Non-unitary Quantum Research Articles

Proposal of a quantum version of active particles via a nonunitary quantum walk.

The main aim of the present paper is to define an active particle in a quantum framework as a minimal model of quantum active matter and investigate the differences and similarities of quantum and classical active matter. Although the field of active matter has been expanding, most research has been conducted on classical systems. Here, we propose a truly deterministic quantum active-particle model with a nonunitary quantum walk as the minimal model of quantum active matter. We aim to reproduce results obtained previously with classical active Brownian particles; that is, a Brownian particle, with finite energy take-up, becomes active and climbs up a potential wall. We realize such a system with nonunitary quantum walks. We introduce new internal states, the ground state and the excited state , and a new nonunitary operator N(g) for an asymmetric transition between and . The non-Hermiticity parameter promotes the transition to the excited state; hence, the particle takes up energy from the environment. For our quantum active particle, we successfully observe that the movement of the quantum walker becomes more active in a nontrivial manner as we increase the non-Hermiticity parameter , which is similar to the classical active Brownian particle. We also observe three unique features of quantum walks, namely, ballistic propagation of peaks in one dimension, the walker staying on the constant energy plane in two dimensions, and oscillations originating from the resonant transition between the ground state and the excited state both in one and two dimensions.

Unambiguous discrimination of general quantum operations.

The discrimination of quantum operations has long been an intriguing challenge, with theoretical research notably advancing our understanding of the quantum features in discriminating quantum objects. This challenge is closely related to the discrimination of quantum states, and proof-of-principle demonstrations of the latter have already been realized using optical photons. However, the experimental demonstration of discriminating general quantum operations, including both unitary and nonunitary operations, has remained elusive. In general quantum systems, especially those with high dimensions, the preparation of arbitrary quantum states and the implementation of arbitrary quantum operations and generalized measurements are nontrivial tasks. Here, we experimentally demonstrate the optimal unambiguous discrimination of up to six displacement operators and the unambiguous discrimination of nonunitary quantum operations. Our results demonstrate powerful tools for experimental research in quantum information processing and are expected to stimulate a wide range of valuable applications in the field of quantum sensing.

Non-unitary quantum many-body dynamics using the Faber polynomial method

Non-unitary quantum many-body dynamics using the Faber polynomial method

Quantum teleportation based on the elegant joint measurement

As a generalization of the well-known Bell state measurement (BSM), the elegant joint measurement (EJM) is a kind of novel two-qubit joint measurement, parameterized by a subtle phase factor θ∈[0,π/2]. We investigate here the quantum teleportation based on the EJM that conceptually goes beyond BSM. It is a probabilistic teleportation caused by nonunitary quantum evolution except for the special case of the BSM with θ=π/2. We show in detail the feasible quantum circuits to realize the present scenario, where a few unitary operations and a nonunitary quantum gate are being utilized. This work suggests that it is feasible to extend the customary (BSM-based) teleportation scenarios to the EJM-based ones, and different from the BSM being single input it may provide a continuously variable input setting or even multiple measurement settings for the sender of the quantum state.

Optimal depth and a novel approach to variational unitary quantum process tomography

In this work, we present two new methods for variational quantum circuit (VQC) process tomography (PT) onto n qubits systems: unitary PT based on VQCs (PT_VQC) and unitary evolution-based variational quantum singular value decomposition (U-VQSVD). Compared to the state of the art, PT_VQC halves in each run the required amount of qubits for unitary PT and decreases the required state initializations from 4 n to just 2 n , all while ensuring high-fidelity reconstruction of the targeted unitary channel U. It is worth noting that, for a fixed reconstruction accuracy, PT_VQC achieves faster convergence per iteration step compared to quantum deep neural network and tensor network schemes. The novel U-VQSVD algorithm utilizes variational singular value decomposition to extract eigenvectors (up to a global phase) and their associated eigenvalues from an unknown unitary representing a universal channel. We assess the performance of U-VQSVD by executing an attack on a non-unitary channel quantum physical unclonable function. By using U-VQSVD we outperform an uninformed impersonation attack (using randomly generated input states) by a factor of 2 to 5, depending on the qubit dimension. For the two presented methods, we propose a new approach to calculate the complexity of the displayed VQC, based on what we denote as optimal depth.

Singular Value Decomposition Quantum Algorithm for Quantum Biology.

There has been a recent interest in quantum algorithms for the modeling and prediction of nonunitary quantum dynamics using current quantum computers. The field of quantum biology is one area where these algorithms could prove to be useful as biological systems are generally intractable to treat in their complete form but amenable to an open quantum systems approach. Here, we present the application of a recently developed singular value decomposition (SVD) algorithm to two systems in quantum biology: excitonic energy transport through the Fenna-Matthews-Olson complex and the radical pair mechanism for avian navigation. We demonstrate that the SVD algorithm is capable of capturing accurate short- and long-time dynamics for these systems through implementation on a quantum simulator and conclude that while the implementation of this algorithm is beyond the reach of current quantum computers, it has the potential to be an effective tool for the future study of systems relevant to quantum biology.

Probabilistic imaginary-time evolution algorithm based on nonunitary quantum circuits

Probabilistic imaginary-time evolution algorithm based on nonunitary quantum circuits

Spread complexity for measurement-induced non-unitary dynamics and Zeno effect

Using spread complexity and spread entropy, we study non-unitary quantum dynamics. For non-hermitian Hamiltonians, we extend the bi-Lanczos construction for the Krylov basis to the Schrödinger picture. Moreover, we implement an algorithm adapted to complex symmetric Hamiltonians. This reduces the computational memory requirements by half compared to the bi-Lanczos construction. We apply this construction to the one-dimensional tight-binding Hamiltonian subject to repeated measurements at fixed small time intervals, resulting in effective non-unitary dynamics. We find that the spread complexity initially grows with time, followed by an extended decay period and saturation. The choice of initial state determines the saturation value of complexity and entropy. In analogy to measurement-induced phase transitions, we consider a quench between hermitian and non-hermitian Hamiltonian evolution induced by turning on regular measurements at different frequencies. We find that as a function of the measurement frequency, the time at which the spread complexity starts growing increases. This time asymptotes to infinity when the time gap between measurements is taken to zero, indicating the onset of the quantum Zeno effect, according to which measurements impede time evolution.

Generalised quantum speed limit for arbitrary time-continuous evolution

The quantum speed limit describes how quickly a quantum system can evolve in time from an initial state to a final state under a given dynamics. Here, we derive a generalised quantum speed limit (GQSL) for arbitrary time-continuous evolution using the geometrical approach of quantum mechanics. The GQSL is applicable for quantum systems undergoing unitary, non-unitary, completely positive, non-completely positive and relativistic quantum dynamics. This reduces to the well known standard quantum speed limit (QSL), i.e. the Mandelstam-Tamm bound when the quantum system undergoes unitary time evolution. Using our formalism, we then obtain a quantum speed limit for non-Hermitian quantum systems. To illustrate our findings, we have estimated the quantum speed limit for a time-independent non-Hermitian system as well as for a time-dependent non-Hermitian system namely the Bethe-Lamb Hamiltonian for general two-level system.

Spectral mapping theorem of an abstract non-unitary quantum walk

This paper continues the previous work (Quantum Inf. Process 11 (2019)) by two authors of the present paper about a spectral mapping property of chiral symmetric unitary operators. In physics, they treat non-unitary time-evolution operators to consider quantum walks in open systems. In this paper, we generalize the above result to include a chiral symmetric non-unitary operator whose coin operator only has two eigenvalues. As a result, the spectra of such non-unitary operators are included in the (possibly non-unit) circle and the real axis in the complex plane. We also give some examples of our abstract results, such as non-unitary quantum walks defined by Mochizuki et al. Furthermore, the main theorem applies not only to quantum walks but also to the Ihara zeta function and correlated random walks on regular graphs.

Anomalous non-Hermitian dynamical phenomenon on the quantum circuit

The anomalous non-Hermitian dynamical phenomenon with the non-Hermitian skin effect (NHSE) attracts wide attention due to its novel physics and promising applications. Here, we propose a new type of non-unitary discrete-time quantum walk system demonstrating the NHSE and anomalous non-Hermitian dynamical phenomena, including the dynamical chiral phenomenon, the funneling phenomenon on the domain wall, and the anomalous reflection on the phase impurity. Furthermore, we design the quantum circuit experiments of these quantum walk systems and numerically simulate them with quantum noises to verify the robustness of the non-Hermitian dynamical phenomenon on the noisy intermediate-scale quantum (NISQ) devices. Our work paves the way for implementing the non-Hermitian dynamical phenomenon on the quantum circuit.

Distinguishability transitions in nonunitary boson-sampling dynamics

We discover novel transitions characterized by distinguishability of bosons in non-unitary dynamics with parity-time ($\mathcal{PT}$) symmetry. We show that $\mathcal{PT}$ symmetry breaking, a unique transition in non-Hermitian open systems, enhances regions in which bosons can be regarded as distinguishable. This means that classical computers can sample the boson distributions efficiently in these regions by sampling the distribution of distinguishable particles. In a $\mathcal{PT}$-symmetric phase, we find one dynamical transition upon which the distribution of bosons deviates from that of distinguishable particles, when bosons are initially put at distant sites. If the system enters a $\mathcal{PT}$-broken phase, the threshold time for the transition is suddenly prolonged, since dynamics of each boson is diffusive (ballistic) in the $\mathcal{PT}$-broken ($\mathcal{PT}$-symmetric) phase. Furthermore, the $\mathcal{PT}$-broken phase also exhibits a notable dynamical transition on a longer time scale, at which the bosons again become distinguishable. This transition, and hence the classical easiness of sampling bosons in long times, are true for generic postselected non-unitary quantum dynamics, while it is absent in unitary dynamics of isolated quantum systems. $\mathcal{PT}$ symmetry breaking can also be characterized by the efficiency of a classical algorithm based on the rank of matrices, which can (cannot) efficiently compute the photon distribution in the long-time regime of the $\mathcal{PT}$-broken ($\mathcal{PT}$-symmetric) phase.

Entanglement entropy distinguishes PT-symmetry and topological phases in a class of non-unitary quantum walks

We calculate the hybrid entanglement entropy between coin and walker degrees of freedom in a non-unitary quantum walk. The model possesses a joint parity and time-reversal symmetry or PT-symmetry and supports topological phases when this symmetry is unbroken by its eigenstates. An asymptotic analysis at long times reveals that the quantum walk can indefinitely sustain hybrid entanglement in the unbroken symmetry phase even when gain and loss mechanisms are present. However, when the gain-loss strength is too large, the PT-symmetry of the model is spontaneously broken and entanglement vanishes. The entanglement entropy is therefore an effective and robust parameter for constructing PT-symmetry and topological phase diagrams in this non-unitary dynamical system.

Fundamental transfer matrix for electromagnetic waves, scattering by a planar collection of point scatterers, and anti- PT -symmetry

We develop a fundamental transfer-matrix formulation of the scattering of electromagnetic (EM) waves that incorporates the contribution of the evanescent waves and applies to general stationary linear media which need not be isotropic, homogenous, or passive. Unlike the traditional transfer matrices whose definition involves slicing the medium, the fundamental transfer matrix is a linear operator acting in an infinite-dimensional function space. It is given in terms of the evolution operator for a nonunitary quantum system and has the benefit of allowing for analytic calculations. In this respect it is the only available alternative to the standard Green's-function approaches to EM scattering. We use it to offer an exact solution of the outstanding EM scattering problem for an arbitrary finite collection of possibly anisotropic nonmagnetic point scatterers lying on a plane. In particular, we provide a comprehensive treatment of doublets consisting of pairs of isotropic point scatterers and study their spectral singularities. We show that identical and $\mathcal{P}\mathcal{T}$-symmetric doublets do not admit spectral singularities and cannot function as a laser unless the real part of their permittivity equals that of the vacuum. This restriction does not apply to doublets displaying anti-$\mathcal{P}\mathcal{T}$-symmetry. We determine the lasing threshold for a generic anti-$\mathcal{P}\mathcal{T}$-symmetric doublet and show that it possesses a continuous lasing spectrum.

Variational Quantum Process Tomography of Non-Unitaries.

Quantum process tomography is a fundamental and critical benchmarking and certification tool that is capable of fully characterizing an unknown quantum process. Standard quantum process tomography suffers from an exponentially scaling number of measurements and complicated data post-processing due to the curse of dimensionality. On the other hand, non-unitary operators are more realistic cases. In this work, we put forward a variational quantum process tomography method based on the supervised quantum machine learning framework. It approximates the unknown non-unitary quantum process utilizing a relatively shallow depth parametric quantum circuit and fewer input states. Numerically, we verified our method by reconstructing the non-unitary quantum mappings up to eight qubits in two cases: the weighted sum of the randomly generated quantum circuits and the imaginary time evolution of the Heisenberg XXZ spin chain Hamiltonian. Results show that those quantum processes could be reconstructed with high fidelities (>99%) and shallow depth parametric quantum circuits (d≤8), while the number of input states required is at least two orders of magnitude less than the demands of the standard quantum process tomography. Our work shows the potential of the variational quantum process tomography method in characterizing non-unitary operators.

Bottomonium Suppression in the Quark–Gluon Plasma — From Effective Field Theories to Non-unitary Quantum Evolution

Bottomonium Suppression in the Quark–Gluon Plasma — From Effective Field Theories to Non-unitary Quantum Evolution

Density correlations from analog Hawking radiation in the presence of atom losses

The sonic analog of Hawking radiation can now be experimentally recreated in Bose-Einstein condensates that contain an acoustic black hole. In these experiments the signal strength and approximate analog Hawking temperature increase for denser condensates, which however also suffer increased atom losses from inelastic collisions. To determine how these affect analog Hawking radiation, we numerically simulate creation of the latter in a Bose-Einstein condensate in the presence of atomic losses, including nonunitary quantum field dynamics using the truncated Wigner approximation. In particular we explore modifications of density-density correlations through which the radiation has been analyzed so far. We find no evidence that losses directly alter the basic picture of the analog Hawking effect; instead all consequences that we find are indirect: Losses increase the contrast of the correlation signal, which we attribute to condensate heating by the losses, in turn leading to a component of stimulated radiation in addition to the spontaneous one. Other indirect consequences are the modification of the white-hole instability pattern and a change of slope of the Hawking tongue.

Co-Design quantum simulation of nanoscale NMR

Quantum computers have the potential to efficiently simulate the dynamics of nanoscale NMR systems. In this work, we demonstrate that a noisy intermediate-scale quantum computer can be used to simulate and predict nanoscale NMR resonances. In order to minimize the required gate fidelities, we propose a superconducting application-specific Co-Design quantum processor that reduces the number of SWAP gates by over 90% for chips with more than 20 qubits. The processor consists of transmon qubits capacitively coupled via tunable couplers to a central co-planar waveguide resonator with a quantum circuit refrigerator (QCR) for fast resonator reset. The QCR implements the nonunitary quantum operations required to simulate nuclear hyperpolarization scenarios.

Integrable nonunitary quantum circuits

We show that the integrable Lindblad superoperators found recently can be used to build integrable nonunitary quantum circuits with two-site gates by demonstrating that the $\check{R}$-matrices are completely positive and trace preserving. Using the bond-site transformation, we obtain the corresponding integrable nonunitary quantum circuits with three-site gates. When restricted to the diagonals of the density matrix, these quantum models reduce to integrable classical cellular automata. This approach may pave the way for a systematic construction of integrable nonunitary quantum circuits.

Criticality and entanglement in nonunitary quantum circuits and tensor networks of noninteracting fermions

Entanglement dynamics in nonunitary quantum systems have been found to exhibit novel nonequilibrium quantum phase transitions and have attracted tremendous attention with connections to various aspects of quantum information theory. This work establishes, for systems of noninteracting fermions, an exact three-way correspondence between (i) nonunitary (as well as unitary) quantum circuits dynamics in $d$ spatial dimensions; (ii) ($d$+1)-dimensional Gaussian tensor networks, and (iii) fermion systems in ($d$+1) spatial dimensions subject to unitary evolution with static Hamiltonians. Through this correspondence, $d$-dimensional random quantum circuits are connected with the classic subject area of Anderson localization in ($d$+1) spatial dimensions and consequently follow the ``tenfold way'' Altland-Zirnbauer classification. Selected examples of quantum circuits exhibiting entanglement phases and criticalities are used to illustrate these general principles.