect from the detection of system leakage current. This paper provides an analytical method to quantify this characteristic from mathematical approaches, and a proper approximation has been made on the CM equivalent model (CEM) such that the CM behavior is accurately characterized. The proposed method will serve the purpose of predicting machine abnormal behavior using the simple RLC circuit. Researchers can adapt this method to quantify and characterize the machine insulation state of health (SOH).

Magnetic circuit decomposition model and novel inner‐turn fault protection scheme for shunt reactor with auxiliary windings

AbstractShunt reactor with auxiliary windings (SRAW) can compensate inductive reactive power for long‐distance transmission lines and supply steady power for low‐voltage devices on offshore platforms. The operation characteristics of SRAW can be commonly described by the air‐core transformer equivalent model. However, this model can only make an approximate simulation of the external characteristics of SRAW, and cannot reflect the actual electrical features inside the SRAW. To solve this problem, the authors propose a three‐segment magnetic circuit equivalent model (TMCEM) of SRAW based on the magnetic circuit decomposition method. This model can accurately describe the coupling relationship inside SRAW and can be used for the analysis of internal fault characteristics. Furthermore, through the fault analysis utilizing TMCEM, a novel protection scheme of SRAW based on virtual magnetizing differential current is proposed for the detection of the inner‐turn fault in SRAW. This protection scheme has high sensitivity and can effectively identify the inner‐turn faults without measuring voltages. By testing the physical model of SRAW, the effectiveness of the TMCEM and the proposed protection scheme against inner‐turn fault has been confirmed.

Phase estimation of local Hamiltonians on NISQ hardware

In this work we investigate a binned version of quantum phase estimation (QPE) set out by Somma (2019 New J. Phys. 21 123025) and known as the quantum eigenvalue estimation problem (). Specifically, we determine whether the circuit decomposition techniques we set out in previous work, Clinton et al (2021 Nat. Commun. 12 1–10), can improve the performance of in the noisy intermediate scale quantum (NISQ) regime. To this end we adopt a physically motivated abstraction of NISQ device capabilities as in Clinton et al (2021 Nat. Commun. 12 1–10). Within this framework, we find that our techniques reduce the threshold at which it becomes possible to perform the minimum two-bin instance of this algorithm by an order of magnitude. This is for the specific example of a two dimensional spin Fermi-Hubbard model. For example, we estimate that the depolarizing single qubit error rate required to implement a minimum two bin example of —with a Fermi-Hubbard model and up to a precision of —can be reduced from 10−7 to 10−5. We explore possible modifications to this protocol and propose an application, which we dub randomized quantum eigenvalue estimation problem (). outputs estimates on the fraction of eigenvalues which lie within randomly chosen bins and upper bounds the total deviation of these estimates from the true values. One use case we envision for this algorithm is resolving density of states features of local Hamiltonians.

Brain-Inspired Interpretable Network Pruning for Smart Vision-Based Defect Detection Equipment

Detection algorithms play an important role in the life-cycle management of smart vision-based defect detection equipment. This article proposes a brain-inspired interpretable network pruning method for smart detection equipment for online defect detection scenarios. A brain-inspired neuronal circuit decomposition model is constructed from the view of the structure physics of artificial neural networks. To meet the real-time requirements, an interpretable network pruning is proposed in three steps: First, a full-size basic convolutional neural network is constructed. Second, the convolutional neural circuit's extraction method based on a genetic algorithm is designed to evaluate the function of different neural units. Third, a pruning method is proposed to eliminate the redundant convolutional neural circuits and retain key units to balance the accuracy and time efficiency. The experimental results demonstrated the proposed pruning method can improve the frame-pre-second by 116% on the premise of maintaining the detection accuracy of 92%.

Trapped-ion quantum simulation of collective neutrino oscillations

It is well known that the neutrino flavor in extreme astrophysical environments changes under the effect of three contributions: the vacuum oscillation, the interaction with the surrounding matter, and the collective oscillations due to interactions between different neutrinos. The latter adds a non-linear contribution to the equations of motion, making the description of their dynamics complex. In this work we study various strategies to simulate the coherent collective oscillations of a system of N neutrinos in the two-flavor approximation using quantum computation. This was achieved by using a pair-neutrino decomposition designed to account for the fact that the flavor Hamiltonian, in the presence of the neutrino-neutrino term, presents an all-to-all interaction that makes the implementation of the evolution dependent on the qubit topology. We analyze the Trotter error caused by the decomposition demonstrating that the complexity of the implementation of time evolution scales polynomially with the number of neutrinos and that the noisy from near-term quantum device simulation can be reduced by optimizing the quantum circuit decomposition and exploiting a full-qubit connectivity. We find that the gate complexity using second order Trotter-Suzuki formulae scales better with system size than with other decomposition methods such as Quantum Signal Processing. We finally present the application and the results of our algorithm on a real quantum device based on trapped-ions qubits.

Interpolatory proper order decomposition of nonlinear transmission line circuits

PurposeThe paper is concerned with interpolatory proper orthogonal decomposition (IPOD) methods for nonlinear transmission line circuits. This paper aims to examine several factors that must be considered when applying such model reduction techniques to this kind of circuit.Design/methodology/approachTwo types of POD will be implemented. In each case, the choice of the order of the reduced model and the order of the interpolation space shall be considered. The stability of the models shall be explored.FindingsThe results indicate that the order for the reduced model to obtain accurate results depends on the chosen method when considering nonlinear transmission lines. The results also indicate that the structure of the nonlinear transmission line is crucial for determining the stability of the reduced models.Originality/valueThe work compares two IPOD methods and discusses the issues involved in achieving an accurate and stable reduced-order model for a nonlinear transmission line.

Quantum state preparation and nonunitary evolution with diagonal operators

Realizing non-unitary transformations on unitary-gate based quantum devices is critically important for simulating a variety of physical problems including open quantum systems and subnormalized quantum states. We present a dilation based algorithm to simulate non-unitary operations using probabilistic quantum computing with only one ancilla qubit. We utilize the singular-value decomposition (SVD) to decompose any general quantum operator into a product of two unitary operators and a diagonal non-unitary operator, which we show can be implemented by a diagonal unitary operator in a 1-qubit dilated space. While dilation techniques increase the number of qubits in the calculation, and thus the gate complexity, our algorithm limits the operations required in the dilated space to a diagonal unitary operator, which has known circuit decompositions. We use this algorithm to prepare random sub-normalized two-level states on a quantum device with high fidelity. Furthermore, we present the accurate non-unitary dynamics of two-level open quantum systems in a dephasing channel and an amplitude damping channel computed on a quantum device. The algorithm presented will be most useful for implementing general non-unitary operations when the SVD can be readily computed, which is the case with most operators in the noisy intermediate-scale quantum computing era.

Tunable quantum logic gate on photonic qubits with a ladder emitter

We describe how a ladder emitter can implement a tunable quantum logic gate on photonic qubits encoded in the frequency basis. The ground-to-first excited state of the ladder emitter interacts with the control photon, and the first-to-second excited state transition interacts with the target photon. By controlling the relative detuning between the target photon and the first-to-second excited state transition of the ladder emitter, we enable any controlled-phase operation from 0 to π. We derive analytical formulas for the performance of the gate through the S-matrix formalism as well as describe the mechanism intuitively. This gate is deterministic, does not utilize any active control, and needs only a single ladder emitter, enabling low-footprint and more efficient decomposition of quantum circuits, especially the quantum Fourier transform. We suggest multiple potential systems for physical realization of our proposal, such as lanthanide ions embedded in Purcell-enhanced cavities. We expect these results to motivate further interest in photonic quantum information processing with designer emitters.

The Classification of Clifford Gates over Qubits

We examine the following problem: given a collection of Clifford gates, describe the set of unitaries generated by circuits composed of those gates. Specifically, we allow the standard circuit operations of composition and tensor product, as well as ancillary workspace qubits as long as they start and end in states uncorrelated with the input, which rule out common "magic state injection" techniques that make Clifford circuits universal. We show that there are exactly 57 classes of Clifford unitaries and present a full classification characterizing the gate sets which generate them. This is the first attempt at a quantum extension of the classification of reversible classical gates introduced by Aaronson et al., another part of an ambitious program to classify all quantum gate sets. The classification uses, at its center, a reinterpretation of the tableau representation of Clifford gates to give circuit decompositions, from which elementary generators can easily be extracted. The 57 different classes are generated in this way, 30 of which arise from the single-qubit subgroups of the Clifford group. At a high level, the remaining classes are arranged according to the bases they preserve. For instance, the CNOT gate preserves the X and Z bases because it maps X-basis elements to X-basis elements and Z-basis elements to Z-basis elements. The remaining classes are characterized by more subtle tableau invariants; for instance, the T_4 and phase gate generate a proper subclass of Z-preserving gates.

Graph-|Q⟩⟨C|, a Graph-Based Quantum/Classical Algorithm for Efficient Electronic Structure on Hybrid Quantum/Classical Hardware Systems: Improved Quantum Circuit Depth Performance.

We present a procedure to reduce the depth of quantum circuits and improve the accuracy of results in computing post-Hartree-Fock electronic structure energies in large molecular systems. The method is based on molecular fragmentation where a molecular system is divided into overlapping fragments through a graph-theoretic procedure. This allows us to create a set of projection operators that decompose the unitary evolution of the full system into separate sets of processes, some of which can be treated on quantum hardware and others on classical hardware. Thus, we develop a procedure for an electronic structure that can be asynchronously spawned onto a potentially large ensemble of classical and quantum hardware systems. We demonstrate this method by computing Unitary Coupled Cluster Singles and Doubles (UCCSD) energies for a set of [H2]n clusters, with n ranging from 4 to 128. We implement our methodology using quantum circuits, and when these quantum circuits are processed on a quantum simulator, we obtain energies in agreement with the UCCSD energies in the milli-hartree energy range. We also show that our circuit decomposition approach yields up to 9 orders of magnitude reduction in the number of CNOT gates and quantum circuit depth for the large-sized clusters when compared to a standard quantum circuit implementation available on IBM's Quantum Information Science kit, known as Qiskit.

SPICE-Based Circuit Analysis of Power Flow Coupling Effect in Double-Input Cuk--Buck DC–DC Converters

An equivalent simulation program with integrated circuit emphasis (SPICE) based circuit is derived from the proposed small-signal averaged model of double-input Cuk--Buck dc–dc converter so that the power flow coupling effect amongst input/output ports is easy to be analyzed in terms of circuit theory rather than pure mathematics. Based on the equivalent SPICE-based circuit, common mode and differential mode power flow decomposition is presented to unveil the power flow coupling between three ports, and furthermore benefits frequency response analysis. It is shown that common mode perturbation analysis reveals the power flow coupling amongst input and output ports, whereas differential mode perturbation analysis does the power flow coupling between input ports. Meanwhile, the explanation of circuit knowledge is provided for power flow coupling effect. Particularly, it is found that the occurrence of the pseudo resonant phenomenon is the result of counteract effect of the common mode and differential mode components in power mismatched condition. Besides, the application of frequency-selective decoupling is proposed to weaken the power flow coupling between ports. Finally, theoretical analysis is verified by experimental ones. These results are useful to understand coupling effects in multiple-input converters and provide a guidance to the controller optimization and engineering application.