Lianao Wu | University of the Basque Country, Euskal Herriko Unibertsitatea (original) (raw)

Papers by Lianao Wu

Academia Quantum, Aug 20, 2024

Decoherence is a major challenge in quantum computing. To enable execution of quantum al- gorithm... more Decoherence is a major challenge in quantum computing. To enable execution of quantum al- gorithms, it is crucial to eliminate decoherence and noise for instance via dynamic decoupling and quantum error correction protocols based on dynamic zero-noise strategy. As potential alternatives we introduced self-protected quantum algorithms over 15 years ago. Quantum algorithms of this kind, based on the living-with-noise strategy, are now used in the Noisy Intermediate-Scale Quan- tum regime. Here we introduce self-protected quantum simulations in the presence of weak classical noises. Notably, we prove the equivalence between weak classical noise and noiseless quantum sim- ulations. This equivalence implies that a self-protected quantum simulation does not require any extra overhead in its experimental implementation. Furthermore, we find that the conventional quantum phase estimation can be upgraded to its corresponding noisy version.

Scientific Reports, 2020

The stationary behavior of a quantum system is determined by its Hamiltonian and its boundary con... more The stationary behavior of a quantum system is determined by its Hamiltonian and its boundary conditions. All quantum phase transitions (QPT) reported previously were induced by changing the Hamiltonian. In a circular spin model with Heisenberg XY interactions and no magnetic field, we observe an anomaly in quantum phases caused by a qualitative change of the boundary condition. The unexpected anomaly features an infinite number of single-particle levels, in the same pattern as the single-photon-triggered quantum phase transition in the Rabi model.

Physical Review A, 2019

We study optimization of fidelity for ultrafast transformation of a spin chain via external contr... more We study optimization of fidelity for ultrafast transformation of a spin chain via external control of a local exchange coupling. We show that infidelity of such a process can be dramatically decreased by choosing a proper control profile in nonadiabatic time domain, predict main features of this profile analytically, corroborate them numerically with a gradient search algorithm, and discuss the corresponding quantum speed limit. For ultrafast transformations, the qualitative features of the obtained optimal control are system-independent. Moreover, the main restrictions on its shape do not depend on the transformation time and remain valid up to the adiabatic limit. Our results can be applied to control a broad variety of quantum systems.

New Journal of Physics, 2018

We propose and analyze, focusing on non-adiabatic effects, a technique of manipulating quantum sp... more We propose and analyze, focusing on non-adiabatic effects, a technique of manipulating quantum spin systems based on local 'cutting' and 'stitching' of the Heisenberg exchange coupling between the spins. This first operation is cutting of a bond separating a single spin from a linear chain, or of two neighboring bonds for a ring-shaped array of spins. We show that the disconnected spin can be in the ground state with a high-fidelity even after a non-adiabatic process. Next, we consider inverse operation of stitching these bonds to increase the system size. We show that the optimal control algorithm can be found by using common numerical procedures with a simple twoparametric control function able to produce a high-fidelity cutting and stitching. These results can be applied for manipulating ensembles of quantum dots, considered as prospective elements for quantum information technologies, and for design of machines based on quantum thermodynamics.

Scientific Reports, 2021

We prove the existence of a unitary transformation that enables two arbitrarily given Hamiltonian... more We prove the existence of a unitary transformation that enables two arbitrarily given Hamiltonians in the same Hilbert space to be transformed into one another. The result is straightforward yet, for example, it lays the foundation to implementing or mimicking dynamics with the most controllable Hamiltonian. As a promising application, this existence theorem allows for a rapidly evolving realization of adiabatic quantum computation by transforming a Hamiltonian where dynamics is in the adiabatic regime into a rapidly evolving one. We illustrate the theorem with examples.

New Journal of Physics, 2020

As first proposed for the adiabatic quantum information processing by Wu et al (2002 Phys. Rev. L... more As first proposed for the adiabatic quantum information processing by Wu et al (2002 Phys. Rev. Lett. 89 057904), the Trotterization technique is a very useful tool for universal quantum computing, and in particular, the adiabatic quantum simulation of quantum systems. Given a boson Hamiltonian involving arbitrary bilinear interactions, we propose a static version of this technique to perform an optical simulation that would enable the identification of the ground state of the Hamiltonian. By this method, the dynamical process of the adiabatic evolution is mapped to a static linear optical array which is robust to the errors caused by dynamical fluctuations. We examine the cost of the physical implementation of the Trotterization, i.e. the number of discrete steps required for a given accuracy. Two conclusions are drawn. One is that the number of required steps grows much more slowly than the system size if the number of non-zero matrix elements of Hamiltonian is not too large. The ...

Physical Review A, 2009

We show how to perfectly transfer, without state initialization and remote collaboration, arbitra... more We show how to perfectly transfer, without state initialization and remote collaboration, arbitrary functions in interacting boson lattices. We describe a possible implementation of state transfer through bosonic atoms trapped in optical lattices or polaritons in on-chip coupled cavities. Significantly, a family of Hamiltonians, both linear and nonlinear, is found which are related to the Bose-Hubbard model and that enable the perfect transfer of arbitrary functions. It is shown that the state transfer between two sites in two-dimensional lattices can result in quantum interference due to the different numbers of intermediate sites in different paths. The signature factor in nuclear physics can be useful to characterize this quantum interference.

Physical Review A, 2014

The adiabatic theorem addresses the dynamics of a target instantaneous eigenstate of a timedepend... more The adiabatic theorem addresses the dynamics of a target instantaneous eigenstate of a timedependent Hamiltonian. We use a Feshbach P-Q partitioning technique to derive a closed onecomponent integro-differential equation. The resultant equation properly traces the footprint of the target eigenstate. The physical significance of the derived dynamical equation is illustrated by both general analysis and concrete examples. Surprisingly, we find an anomalous phenomenon showing that a dephasing white noise can enhance and even induce adiabaticity. This new phenomenon may naturally occur in many physical systems. We also show that white noises can also shorten the total duration of dynamic processes such as adiabatic quantum computing.

Physical Review A, 2012

This paper considers the extension of the non-Markovian stochastic approach for quantum open syst... more This paper considers the extension of the non-Markovian stochastic approach for quantum open systems strongly coupled to a fermionic bath, to the models in which the system operators commute with the fermion bath. This technique can also be a useful tool for studying open quantum systems coupled to a spin-chain environment, which can be further transformed into an effective fermionic bath. We derive an exact stochastic Schrödinger equation (SSE), called fermionic quantum state diffusion (QSD) equation, from the first principle by using the fermionic coherent state representation. The reduced density operator for the open system can be recovered from the average of the solutions to the QSD equation over the Grassmann-type noise. By employing the exact fermionic QSD equation, we can derive the corresponding exact master equation. The power of our approach is illustrated by the applications of our stochastic approach to several models of interest including the one-qubit dissipative model, the coupled two-qubit dissipative model, the quantum Brownian motion model and the N-fermion model coupled to a fermionic bath. Different effects caused by the fermionic and bosonic baths on the dynamics of open systems are also discussed.

Physical Review A, 2013

ABSTRACT A uniformly coupled double-quantum Hamiltonian for a spin chain has recently been implem... more ABSTRACT A uniformly coupled double-quantum Hamiltonian for a spin chain has recently been implemented experimentally. We propose a method for the determination of initial quantum states that will provide perfect or near-perfect state transmission for an arbitrary Hamiltonian including this one. By calculating the eigenvalues and eigenvectors of a unitary operator obtained from the free evolution plus an exchange operator, we find that the double-quantum Hamiltonian spin chain will support a three-spin initial encoding that will transfer along the chain with remarkably high fidelity. The fidelity is also found to decrease very slowly with increasing chain length. In addition, we are able to explain previous results showing exceptional transfer using this method.

Physical Review A, 2013

Protection of quantum states in a noisy environment is essential for reliable quantum information... more Protection of quantum states in a noisy environment is essential for reliable quantum information processing. In this Letter, through a sequence of unoptimized periodical rectangular pulses we show that beyond perturbation, dynamical decoupling can be a powerful tool for the control of fidelity and entanglement of the open system in a non-Markovian bath. With this non-perturbative approach, we have found, for the first time, the threshold and pulse parameter regions in which the non-idealized pulses are effective in controlling quantum coherence.

Physical Review A, 2013

ABSTRACT We present a method to numerically calculate the dynamics driven by arbitrary Hamiltonia... more ABSTRACT We present a method to numerically calculate the dynamics driven by arbitrary Hamiltonians, in particular those with symmetry. The method enables us to study quantum state and entanglement transmission through a uniformly coupled two-dimensional square lattice with XY-type interaction. Significantly, we find that the central symmetry between sending and receiving nodes plays a crucial role in attaining maximal fidelity and entanglement transmission. In other words, the quality of a two-dimensional transmission is determined by the geometry of the nodes involved.

Physical Review A, 2010

We propose a new quantum algorithm for finding eigenvalues of non-Hermitian matrices. We show how... more We propose a new quantum algorithm for finding eigenvalues of non-Hermitian matrices. We show how to construct, through interactions in a quantum system and partial measurements, a non-Hermitian matrix and obtain its eigenvalues and eigenvectors. This proposal combines ideas of frequent partial measurement, measured quantum Fourier transform, and quantum state tomography. Similar to the conventional phase estimation algorithm, our algorithm provides a speed-up over its classical counterpart. Moreover, in our approach the controlled unitary operation is implemented only once. In addition, the algorithm provides a high success probability.

Physical Review A, 2011

... Under the Born-Oppenheimer approximation, the whole dynamics of the mechanical resonator and ... more ... Under the Born-Oppenheimer approximation, the whole dynamics of the mechanical resonator and ... Significantly, we further show that the ground-state cooling may be achieved via the three-mirror cavity optomechanical system without the resolved sideband condition. ...

Physical Review A, 2005

Leakage" errors are particularly serious errors which couple states within a code subspace to sta... more Leakage" errors are particularly serious errors which couple states within a code subspace to states outside of that subspace thus destroying the error protection benefit afforded by an encoded state. We generalize an earlier method for producing leakage elimination decoupling operations and examine the effects of the leakage eliminating operations on decoherence-free or noiseless subsystems which encode one logical, or protected qubit into three or four qubits. We find that by eliminating the large class of leakage errors, under some circumstances, we can create the conditions for a decoherence free evolution. In other cases we identify a combination decoherence-free and quantum error correcting code which could eliminate errors in solid-state qubits with anisotropic exchange interaction Hamiltonians and enable universal quantum computing with only these interactions.

Physical Review A, 2005

We discuss the detection of entanglement in interacting quantum spin systems. First, thermodynami... more We discuss the detection of entanglement in interacting quantum spin systems. First, thermodynamic Hamiltonian-based witnesses are computed for a general class of one-dimensional spin-1/2 models. Second, we introduce optimal bipartite entanglement observables. We show that a bipartite entanglement measure can generally be associated to a set of independent two-body spin observables whose expectation values can be used to witness entanglement. The number of necessary observables is ruled by the symmetries of the model. Illustrative examples are presented.

Physical Review A, 2011

We study the effect of Dzyaloshinskii-Moriya (DM) interaction on pairwise quantum discord, entang... more We study the effect of Dzyaloshinskii-Moriya (DM) interaction on pairwise quantum discord, entanglement, and classical correlation in the anisotropic XY spin-half chain. Analytical expressions for both quantum and classical correlations are obtained from the spin-spin correlation functions. We show that these pairwise quantities exhibit various behaviors in relation to the relative strengths of the DM interaction, the anisotropy and the magnetic intensity. We observe non-analyticities of the derivatives of both quantum and classical correlations with respect to the magnetic intensity at the critical point, with consideration of the DM interaction.

Physical Review A, 2012

We consider an exact state swap, defined as the swap between two quantum states |A and |B in the ... more We consider an exact state swap, defined as the swap between two quantum states |A and |B in the Hilbert space of a quantum system. We show that, given an arbitrary Hamiltonian dynamics, there is a straightforward approach to calculating the probability of the occurrence of an exact state swap, by employing an exchange operator PAB. For a given dynamics, the feasibilities of proposed quantum setups, such as quantum state amplifications and transfers can be evaluated. These setups are only distinguished by different forms of PAB, which easily lead to innovative designs of quantum setups or devices. We illustrate the method with the isotropic XY model, whose unnoticed features are revealed.

Academia Quantum, Aug 20, 2024

Decoherence is a major challenge in quantum computing. To enable execution of quantum al- gorithm... more Decoherence is a major challenge in quantum computing. To enable execution of quantum al- gorithms, it is crucial to eliminate decoherence and noise for instance via dynamic decoupling and quantum error correction protocols based on dynamic zero-noise strategy. As potential alternatives we introduced self-protected quantum algorithms over 15 years ago. Quantum algorithms of this kind, based on the living-with-noise strategy, are now used in the Noisy Intermediate-Scale Quan- tum regime. Here we introduce self-protected quantum simulations in the presence of weak classical noises. Notably, we prove the equivalence between weak classical noise and noiseless quantum sim- ulations. This equivalence implies that a self-protected quantum simulation does not require any extra overhead in its experimental implementation. Furthermore, we find that the conventional quantum phase estimation can be upgraded to its corresponding noisy version.

Scientific Reports, 2020

The stationary behavior of a quantum system is determined by its Hamiltonian and its boundary con... more The stationary behavior of a quantum system is determined by its Hamiltonian and its boundary conditions. All quantum phase transitions (QPT) reported previously were induced by changing the Hamiltonian. In a circular spin model with Heisenberg XY interactions and no magnetic field, we observe an anomaly in quantum phases caused by a qualitative change of the boundary condition. The unexpected anomaly features an infinite number of single-particle levels, in the same pattern as the single-photon-triggered quantum phase transition in the Rabi model.

Physical Review A, 2019

We study optimization of fidelity for ultrafast transformation of a spin chain via external contr... more We study optimization of fidelity for ultrafast transformation of a spin chain via external control of a local exchange coupling. We show that infidelity of such a process can be dramatically decreased by choosing a proper control profile in nonadiabatic time domain, predict main features of this profile analytically, corroborate them numerically with a gradient search algorithm, and discuss the corresponding quantum speed limit. For ultrafast transformations, the qualitative features of the obtained optimal control are system-independent. Moreover, the main restrictions on its shape do not depend on the transformation time and remain valid up to the adiabatic limit. Our results can be applied to control a broad variety of quantum systems.

New Journal of Physics, 2018

We propose and analyze, focusing on non-adiabatic effects, a technique of manipulating quantum sp... more We propose and analyze, focusing on non-adiabatic effects, a technique of manipulating quantum spin systems based on local 'cutting' and 'stitching' of the Heisenberg exchange coupling between the spins. This first operation is cutting of a bond separating a single spin from a linear chain, or of two neighboring bonds for a ring-shaped array of spins. We show that the disconnected spin can be in the ground state with a high-fidelity even after a non-adiabatic process. Next, we consider inverse operation of stitching these bonds to increase the system size. We show that the optimal control algorithm can be found by using common numerical procedures with a simple twoparametric control function able to produce a high-fidelity cutting and stitching. These results can be applied for manipulating ensembles of quantum dots, considered as prospective elements for quantum information technologies, and for design of machines based on quantum thermodynamics.

Scientific Reports, 2021

We prove the existence of a unitary transformation that enables two arbitrarily given Hamiltonian... more We prove the existence of a unitary transformation that enables two arbitrarily given Hamiltonians in the same Hilbert space to be transformed into one another. The result is straightforward yet, for example, it lays the foundation to implementing or mimicking dynamics with the most controllable Hamiltonian. As a promising application, this existence theorem allows for a rapidly evolving realization of adiabatic quantum computation by transforming a Hamiltonian where dynamics is in the adiabatic regime into a rapidly evolving one. We illustrate the theorem with examples.

New Journal of Physics, 2020

As first proposed for the adiabatic quantum information processing by Wu et al (2002 Phys. Rev. L... more As first proposed for the adiabatic quantum information processing by Wu et al (2002 Phys. Rev. Lett. 89 057904), the Trotterization technique is a very useful tool for universal quantum computing, and in particular, the adiabatic quantum simulation of quantum systems. Given a boson Hamiltonian involving arbitrary bilinear interactions, we propose a static version of this technique to perform an optical simulation that would enable the identification of the ground state of the Hamiltonian. By this method, the dynamical process of the adiabatic evolution is mapped to a static linear optical array which is robust to the errors caused by dynamical fluctuations. We examine the cost of the physical implementation of the Trotterization, i.e. the number of discrete steps required for a given accuracy. Two conclusions are drawn. One is that the number of required steps grows much more slowly than the system size if the number of non-zero matrix elements of Hamiltonian is not too large. The ...

Physical Review A, 2009

We show how to perfectly transfer, without state initialization and remote collaboration, arbitra... more We show how to perfectly transfer, without state initialization and remote collaboration, arbitrary functions in interacting boson lattices. We describe a possible implementation of state transfer through bosonic atoms trapped in optical lattices or polaritons in on-chip coupled cavities. Significantly, a family of Hamiltonians, both linear and nonlinear, is found which are related to the Bose-Hubbard model and that enable the perfect transfer of arbitrary functions. It is shown that the state transfer between two sites in two-dimensional lattices can result in quantum interference due to the different numbers of intermediate sites in different paths. The signature factor in nuclear physics can be useful to characterize this quantum interference.

Physical Review A, 2014

The adiabatic theorem addresses the dynamics of a target instantaneous eigenstate of a timedepend... more The adiabatic theorem addresses the dynamics of a target instantaneous eigenstate of a timedependent Hamiltonian. We use a Feshbach P-Q partitioning technique to derive a closed onecomponent integro-differential equation. The resultant equation properly traces the footprint of the target eigenstate. The physical significance of the derived dynamical equation is illustrated by both general analysis and concrete examples. Surprisingly, we find an anomalous phenomenon showing that a dephasing white noise can enhance and even induce adiabaticity. This new phenomenon may naturally occur in many physical systems. We also show that white noises can also shorten the total duration of dynamic processes such as adiabatic quantum computing.

Physical Review A, 2012

This paper considers the extension of the non-Markovian stochastic approach for quantum open syst... more This paper considers the extension of the non-Markovian stochastic approach for quantum open systems strongly coupled to a fermionic bath, to the models in which the system operators commute with the fermion bath. This technique can also be a useful tool for studying open quantum systems coupled to a spin-chain environment, which can be further transformed into an effective fermionic bath. We derive an exact stochastic Schrödinger equation (SSE), called fermionic quantum state diffusion (QSD) equation, from the first principle by using the fermionic coherent state representation. The reduced density operator for the open system can be recovered from the average of the solutions to the QSD equation over the Grassmann-type noise. By employing the exact fermionic QSD equation, we can derive the corresponding exact master equation. The power of our approach is illustrated by the applications of our stochastic approach to several models of interest including the one-qubit dissipative model, the coupled two-qubit dissipative model, the quantum Brownian motion model and the N-fermion model coupled to a fermionic bath. Different effects caused by the fermionic and bosonic baths on the dynamics of open systems are also discussed.

Physical Review A, 2013

ABSTRACT A uniformly coupled double-quantum Hamiltonian for a spin chain has recently been implem... more ABSTRACT A uniformly coupled double-quantum Hamiltonian for a spin chain has recently been implemented experimentally. We propose a method for the determination of initial quantum states that will provide perfect or near-perfect state transmission for an arbitrary Hamiltonian including this one. By calculating the eigenvalues and eigenvectors of a unitary operator obtained from the free evolution plus an exchange operator, we find that the double-quantum Hamiltonian spin chain will support a three-spin initial encoding that will transfer along the chain with remarkably high fidelity. The fidelity is also found to decrease very slowly with increasing chain length. In addition, we are able to explain previous results showing exceptional transfer using this method.

Physical Review A, 2013

Protection of quantum states in a noisy environment is essential for reliable quantum information... more Protection of quantum states in a noisy environment is essential for reliable quantum information processing. In this Letter, through a sequence of unoptimized periodical rectangular pulses we show that beyond perturbation, dynamical decoupling can be a powerful tool for the control of fidelity and entanglement of the open system in a non-Markovian bath. With this non-perturbative approach, we have found, for the first time, the threshold and pulse parameter regions in which the non-idealized pulses are effective in controlling quantum coherence.

Physical Review A, 2013

ABSTRACT We present a method to numerically calculate the dynamics driven by arbitrary Hamiltonia... more ABSTRACT We present a method to numerically calculate the dynamics driven by arbitrary Hamiltonians, in particular those with symmetry. The method enables us to study quantum state and entanglement transmission through a uniformly coupled two-dimensional square lattice with XY-type interaction. Significantly, we find that the central symmetry between sending and receiving nodes plays a crucial role in attaining maximal fidelity and entanglement transmission. In other words, the quality of a two-dimensional transmission is determined by the geometry of the nodes involved.

Physical Review A, 2010

We propose a new quantum algorithm for finding eigenvalues of non-Hermitian matrices. We show how... more We propose a new quantum algorithm for finding eigenvalues of non-Hermitian matrices. We show how to construct, through interactions in a quantum system and partial measurements, a non-Hermitian matrix and obtain its eigenvalues and eigenvectors. This proposal combines ideas of frequent partial measurement, measured quantum Fourier transform, and quantum state tomography. Similar to the conventional phase estimation algorithm, our algorithm provides a speed-up over its classical counterpart. Moreover, in our approach the controlled unitary operation is implemented only once. In addition, the algorithm provides a high success probability.

Physical Review A, 2011

... Under the Born-Oppenheimer approximation, the whole dynamics of the mechanical resonator and ... more ... Under the Born-Oppenheimer approximation, the whole dynamics of the mechanical resonator and ... Significantly, we further show that the ground-state cooling may be achieved via the three-mirror cavity optomechanical system without the resolved sideband condition. ...

Physical Review A, 2005

Leakage" errors are particularly serious errors which couple states within a code subspace to sta... more Leakage" errors are particularly serious errors which couple states within a code subspace to states outside of that subspace thus destroying the error protection benefit afforded by an encoded state. We generalize an earlier method for producing leakage elimination decoupling operations and examine the effects of the leakage eliminating operations on decoherence-free or noiseless subsystems which encode one logical, or protected qubit into three or four qubits. We find that by eliminating the large class of leakage errors, under some circumstances, we can create the conditions for a decoherence free evolution. In other cases we identify a combination decoherence-free and quantum error correcting code which could eliminate errors in solid-state qubits with anisotropic exchange interaction Hamiltonians and enable universal quantum computing with only these interactions.

Physical Review A, 2005

We discuss the detection of entanglement in interacting quantum spin systems. First, thermodynami... more We discuss the detection of entanglement in interacting quantum spin systems. First, thermodynamic Hamiltonian-based witnesses are computed for a general class of one-dimensional spin-1/2 models. Second, we introduce optimal bipartite entanglement observables. We show that a bipartite entanglement measure can generally be associated to a set of independent two-body spin observables whose expectation values can be used to witness entanglement. The number of necessary observables is ruled by the symmetries of the model. Illustrative examples are presented.

Physical Review A, 2011

We study the effect of Dzyaloshinskii-Moriya (DM) interaction on pairwise quantum discord, entang... more We study the effect of Dzyaloshinskii-Moriya (DM) interaction on pairwise quantum discord, entanglement, and classical correlation in the anisotropic XY spin-half chain. Analytical expressions for both quantum and classical correlations are obtained from the spin-spin correlation functions. We show that these pairwise quantities exhibit various behaviors in relation to the relative strengths of the DM interaction, the anisotropy and the magnetic intensity. We observe non-analyticities of the derivatives of both quantum and classical correlations with respect to the magnetic intensity at the critical point, with consideration of the DM interaction.

Physical Review A, 2012

We consider an exact state swap, defined as the swap between two quantum states |A and |B in the ... more We consider an exact state swap, defined as the swap between two quantum states |A and |B in the Hilbert space of a quantum system. We show that, given an arbitrary Hamiltonian dynamics, there is a straightforward approach to calculating the probability of the occurrence of an exact state swap, by employing an exchange operator PAB. For a given dynamics, the feasibilities of proposed quantum setups, such as quantum state amplifications and transfers can be evaluated. These setups are only distinguished by different forms of PAB, which easily lead to innovative designs of quantum setups or devices. We illustrate the method with the isotropic XY model, whose unnoticed features are revealed.