The problem of the quantitative degradation of the performance of a quantum computer due to noisy unitary gates (imperfect external control) is studied. It is shown that quite general conclusions on the evolution of the fidelity can be reached by using the conjecture that the set of states visited by a quantum algorithm can be replaced by the uniform (Haar) ensemble. These general results are tested numerically against quantum computer simulations of two particular periodically driven quantum systems.
We propose schemes that are efficient when each pair of qubits undergoes some imperfect collective decoherence with different baths. In the proposed scheme, each pair of qubits is first encoded in a decoherence-free subspace composed of two qubits. Leakage out of the encoding space generated by the imperfection is reduced by the quantum Zeno effect. Phase errors in the encoded bits generated by the imperfection are reduced by concatenation of the decoherence-free subspace with either a three-qubit quantum error correcting code that corrects only phase errors or a two-qubit quantum error detect…
Dissipation and decoherence, and the evolution from pure to mixed states in quantum physics are handled through master equations for the density matrix. By embedding elements of this matrix in a higher-dimensional Liouville-Bloch equation, the methods of unitary integration are adapted to solve for the density matrix as a function of time, including the non-unitary effects of dissipation and decoherence. The input requires only solutions of classical, initial value time-dependent equations. Results are illustrated for a damped driven two-level system.
We study decoherence of propagating spin-1/2 excitations in generic (non-integrable and/or disordered) spin chains. We find the relevant decoherence times to be shorter in both the near-critical and diffusive regimes (if any), which fact might have important implications for the recently proposed spin chain-based implementations of quantum information processing.
We study effects of static inter-qubit interactions and random errors in quantum gates on the stability of various quantum algorithms including the Grover quantum search algorithm and the quantum chaos maps. For the Grover algorithm our numerical and analytical results show existence of regular and chaotic phases depending on the static imperfection strength $ε$. The critical border $ε_c$ between two phases drops polynomially with the number of qubits $n_q$ as $ε_c \sim n_q^{-3/2}$. In the regular phase $(ε< ε_c)$ the algorithm remains robust against imperfections showing the efficiency gain $…
Decoherence is a fundamental obstacle to the implementation of large-scale and low-noise quantum information processing devices. In this work, we suggest an approach for suppressing errors by employing pre-processing and post-processing unitary operations, which precede and follow the action of a decoherence channel. In contrast to quantum error correction and measurement-based methods, the suggested approach relies on specifically designed unitary operators for a particular state without the need in ancillary qubits or post-selection procedures. We consider the case of decoherence channels ac…
We study the behavior of Quantum Darwinism (Zurek, [8]) within the iterative, random unitary operations qubit-model of pure decoherence (Novotny et al, [6]). We conclude that Quantum Darwinism, which describes the quantum mechanical evolution of an open system S from the point of view of its environment E, is not a generic phenomenon, but depends on the specific form of input states and on the type of S-E-interactions. Furthermore, we show that within the random unitary model the concept of Quantum Darwinism enables one to explicitly construct and specify artificial input states of environment…
We present a method for performing quantum state reconstruction on qubits and qubit registers in the presence of decoherence and inhomogeneous broadening. The method assumes only rudimentary single qubit rotations as well as knowledge of decoherence and loss mechanisms. We show that full state reconstruction is possible even in the case where single qubit rotations may only be performed imperfectly. Furthermore we show that for ensemble quantum computing proposals, quantum state reconstruction is possible even if the ensemble experiences inhomogeneous broadening and if only imperfect qubit man…
We present a model of an N-qubit channel where consecutive qubits experience correlated random rotations. Our model is an extension to the standard decoherence-free subsystems approach (DFS) which assumes that all the qubits experience the same disturbance. The variation of rotations acting on consecutive qubits is modeled as diffusion on the SU(2) group. The model may be applied to spins traveling in a varying magnetic field, or to photons passing through a fiber whose birefringence fluctuates over the time separation between photons. We derive an explicit formula describing the action of the…
It is commonly stated that decoherence in open quantum systems is due to growing entanglement with an environment. In practice, however, surprisingly often decoherence may equally well be described by random unitary dynamics without invoking a quantum environment at all. For a single qubit, for instance, pure decoherence (or phase damping) is always of random unitary type. Here, we construct a simple example of true quantum decoherence of two qubits: we present a feasible phase damping channel of which we show that it cannot be understood in terms of random unitary dynamics. We give a very int…
Decoherence is the fundamental obstacle limiting the performance of quantum information processing devices. The problem of transmitting a quantum state (known or unknown) from one place to another is of great interest in this context. In this work, by following the recent theoretical proposal [Opt. Eng. {\bf 59}, 061625 (2020)] we study an application of quantum state-dependent pre- and post-processing unitary operations for protecting the given (multi-qubit) quantum state against the effect of decoherence acting on all qubits. We observe the increase in the fidelity of the output quantum stat…
Non-adiabatic holonomic quantum gate in decoherence-free subspaces is of greatly practical importance due to its built-in fault tolerance, coherence stabilization virtues, and short run-time. Here we propose some compact schemes to implement two- and three-qubit controlled unitary quantum gates and Fredkin gate. For the controlled unitary quantum gates, the unitary operator acting on the target qubit is an arbitrary single-qubit gate operation. The controlled quantum gates can be directly implemented using non-adiabatic holonomy in decoherence-free subspaces and the required resource for the d…
Tomography of a quantum state is usually based on positive operator-valued measure (POVM) and on their experimental statistics. Among the available reconstructions, the maximum-likelihood (MaxLike) technique is an efficient one. We propose an extension of this technique when the measurement process cannot be simply described by an instantaneous POVM. Instead, the tomography relies on a set of quantum trajectories and their measurement records. This model includes the fact that, in practice, each measurement could be corrupted by imperfections and decoherence, and could also be associated with …
The ability to construct large photonic cluster states capable of supporting universal quantum computation relies on fusing together cluster primitives. These fusion operations are probabilistic and the efficiency of the construction process relies on recycling remains of cluster primitives that have undergone failed fusion attempts. Here I consider the effects of the inevitible decoherence that must arise while storing cluster primitives. First, I explore the case where dephased two-qubit cluster states are the basic resource for the construction of all larger cluster states, all fusion opera…
We study the influence of errors and decoherence on both the performance of Shor's factoring algorithm and Grover's search algorithm, and on the amount of interference in these algorithms using a recently proposed interference measure. We consider systematic unitary errors, random unitary errors, and decoherence processes. We show that unitary errors which destroy the interference destroy the efficiency of the algorithm, too. However, unitary errors may also create useless additional interference. In such a case the total amount of interference can increase, while the efficiency of the quantum…
We study three methods of obtaining an approximation of unitary evolution of a quantum system under decoherence. We use three methods of optimizing the control pulses: genetic optimization, approximate evolution method and approximate gradient method. To model the noise in the system we use the Lindblad equaiton. We obtain results showing that genetic optimization may give a better approximation of a unitary evolution in the case of high noise.
The inevitable existence of static internal imperfections and residual interactions in some quantum computer architectures result in internal decoherence, dissipation, and destructive unitary shifts of active algorithms. By exact numerical simulations we determine the relative importance and origin of these errors for a Josephson charge qubit quantum computer. In particular we determine that the dynamics of a CNOT gate interacting with its idle neighboring qubits via native residual coupling behaves much like a perturbed kicked top in the exponential decay regime, where fidelity decay is only …
The development of quantum walks in the context of quantum computation, as generalisations of random walk techniques, led rapidly to several new quantum algorithms. These all follow unitary quantum evolution, apart from the final measurement. Since logical qubits in a quantum computer must be protected from decoherence by error correction, there is no need to consider decoherence at the level of algorithms. Nonetheless, enlarging the range of quantum dynamics to include non-unitary evolution provides a wider range of possibilities for tuning the properties of quantum walks. For example, small …
If a quantum experiment includes random processes, then the results of repeated measurements can appear consistent with irreversible decoherence even if the system's evolution prior to measurement was reversible and unitary. Two thought experiments are constructed as examples.
We study the behavior of an open quantum system, with an $N$--dimensional space of states, whose density matrix evolves according to a non--unitary map defined in two steps: A unitary step, where the system evolves with an evolution operator obtained by quantizing a classically chaotic map (baker's and Harper's map are the two examples we consider). A non--unitary step where the evolution operator for the density matrix mimics the effect of diffusion in the semiclassical (large $N$) limit. The process of decoherence and the transition from quantum to classical behavior are analyzed in detail b…
Entanglement between a quantum system and its environment leads to loss of coherence in the former. In general, the temporal fate of coherences is complicated. Here, we establish the connection between decoherence of a central system and fidelity decay in the environment for a variety of situations, including both, energy conserving and dissipative couplings. We show how properties of unitary time evolution of the environment can be inferred from the non-unitary evolution of coherences in the central system. This opens up promising ways for measuring Loschmidt echoes in a variety of situations…
In the framework of an interference setup in which only two outcomes are possible (such as in the case of a Mach-Zehnder interferometer), we discuss in a simple and pedagogical way the difference between a standard, unitary quantum mechanical evolution and the existence of a real collapse of the wave function. Moreover, we also present the Elitzur-Vaidman bomb, the delayed choice experiment, and the effect of decoherence. In the end, we propose two simple experiments to visualize decoherence and to test the role of an entagled particle.
It is shown that Non-unitary Newtonian Gravity (NNG) model admits a simple interpretation in terms of Feynman path integral, in which the sum over all possible histories is replaced by a summation over pairs of paths. Correlations between different paths are allowed by a fundamental decoherence mechanism of gravitational origin and can be interpreted as a kind of communication between different branches of the wave function. The ensuing formulation could be used in turn as a motivation to introduce Non-unitary Gravity itself.
We study pure phase damping of two qubits due to fluctuating fields. As frequently employed, decoherence is thus described in terms of random unitary (RU) dynamics, i.e., a convex mixture of unitary transformations. Based on a separation of the dynamics into an average Hamiltonian and a noise channel, we are able to analytically determine the evolution of both entanglement and purity. This enables us to characterize the dynamics in a concurrence-purity (CP) diagram: we find that RU phase damping dynamics sets constraints on accessible regions in the CP plane. We show that initial state and dyn…
We study the statistics of quantum interference for completely positive maps. We calculate analytically the mean interference and its second moment for finite dimensional quantum systems interacting with a simple environment consisting of one or several spins (qudits). The joint propagation of the entire system is taken as unitary with an evolution operator drawn from the Circular Unitary Ensemble (CUE). We show that the mean interference decays with a power law as function of the dimension of the Hilbert space of the environment, with a power that depends on the temperature of the environment…
The realisation of quantum computers based on molecular electronic spins requires the design of qubits with very long coherence times, T2. Dephasing can proceed over several different microscopic pathways, active at the same time and in different regimes. This makes the rationalisation of the dephasing process not straightforward. Here we present a computational methodology able to address spin decoherence processes for a general ensemble of spins. The method consists in the propagation of the unitary quantum spin dynamics on a reduced Hilbert space. Then we study the dependence of spin dephas…
We investigate the influence of dissipation and decoherence on quantum Darwinism by generalizing Zurek's original qubit model of decoherence and the establishment of pointer states (Zurek, Nature Physics 5, 181 - 188 (2009)). Our model allows for repeated multiple qubit-qubit couplings between system and environment which are described by randomly applied two-qubit quantum operations inducing entanglement, dissipation and dephasing. The resulting stationary qubit states of system and environment are investigated. They exhibit the intricate influence of entanglement generation, dissipation and …
Dynamically corrected gates were recently introduced [Khodjasteh and Viola, Phys. Rev. Lett. 102, 080501 (2009)] as a tool to achieve decoherence-protected quantum gates based on open-loop Hamiltonian engineering. Here, we further expand the framework of dynamical quantum error correction, with emphasis on elucidating under what conditions decoherence suppression can be ensured while performing a generic target quantum gate, using only available bounded-strength control resources. Explicit constructions for physically relevant error models are detailed, including arbitrary linear decoherence a…
Tensor network quantum machine learning (QML) models are promising applications on near-term quantum hardware. While decoherence of qubits is expected to decrease the performance of QML models, it is unclear to what extent the diminished performance can be compensated for by adding ancillas to the models and accordingly increasing the virtual bond dimension of the models. We investigate here the competition between decoherence and adding ancillas on the classification performance of two models, with an analysis of the decoherence effect from the perspective of regression. We present numerical …
Quantum random walk in a two-dimensional lattice with randomly distributed traps is investigated. Distributions of quantum walkers are evaluated dynamically for the cases of Hadamard, Fourier, and Grover coins, and quantum to classical transition is examined as a function of the density of the traps. It is shown that traps act as a serious and additional source of quantum decoherence. Furthermore, non-trivial temporal dependence of the standard deviation of the probability distribution of the walker is found when the trapping imperfections are introduced.
In many quantum information processing applications, it is important to be able to transfer a quantum state from one location to another - even within a local device. Typical approaches to implement the quantum state transfer rely on unitary evolutions or measurement feedforward operations. However, these existing schemes require accurate pulse operations and/or precise timing controls. Here, we propose a one-way transfer of the quantum state with near unit efficiency using dissipation from a tailored environment. After preparing an initial state, the transfer can be implemented without extern…
Even in the absence of external influences the operability of a quantum computer (QC) is not guaranteed because of the effects of residual one- and two-body imperfections. Here we investigate how these internal flaws affect the performance of a quantum controlled-NOT (CNOT) gate in an isolated flawed QC. First we find that the performance of the CNOT gate is considerably better when the two-body imperfections are strong. Secondly, we find that the largest source of error is due to a coherent shift rather than decoherence or dissipation. Our results suggest that the problem of internal imperfec…
Large scale quantum information processing requires stable and long-lived quantum memories. Here, using atom-photon entanglement, we propose an experimentally feasible scheme to realize decoherence-free quantum memory with atomic ensembles, and show one of its applications, remote transfer of unknown quantum state, based on laser manipulation of atomic ensembles, photonic state operation through optical elements, and single-photon detection with moderate efficiency. The scheme, with inherent fault-tolerance to the practical noise and imperfections, allows one to retrieve the information in the…
Universality classes of non-unitary critical theories in two-dimensions are characterized by a dimensional number, termed central charge or conformal anomaly. Conformal invariance predicts that the leading finite-size correction to the free energy of a two-dimensional system at a conformal invariant critical point is linearly related to the central charge of the corresponding conformal field theory. However, experimental determination of the central charge of a non-unitary conformal invariant critical theory has not been done before because of the intrinsic difficulty that complex parameters o…
We consider quantum enhancement of direct-detection interferometric measurements to increase telescope resolution. We propose a protocol of measuring interferometric visibility function using imperfectly entangled states shared between remote telescopes. We show how errors in visibility measurement, and in turn, errors in intensity distribution of a distant object depend on the degree of entanglement of the shared quantum resource. We determine that these errors are sufficiently small over a wide range of resource states which makes our technique feasible in practical environments.
Developing quantum technologies requires the control and understanding of the non-equilibrium dynamics of quantum information in many-body systems. Local information propagates in the system by creating complex correlations known as information scrambling, as this process prevents extracting the information from local measurements. In this work, we develop a model adapted from solid-state NMR methods, to quantify the information scrambling. The scrambling is measured via time-reversal Loschmidt echoes (LE) and Multiple Quantum Coherences experiments that intrinsically contain imperfections. Co…
We present a scheme to implement a universal set of quantum gates based on achievable interactions, and the gates can be protected against decoherences through dynamical-decoupling approach without encoding. By properly designing system evolutions, the desired system interactions commute with the elements forming dynamical decoupling pulses. Thus, the effect of decoherences can be eliminated by repeatedly applying the pulses, without noticeably affecting the system evolutions governed by the desired system interactions given small enough time interval between pulses. Moreover, due to the commu…
We present analytical treatment of quantum walks on multidimensional hyper-cycle graphs. We derive the analytical expression of the probability distribution for strong and weak decoherence regimes. Upper bound to mixing time is obtained.
We present an all-optical implementation of quantum computation using semiconductor quantum dots. Quantum memory is represented by the spin of an excess electron stored in each dot. Two-qubit gates are realized by switching on trion-trion interactions between different dots. State selectivity is achieved via conditional laser excitation exploiting Pauli exclusion principle. Read-out is performed via a quantum-jump technique. We analyze the effect on our scheme's performance of the main imperfections present in real quantum dots: exciton decay, hole mixing and phonon decoherence. We introduce a…
We suggest a novel proposal to express decoherence in open quantum systems by jointly employing spectral and stochastic methods. This proposal, which basically perturbs the unitary evolution operator in a random fashion, allows us to embrace both markovian and nonmarkovian situations with little extra effort. We argue that it can be very suitable to deal with models where an approximation neglecting some degrees of freedom is undertaken. Mathematical simplicity is also obtained both to solve some master equations and to arrive at experimentally measured decoherence functions.
Within the decoherent histories formulation of quantum mechanics, we investigate necessary conditions for decoherence of arbitrarily long histories. We prove that fine-grained histories of arbitrary length decohere for all classical initial states if and only if the unitary evolution preserves classicality of states (using a natural formal definition of classicality). We give a counterexample showing that this equivalence does not hold for coarse-grained histories.
Using the methods of quantum trajectories we investigate the effects of dissipative decoherence in a quantum computer algorithm simulating dynamics in various regimes of quantum chaos including dynamical localization, quantum ergodic regime and quasi-integrable motion. As an example we use the quantum sawtooth algorithm which can be implemented in a polynomial number of quantum gates. It is shown that the fidelity of quantum computation decays exponentially with time and that the decay rate is proportional to the number of qubits, number of quantum gates and per gate dissipation rate induced b…
Decoherence is the phenomenon of non-unitary dynamics that arises as a consequence of coupling between a system and its environment. It has important harmful implications for quantum information processing, and various solutions to the problem have been proposed. Here we provide a detailed a review of the theory of decoherence-free subspaces and subsystems, focusing on their usefulness for preservation of quantum information.
In this paper we consider decoherence-free communication over multiple access and $k$-user quantum channels. First, we concentrate on a hermitian unitary noise model $U$ for a two-access bi-unitary channel and show that in this case a decoherence-free code exists if the space of Schmidt matrices of an eigensubspace of $U$ exhibits certain properties of decomposability. Then, we show that our technique is also applicable for generic random unitary two-access channels. Finally, we consider the applicability of the result to the case of a larger number of senders and general Kraus operators.
Decoherence phenomenon has been widely studied in different types of quantum walks. In this work we show how to model decoherence inspired by percolation on staggered quantum walks. Two models of unitary noise are described: breaking polygons and breaking vertices. The evolution operators subject to these noises are obtained and the equivalence to the coined quantum walk model is presented. Further, we numerically analyze the effect of these decoherence models on the two-dimensional grid of $4$-cliques. We examine how these perturbations affect the quantum walk based search algorithm in this g…
We demonstrate implementations of the Eisert-Wilkens-Lewenstein scheme be- yond normal-form games. The scope of our research includes decision problems, i.e., one-player extensive games. The research is based on the examination of their features when the decision problems are carried out via the EWL protocol. We prove that unitary operators can be adapted to play the role of strategies in deci- sion problems with imperfect recall. Furthermore, we prove that unitary operators provide the decision maker possibilities that are inaccessible for classical strategies.
We study the quantum kicked rotor in resonance subjected to an unitary noise defined through Kraus operators, we show that this type of decoherence does not, in general, lead to the classical diffusive behavior. We find exact analytical expressions for the density matrix and the variance in the primary resonances. The variance does not loose its ballistic behavior, however the coherence decays as a power law. The secondary resonances are treated numerically, obtaining a power-law decay for the variance and an exponential law decay for the coherence.
We describe a model for the interaction of the internal (spin) degree of freedom of a quantum lattice-gas particle with an environmental bath. We impose the constraints that the particle-bath interaction be fixed, while the state of the bath is random, and that the effect of the particle-bath interaction be parity invariant. The condition of parity invariance defines a subgroup of the unitary group of actions on the spin degree of freedom and the bath. We derive a general constraint on the Lie algebra of the unitary group which defines this subgroup, and hence guarantees parity invariance of t…
We study the problem of driving an unknown initial mixed quantum state onto a known pure state without using unitary transformations. This can be achieved, in an efficient manner, with the help of sequential measurements on at least two unbiased bases. However here we found that, when the system is affected by a decoherence mechanism, only one observable is required in order to achieve the same goal. In this way the decoherence can assist the process. We show that, depending on the sort of decoherence, the process can converge faster or slower than the method implemented by means of two comple…
We study adiabatic reverse annealing (ARA) in an open system. In the closed system (unitary) setting, this annealing protocol allows avoidance of first-order quantum phase transitions of selected models, resulting in an exponential speedup compared with standard quantum annealing, provided that the initial state of the algorithm is close in Hamming distance to the target one. Here, we show that decoherence can significantly modify this conclusion: by resorting to the adiabatic master equation approach, we simulate the dynamics of the ferromagnetic $p$-spin model with $p=3$ under independent an…
No-cloning theorem says that there is no unitary operation that makes perfect clones of non-orthogonal quantum states. The objective of the present paper is to examine whether an imperfect cloning operation exists or not in a C*-algebraic framework. We define a universal $ε$-imperfect cloning operation which tolerates a finite loss $ε$ of fidelity in the cloned state, and show that an individual system's algebra of observables is Abelian if and only if there is a universal $ε$-imperfect cloning operation in the case where the loss of fidelity is less than 1/4. Therefore, in this case no univer…
It is shown how classical states, meant as states representing a classical object, can be produced in the thermodynamic limit, retaining the unitary evolution of quantum mechanics. Besides, using a simple model of a single spin interacting with a spin-bath, it is seen how decoherence, with the off-diagonal terms in the density matrix going to zero, can be obtained when the number of the spins in the bath is taken to go formally to infinity. In this case, indeed, the system appears to flop at a frequency being formally infinity that, from a physical standpoint, can be proved equivalent to a tim…
Decoherence without the state: A causal quantum Darwinist approach
Perimeter Institute for Theoretical Physics（perimeter 理论物理研究所）；University of Waterloo（滑铁卢大学）；Center for Theoretical Physics, Polish Academy of Sciences（波兰科学院理论物理中心）
We propose easy implementable protocols for robust quantum key distribution with the collective dephasing channel or collective rotating channel. In these protocols, Bob only takes passive photon detection to measure the polarization qubits in the random bases. The source for the protocol with collective rotating channel is made by type 2 spontaneous parametric down conversion with random unitary rotation and phase shifter, no quantum disentangler is required. A simple proof for unconditionally security is shown.
