arXiv subjects

Zixuan Hu

Publications and source records attributed to Zixuan Hu.

At least 55 records · Page 3Linked to original sources

arXiv2022

Characterizing quantum circuits with qubit functional configurations

We propose a theory of characterizing quantum circuits with qubit functional configurations. Any quantum circuit can be decomposed into alternating sequences of 1-qubit unitary gates and CNOT gates. Each CNOT sequence prepares the current quantum state into a layer of qubit functional configuration to specify the rule for the next 1-qubit unitary sequence on how to collectively modify the state vector entries. All the functional configuration layers on a quantum circuit define its type which can include many other circuits sharing the same configuration layers. Studying the functional configuration types allows us to collectively characterize the properties and behaviors of many quantum circuits. We demonstrate the theory's application to the hardware-efficient ansatzes of variational quantum algorithms. For potential applications, the functional configuration theory may allow systematic understanding and development of quantum algorithms based on their functional configuration types.

quant-ph↗

arXiv2022

The unitary dependence theory for understanding quantum circuits and states

We develop a unitary dependence theory to characterize the behaviors of quantum circuits and states in terms of how quantum gates manipulate qubits and determine their measurement probabilities. A qubit has dependence on a 1-qubit unitary gate if its measurement probabilities depend on the parameters of the gate. A 1-qubit unitary creates such a dependence onto the target qubit, and a CNOT gate copies all the dependences from the control qubit to the target qubit. The complete dependence picture of the output state details the connections qubits may have when being manipulated or measured. Compared to the conventional entanglement description of quantum circuits and states, the dependence picture offers more practical information, easier generalization to many-qubit systems, and better robustness upon partitioning of the system. The unitary dependence theory is a useful tool for understanding quantum circuits and states that is based on the practical ideas of how manipulations and measurements are affected by elementary gates.

quant-ph↗

arXiv2021

The quantum condition space

In this work we first propose to exploit the fundamental properties of quantum physics to evaluate the probability of events with projection measurements. Next, to study what events can be specified by quantum methods, we introduce the concept of the condition space, which is found to be the dual space of the classical outcome space of bit strings. Just like the classical outcome space generates the quantum state space, the condition space generates the quantum condition space that is the central idea of this work. The quantum condition space permits the existence of entangled conditions that have no classical equivalent. In addition, the quantum condition space is related to the quantum state space by a Fourier transform guaranteed by the Pontryagin duality, and therefore an entropic uncertainty principle can be defined. The quantum condition space offers a novel perspective of understanding quantum states with the duality picture. In addition, the quantum conditions have physical meanings and realizations of their own and thus may be studied for purposes beyond the original motivation of characterizing events for probability evaluation. Finally, the relation between the condition space and quantum circuits provides insights into how quantum states are collectively modified by quantum gates, which may lead to deeper understanding of the complexity of quantum circuits.

quant-ph↗

arXiv2021

A practical quantum encryption protocol with varying encryption configurations

Quantum communication is an important application that derives from the burgeoning field of quantum information and quantum computation. Focusing on secure communication, quantum cryptography has two major directions of development, namely quantum key distribution and quantum encryption. In this work we propose a quantum encryption protocol that utilizes a quantum algorithm to create blocks of ciphertexts based on quantum states. The main feature of our quantum encryption protocol is that the encryption configuration of each block is determined by the previous blocks, such that additional security is provided. We then demonstrate our method by an example model encrypting the English alphabet, with numerical simulation results showing the large error rate of a mock attack by a potential adversary. With possible future improvements in mind, our quantum encryption protocol is a capable addition to the toolbox of quantum cryptography.

quant-ph↗

arXiv2021

Relaxation of a Stationary State on a Quantum Computer Yields Unique Spectroscopic Fingerprint of the Computer's Noise

Quantum computing has the potential to revolutionize computing for certain classes of problems with exponential scaling, and yet this potential is accompanied by significant sensitivity to noise, requiring sophisticated error correction and mitigation strategies. Here we simulate the relaxations of stationary states at different frequencies on several quantum computers to obtain unique spectroscopic fingerprints of their noise. Response functions generated from the data reveal a clear signature of non-Markovian dynamics, demonstrating that each of the quantum computers acts as a non-Markovian bath with a unique colored noise profile. The study suggest that noisy intermediate-scale quantum computers (NISQ) provide a built-in noisy bath that can be analyzed from their simulation of closed quantum systems with the results potentially being harnessed for error mitigation or open-system simulation.

quant-ph↗

arXiv2021

Statistical Approach to Quantum Phase Estimation

We introduce a new statistical and variational approach to the phase estimation algorithm (PEA). Unlike the traditional and iterative PEAs which return only an eigenphase estimate, the proposed method can determine any unknown eigenstate-eigenphase pair from a given unitary matrix utilizing a simplified version of the hardware intended for the Iterative PEA (IPEA). This is achieved by treating the probabilistic output of an IPEA-like circuit as an eigenstate-eigenphase proximity metric, using this metric to estimate the proximity of the input state and input phase to the nearest eigenstate-eigenphase pair and approaching this pair via a variational process on the input state and phase. This method may search over the entire computational space, or can efficiently search for eigenphases (eigenstates) within some specified range (directions), allowing those with some prior knowledge of their system to search for particular solutions. We show the simulation results of the method with the Qiskit package on the IBM Q platform and on a local computer.

quant-ph↗

arXiv2021

A quantum encryption design featuring confusion, diffusion, and mode of operation

Quantum cryptography -- the application of quantum computing techniques to cryptography has been extensively investigated. Two major directions of quantum cryptography are quantum key distribution (QKD) and quantum encryption, with the former focusing on secure key distribution and the latter focusing on encryption using quantum algorithms. In contrast to the success of the QKD, the development of quantum encryption algorithms is limited to designs of mostly one-time pads (OTP) that are unsuitable for most communication needs. In this work we propose a non-OTP quantum encryption scheme utilizing a quantum state creation process to encrypt messages. As essentially a non-OTP quantum block cipher the method stands out against existing methods with the following features: 1. complex key-ciphertext relation (i.e. confusion) and complex plaintext-ciphertext relation (i.e. diffusion); 2. mode of operation design for practical encryption on multiple blocks. These features provide key reusability and protection against eavesdropping and standard cryptanalytic attacks.

quant-ph↗

arXiv2020

Qudits and high-dimensional quantum computing

Qudit is a multi-level computational unit alternative to the conventional 2-level qubit. Compared to qubit, qudit provides a larger state space to store and process information, and thus can provide reduction of the circuit complexity, simplification of the experimental setup and enhancement of the algorithm efficiency. This review provides an overview of qudit-based quantum computing covering a variety of topics ranging from circuit building, algorithm design, to experimental methods. We first discuss the qudit gate universality and a variety of qudit gates including the pi/8 gate, the SWAP gate, and the multi-level-controlled gate. We then present the qudit version of several representative quantum algorithms including the Deutsch-Jozsa algorithm, the quantum Fourier transform, and the phase estimation algorithm. Finally we discuss various physical realizations for qudit computation such as the photonic platform, iron trap, and nuclear magnetic resonance.

quant-ph↗

arXiv2020

Characterization of quantum states based on creation complexity

The creation complexity of a quantum state is the minimum number of elementary gates required to create it from a basic initial state. The creation complexity of quantum states is closely related to the complexity of quantum circuits, which is crucial in developing efficient quantum algorithms that can outperform classical algorithms. A major question unanswered so far is what quantum states can be created with a number of elementary gates that scales polynomially with the number of qubits. In this work we first show for an entirely general quantum state it is exponentially hard (requires a number of steps that scales exponentially with the number of qubits) to determine if the creation complexity is polynomial. We then show it is possible for a large class of quantum states with polynomial creation complexity to have common coefficient features such that given any candidate quantum state we can design an efficient coefficient sampling procedure to determine if it belongs to the class or not with arbitrarily high success probability. Consequently partial knowledge of a quantum state's creation complexity is obtained, which can be useful for designing quantum circuits and algorithms involving such a state.

quant-ph↗

arXiv2020

Developable B-spline surface generation from control rulings

An intuitive design method is proposed for generating developable ruled B-spline surfaces from a sequence of straight line segments indicating the surface shape. The first and last line segments are enforced to be the head and tail ruling lines of the resulting surface while the interior lines are required to approximate rulings on the resulting surface as much as possible. This manner of developable surface design is conceptually similar to the popular way of the freeform curve and surface design in the CAD community, observing that a developable ruled surface is a single parameter family of straight lines. This new design mode of the developable surface also provides more flexibility than the widely employed way of developable surface design from two boundary curves of the surface. The problem is treated by numerical optimization methods with which a particular level of distance error is allowed. We thus provide an effective tool for creating surfaces with a high degree of developability when the input control rulings do not lie in exact developable surfaces. We consider this ability as the superiority over analytical methods in that it can deal with arbitrary design inputs and find practically useful results.

cs.GR↗

arXiv2019

Enhancement of Photovoltaic Current Generation through Dark States in Donor-Acceptor Pairs of Tungsten-based Transition Metal Di-Chalcogenides (TMDCs)

As several photovoltaic materials experimentally approach the Shockley-Queisser limit, there has been a growing interest in unconventional materials and approaches with the potential to cross this efficiency barrier. One such candidate is dark state protection induced by the dipole-dipole interaction between molecular excited states. This phenomenon has been shown to significantly reduce carrier recombination rate and enhance photon-to-current conversion, in elementary models consisting of few interacting chromophore centers. Atomically thin 2D transition metal di-chalcogenides (TMDCs) have shown great potential for use as ultra-thin photovoltaic materials in solar cells due to their favorable photon absorption and electronic transport properties. TMDC alloys exhibit tunable direct bandgaps and significant dipole moments. In this work, we introduce the dark state protection mechanism to a TMDC based photovoltaic system with pure tungsten diselenide (WSe2) as the acceptor material and the TMDC alloy tungsten sulfo-selenide (WSeS) as the donor material. Our numerical model demonstrates the first application of the dark state protection mechanism to a photovoltaic material with a photon current enhancement of up to 35% and an ideal photon-to-current efficiency exceeding the Shockley-Queisser limit.

physics.app-ph↗

arXiv2019

Quantum Phase Estimation with Time-Frequency Qudits in a Single Photon

The Phase Estimation Algorithm (PEA) is an important quantum algorithm used independently or as a key subroutine in other quantum algorithms. Currently most implementations of the PEA are based on qubits, where the computational units in the quantum circuits are two-dimensional states. Performing quantum computing tasks with higher dimensional states -- qudits -- has been proposed, yet a qudit-based PEA has not been realized. Using qudits can reduce the resources needed for achieving a given precision or success probability. Compared to other quantum computing hardware, photonic systems have the advantage of being resilient to noise, but the probabilistic nature of photon-photon interaction makes it difficult to realize two-photon controlled gates that are necessary components in many quantum algorithms. In this work, we report an experimental realization of a qudit-based PEA on a photonic platform, utilizing the high dimensionality in time and frequency degrees of freedom (DoFs) in a single photon. The controlled-unitary gates can be realized in a deterministic fashion, as the control and target registers are now represented by two DoFs in a single photon. This first implementation of a qudit PEA, on any platform, successfully retrieves any arbitrary phase with one ternary digit of precision.

quant-ph↗

arXiv2019

A quantum algorithm for evolving open quantum dynamics on quantum computing devices

Designing quantum algorithms for simulating quantum systems has seen enormous progress, yet few studies have been done to develop quantum algorithms for open quantum dynamics despite its importance in modeling the system-environment interaction found in most realistic physical models. In this work we propose and demonstrate a general quantum algorithm to evolve open quantum dynamics on quantum computing devices. The Kraus operators governing the time evolution can be converted into unitary matrices with minimal dilation guaranteed by the Sz.-Nagy theorem. This allows the evolution of the initial state through unitary quantum gates, while using significantly less resource than required by the conventional Stinespring dilation. We demonstrate the algorithm on an amplitude damping channel using the IBM Qiskit quantum simulator and the IBM Q 5 Tenerife quantum device. The proposed algorithm does not require particular models of dynamics or decomposition of the quantum channel, and thus can be easily generalized to other open quantum dynamical models.

quant-ph↗

arXiv2018

Double-excitation manifold's effect on exciton transfer dynamics and the efficiency of coherent light harvesting

The efficiency of natural light harvesting systems is largely determined by their ability to transfer excitations from the antenna to the energy trapping center before recombination. Exciton diffusion length similarly limits organic photovoltaics and demands bulk heterojunction architectures. Dark state protection, achieved by coherent coupling between subunits within the antenna, can significantly reduce radiative recombination and enhance the efficiency of energy trapping. In this work we extend the dark state concept to the double-excitation manifold by studying the dynamical flow of excitations. We show the lowest double-excitation state carries minimal oscillator strength but relaxation to this state from higher lying double excitations can be relatively rapid such that the lowest double excitation state can act as a dynamical dark state protecting excitation from radiative recombination. This mechanism is sensitive to topology and operates differently for chain and ring structures, while becoming more pronounced in both geometries when the size of the antenna increases. When the exciton-exciton annihilation (EEA) mechanism is considered, the double-excitation population is quickly depleted and the dynamics changes dramatically. However the efficiency and output power are still significantly different from those calculated using the single-excitation manifold alone, justifying the necessity of considering the double-excitation manifold. Remarkably, in certain scenarios, the EEA can even increase the overall light harvesting efficiency by bringing population down from the double-excitation dark states to the single-excitation manifold.

physics.chem-ph↗

arXiv2018

Connecting bright and dark states through accidental degeneracy caused by lack of symmetry

Coupled excitonic structures are found in natural and artificial light harvesting systems where optical transitions link different excitation manifolds. In systems with symmetry, some optical transitions are allowed, while others are forbidden. Here we examine an excitonic ring structure and identify an accidental degeneracy between two categories of double-excitation eigenstates with distinct symmetries and optical transition properties. To understand the accidental degeneracy, a complete selection rule between two arbitrary excitation manifolds is derived with a physically motivated proof. Remarkably, symmetry analysis shows the lack of certain symmetry elements in the Hamiltonian is responsible for this degeneracy, which is unique to rings with size N=4l+2 (l being an integer).

quant-ph↗

arXiv2018

Theory for polariton-assisted remote energy transfer

Strong-coupling between light and matter produces hybridized states (polaritons) whose delocalization and electromagnetic character allow for novel modifications in spectroscopy and chemical reactivity of molecular systems. Recent experiments have demonstrated remarkable distance-independent long-range energy transfer between molecules strongly coupled to optical microcavity modes. To shed light on the mechanism of this phenomenon, we present the first comprehensive theory of polariton-assisted remote energy transfer (PARET) based on strong-coupling of donor and/or acceptor chromophores to surface plasmons. Application of our theory demonstrates that PARET up to a micron is indeed possible via strong-coupling. In particular, we report two regimes for PARET: in one case, strong-coupling to a single type of chromophore leads to transfer mediated largely by surface plasmons while in the other case, strong-coupling to both types of chromophores creates energy transfer pathways mediated by vibrational relaxation. Importantly, we highlight conditions under which coherence enhances or deteriorates these processes. For instance, while exclusive strong-coupling to donors can enhance transfer to acceptors, the reverse turns out not to be true. However, strong-coupling to acceptors can shift energy levels in a way that transfer from acceptors to donors can occur, thus yielding a chromophore role-reversal or "carnival effect." This theoretical study demonstrates the potential for confined electromagnetic fields to control and mediate PARET, thus opening doors to the design of remote mesoscale interactions between molecular systems.

quant-ph↗

arXiv2017

Dark states and delocalization: competing effects of quantum coherence on the efficiency of light harvesting systems

Natural light harvesting systems exploit electronic coupling of identical chromophores to generate efficient and robust excitation transfer and conversion. Dark states created by strong coupling between chromophores in the antenna structure can significantly reduce radiative recombination and enhance energy conversion efficiency. Increasing the number of the chromophores increases the number of dark states and the associated enhanced energy conversion efficiency, yet also delocalizes excitations away from the trapping center and reduces the energy conversion rate. Therefore, a competition between dark state protection and delocalization must be considered when designing the optimal size of a light harvesting system. In this study, we explore the two competing mechanisms in a chain-structured antenna and show that dark state protection is the dominant mechanism, with an intriguing dependence on the parity of the number of chromophores. This dependence is linked to the exciton distribution among eigenstates which is strongly affected by the coupling strength between chromophores and the temperature. Combining these findings, we propose that increasing the coupling strength between the chromophores can significantly increase the power output of the light harvesting system.

physics.chem-ph↗

arXiv2017

Accessing dark states optically through excitation-ferrying states

The efficiency of solar energy harvesting systems is largely determined by their ability to transfer excitations from the antenna to the energy trapping center before recombination. Dark state protection, achieved by coherent coupling between subunits in the antenna structure, can significantly reduce radiative recombination and enhance the efficiency of energy trapping. Because the dark states cannot be populated by optical transitions from the ground state, they are usually accessed through phononic relaxation from the bright states. In this study, we explore a novel way of connecting the dark states and the bright states via optical transitions. In a ring-like chromophore system inspired by natural photosynthetic antennae, the single-excitation bright state can be optically connected to the lowest energy single-excitation dark state through certain double-excitation states. We call such double-excitation states the ferry states and show that they are the result of accidental degeneracy between two categories of double-excitation states. We then mathematically prove that the ferry states are only available when N, the number of subunits on the ring, satisfies N=4l+2 (l being an integer). Numerical calculations confirm that the ferry states enhance the energy transfer power of our model, showing a significant energy transfer power spike at N=6 compared with smaller N values, even without phononic relaxation. The proposed mathematical theory for the ferry states is not restricted to this one particular system or numerical model. In fact, it is potentially applicable to any coherent optical system that adopts a ring-shaped chromophore arrangement. Beyond the ideal case, the ferry state mechanism also demonstrates robustness under weak phononic dissipation, weak site energy disorder, and large coupling strength disorder.

physics.chem-ph↗