We investigate the impact of loss (amplitude damping) and decoherence (phase damping) on the performance of a simple quantum computer which solves the one-bit Deutsch problem. The components of this machine are beamsplitters and nonlinear optical Kerr cells, but errors primarily originate from the latter. We develop models to describe the effect of these errors on a quantum optical Fredkin gate. The results are used to analyze possible error correction strategies in a complete quantum computer. We find that errors due to loss can be avoided perfectly by appropriate design techniques, while decoherence can be partially dealt with using projective error correction.
Liquid-state NMR quantum computer has demonstrated the possibility of quantum computation and supported its development. Using NMR quantum computer techniques, we observed phase decoherence under two kinds of artificial noise fields; one a noise with a long period, and the other with shorter random period. The first one models decoherence in a quantum channel while the second one models transverse relaxation. We demonstrated that the bang-bang control suppresses decoherence in both cases.
We argue that superradiance (collective emission) due to radiative coupling of qubit states results in non-local noise, and thus introduces an error source that cannot be corrected using current models of fault-tolerant quantum computation.
Decoherence in quantum computer memory due to the inevitable coupling to the external environment is examined. We take the assumption that all quantum bits (qubits) interact with the same environment rather than the assumption of separate environments for different qubits. It is found that the qubits are decohered collectively. For some kinds of entangled input states, no decoherence occurs at all in the memory even if the qubits are interacting with the environment. Based on this phenomenon, a scheme is proposed for reducing the collective decoherence. We also discuss possible implications of…
A Quantum Computer is a new type of computer which can solve problems such as factoring and database search very efficiently. The usefulness of a quantum computer is limited by the effect of two different types of errors, decoherence and inaccuracies. In this paper we show the results of simulations of a quantum computer which consider both decoherence and inaccuracies. We simulate circuits which factor the numbers 15, 21, 35, and 57 as well as circuits which use database search to solve the circuit satisfaction problem. Our simulations show that the error rate per gate is on the order of 10^-…
In this thesis we describe methods for avoiding the detrimental effects of decoherence while at the same time still allowing for computation of the quantum information. The philosophy of the method discussed in the first part of this thesis is to use a symmetry of the decoherence mechanism to find robust encodings of the quantum information. Stability, control, and methods for using decoherence-free information in a quantum computer are presented with a specific emphasis on decoherence due to a collective coupling between the system and its environment. Universal quantum computation on such co…
Decoherence is the major stumbling block in the realization of a large-scale quantum computer. Ingenious methods have been devised to overcome decoherence, but their success has been proven only for over-simplified models of system-environment interaction. Whether such methods will be reliable in the face of more realistic models is a fundamental open question. In this partly pedagogical article, we study two toy models of quantum information processing, using the language of \emph{quantum walks}. Decoherence is incorporated in 3 ways - by coupling to a noisy `projective measurement' system, a…
Using a numerical simulation of the evolution of a qubit interacting with the environment we show that quantum error detection and correction can work effectively even when the recovery procedure introduces errors.
We report the realization, using nuclear magnetic resonance techniques, of the first quantum computer that reliably executes an algorithm in the presence of strong decoherence. The computer is based on a quantum error avoidance code that protects against a class of multiple-qubit errors. The code stores two decoherence-free logical qubits in four noisy physical qubits. The computer successfully executes Grover's search algorithm in the presence of arbitrarily strong engineered decoherence. A control computer with no decoherence protection consistently fails under the same conditions.
Mathematical models of quantum computers such as a multidimensional quantum Turing machine and quantum circuits are described and its relations with lattice spin models are discussed. One of the main open problems one has to solve if one wants to build a quantum computer is the decoherence due to the coupling with the environment. We propose a possible solution of this problem by using a control of parameters of the system. This proposal is based on the analysis of the spin-boson Hamiltonian performed in the stochastic limit approximation.
We examine a stochastic noise process that has a decohering effect on the average evolution of qubits in the quantum register of the solid state quantum computer proposed by Kane. We consider the effects of this process on the single qubit operations necessary to perform quantum logical gates and derive an expression for the fidelity of these gates in this system. We then calculate an upper bound on the level of this stochastic noise tolerable in a workable quantum computer.
Decoherence is studied in an attractive proposal for an actual implementation of a quantum computer based on trapped ions. Emphasis is placed on the decoherence arising from the vibrational motion of the ions, which is compared with that due to spontaneous emission from excited states of the ions. The calculation is made tractable by exploiting the vast difference in time scales between the vibrational excitations and the intra-ionic electronic excitations. Since the latter are several orders of magnitude faster, an adiabatic approximation is used to integrate them out and find the inclusive p…
It is discussed the decoherence problems in ensemble large-scale solid state NMR quantum computer based on the array of P donor atoms having nuclear spin I = 1/2. It is considered here, as main mechanisms of decoherence for low temperature (< 0.1 K), the adiabatic processes of random modulation of qubit resonance frequency determined by secular part of nuclear spin interaction with electron spin of the basic atoms, with impurity paramagnetic atoms and also with nuclear spins of impurity diamagnetic atoms. It was made estimations of allowed concentrations of magnetic impurities and of spin temp…
Markovian regime decoherence effects in quantum computers are studied in terms of the fidelity for the situation where the number of qubits N becomes large. A general expression giving the decoherence time scale in terms of Markovian relaxation elements and expectation values of products of system fluctuation operators is obtained, which could also be applied to study decoherence in other macroscopic systems such as Bose condensates and superconductors. A standard circuit model quantum computer involving three-state lambda system ionic qubits is considered, with qubits localised around well-se…
Decoherence is the main obstacle to the realization of quantum computers. Until recently it was thought that quantum error correcting codes are the only complete solution to the decoherence problem. Here we present an alternative that is based on a combination of a decoherence-free subspace encoding and the application of strong and fast pulses: ``encoded recoupling and decoupling'' (ERD). This alternative has the advantage of lower encoding overhead (as few as two physical qubits per logical qubit suffice), and direct application to a number of promising proposals for the experimental realiza…
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.
The scaling of decoherence rates with the number of q-bits is studied for a simple quantum computer model. Two state q-bits are localised around well-separated positions via trapping potentials, but vibrational motion of q-bits centre of mass motion occurs. Coherent one and two q-bit gating processes are controlled by external classical fields and facilitated by a high Q cavity mode. Decoherence due to q-bit and cavity mode coupling to a bath of spontaneous emission modes, cavity decay modes and to the vibrational modes is treated. A non-Markovian treatment of the short time behaviour of the f…
In a quantum computer any superposition of inputs evolves unitarily into the corresponding superposition of outputs. It has been recently demonstrated that such computers can dramatically speed up the task of finding factors of large numbers -- a problem of great practical significance because of its cryptographic applications. Instead of the nearly exponential ($\sim \exp L^{1/3}$, for a number with $L$ digits) time required by the fastest classical algorithm, the quantum algorithm gives factors in a time polynomial in $L$ ($\sim L^2$). This enormous speed-up is possible in principle because …
We define formally decohered quantum computers (using density matrices), and present a simulation of them by a probabalistic classical Turing Machine. We study the slowdown of the simulation for two cases: (1) sequential quantum computers, or quantum Turing machines(QTM), and (2) parallel quantum computers, or quantum circuits. This paper shows that the computational power of decohered quantum computers depends strongly on the amount of parallelism in the computation. The expected slowdown of the simulation of a QTM is polynomial in time and space of the quantum computation, for any non zero d…
We develop in the weak coupling approximation a quasi-non-Markovian master equation and study the phenomenon of decoherence during the operation of a controlled-not (CNOT) quantum gate in a quantum computer model formed by a linear chain of three nuclear spins system with second neighbor Ising interaction between them. We compare with the behavior of the Markovian counterpart for temperature different from zero (thermalization) and at zero temperature for low and high dissipation rates. At low dissipation there is a very small difference between Markovian and quasi no-Markovian at any temperat…
Cooperative effects in the loss (the amplitude damping) and decoherence (the phase damping) of the qubits (two-state quantum systems) due to the inevitable coupling to the same environment are investigated. It is found that the qubits undergo the dissipation coherently in this case. In particular, for a special kind of input states (called the coherence-preserving states), whose form depends on the type of the coupling, loss and decoherence in quantum memory are much reduced. Based on this phenomenon, a scheme by encoding the general input states of the qubits into the corresponding coherence-…
The ion trap quantum computer proposed by Cirac and Zoller is analyzed for decoherence due to vibrations of the ions. An adiabatic approximation exploiting the vast difference between the frequencies of the optical intraionic transition and the vibrational modes is used to find the decoherence time at any temperature T. The scaling of this decoherence time with the number of ions is discussed, and compared to that due to spontaneous emission.
We discuss the operational definition of decoherence in various solid state systems. In particular, we review, in the context of spin-based solid state quantum computation, the introduction of $T_1$ and $T_2$ to describe decoherence in a two level system. We provide a perspective on recent experiments involving the manipulation of spin coherence in semiconductors, and discuss specific decoherence and dephasing issues in electron spin-based quantum dot quantum computer architectures.
The information rates achievable by using electromagnetic radiation affected by thermal noise and signal decoherence are studied. The standard coherent Gaussian model is compared with an alternative photon gas model which represents lack of a shared phase reference between transmitter and receiver. At any frequency, information rates over the photon gas model essentially coincide with those over the Gaussian model when the signal-to-noise ratio is below a threshold. Only above the threshold does decoherence cause a loss in information rates; the loss can amount to half of the capacity. The thr…
Single-photon entanglement may be the simplest type of entanglement but it is of vice importance in quantum communication. Here we present a practical protocol for distilling the single-photon entanglement from both photon loss and decoherence. With the help of some local single photons, the probability of single photon loss can be decreased and the less-entangled state can also be recovered to maximally entangled state simultaneously. It only requires some linear optical elements which makes it feasible in current experiment condition. This protocol might find applications in current quantum …
Any residual coupling of a quantum computer to the environment results in computational errors. Encoding quantum information in a so-called decoherence-free subspace provides means to avoid these errors. Despite tremendous progress in employing this technique to extend memory storage times by orders of magnitude, computation within such subspaces has been scarce. Here, we demonstrate the realization of a universal set of quantum gates acting on decoherence-free ion qubits. We combine these gates to realize the first controlled-NOT gate within a decoherence-free, scalable quantum computer.
A scheme to implement a quantum computer subjected to decoherence and governed by an untunable qubit-qubit interaction is presented. By concatenating dynamical decoupling through bang-bang (BB) pulse with decoherence-free subspaces (DFSs) encoding, we protect the quantum computer from environment-induced decoherence that results in quantum information dissipating into the environment. For the inherent qubit-qubit interaction that is untunable in the quantum system, BB control plus DFSs encoding will eliminate its undesired effect which spoils quantum information in qubits. We show how this qua…
In the viewpoint of quasi normal modes, we describe a novel decoherence mechanism of charge qubit of Josephson Junctions (JJ) in a lossy micro-cavity, which can appear in the realistic experiment for quantum computation based on JJ qubit. We show that the nonlinear coupling of a charge qubit to quantum cavity field can result in an additional dissipation of resonant mode due to its effective interaction between those non-resonant modes and a resonant mode, which is induced by the charge qubit itself. We calculate the characterized time of the novel decoherence by making use of the system plus …
A thought experiment is discussed to clarify the concept of decoherence. Superposition of states consisting of ground state of a single hydrogen atom and its excited state after a huge amount of time is discussed to show that the decoherence of the state, more precisely the loss of coherence, is literally the loss of ability of interference. The loss of superposition of states is just apparent or even superfacial. Applications of this example in its relation to many-world interpretation of observation of a quantum state, decoherence in usual cases, and weak collapse of wavepackets are discusse…
We propose and demonstrate a scheme for boosting up the efficiency of entanglement distribution based on a decoherence-free subspace (DFS) over lossy quantum channels. By using backward propagation of a coherent light, our scheme achieves an entanglement-sharing rate that is proportional to the transmittance T of the quantum channel in spite of encoding qubits in multipartite systems for the DFS. We experimentally show that highly entangled states, which can violate the Clauser-Horne-Shimony-Holt inequality, are distributed at a rate proportional to T.
In this paper we investigate a open two-qubit model whose dynamics is not exactly solvable. When the initial state is the maximum entangled state, as the exactly solvable open two-qubit model [D. Tolkunov and V. Privman, Phys. Rev. A 71, 060308(R) (2005)], the decay of entanglement of formation of the model, expressed by concurrence is also governed by the product of suppression factors describing decoherence of the subsystems (qubits). However, if the initial state is not the maximum entangled state, its concurrence will decrease faster than the product of the suppression factors describing d…
We design an effect protocol for protecting the single-photon entanglement from photon loss and decoherence. The protocol only requires some auxiliary single photons and the linear optical elements. By operating the protocol, the photon loss can be effectively decreased and the less entangled single photon state can be recovered to the maximally entangled state with some probability. Moreover, the polarization information encoded in the single photon state can be perfectly contained. The protocol can be realized under current experimental condition. As the single photon entanglement is quite i…
Using the normally ordered Gaussian form of displaced-squeezed thermal field characteristic of average photon number n, we introduce the photon-added squeezed thermo state (PASTS) and investigate its statistical properties, such as Mandel's Q-parameter, number distribution (as a Legendre polynomial), the Wigner function. We then study its decoherence in a photon-loss channel in term of the negativity of WF by deriving the analytical expression of WF for PASTS. It is found that the WF with single photon-added is always partial negative for the arbitrary values of n and the squeezing parameter r…
Current and near term quantum computers (i.e. NISQ devices) are limited in their computational power in part due to qubit decoherence. Here we seek to take advantage of qubit decoherence as a resource in simulating the behavior of real world quantum systems, which are always subject to decoherence, with no additional computational overhead. As a first step toward this goal we simulate the thermal relaxation of quantum beats in radical ion pairs (RPs) on a quantum computer as a proof of concept of the method. We present three methods for implementing the thermal relaxation, one which explicitly…
By using quantum mechanical effects, quantum computers promise significant speedups in solving problems intractable for conventional computers. However, despite recent progress they remain limited in scaling and availability-making quantum software and hardware development heavily reliant on quantum simulators running on conventional hardware. However, most of those simulators mimic perfect quantum computers and, hence, ignore the fragile nature of quantum mechanical effects which frequently yield to decoherence errors in real quantum devices. Considering those errors during the simulation is …
We investigate cat codes that can correct multiple excitation losses and identify two types of logical errors: bit-flip errors due to excessive excitation loss and dephasing errors due to quantum back-action from the environment. We show that selected choices of logical subspace and coherent amplitude can efficiently reduce dephasing errors. The trade-off between the two major errors enables optimized performance of cat codes in terms of minimized decoherence. With high coupling efficiency, we show that one-way quantum repeaters with cat codes feature drastically boosted secure communication r…
We investigate the decoherence process for a quantum register composed of N qubits coupled to an environment. We consider an environment composed of one common phonon bath and several electronic baths. This environment is relevant to the implementation of a charge based solid-state quantum computer. We explicitly compute the time evolution of all off-diagonal terms of the register's reduced density matrix. We find that in realistic configurations, "superdecoherence" and "decoherence free subspaces" do not exist for an N-qubit system. This means that all off-diagonal terms decay like exp(-q(t)N…
We propose and discuss two conjectures on the nature of information leaks (decoherence) for quantum computers. These conjectures, if (or when) they hold, are damaging for quantum error-correction as required by fault-tolerant quantum computation. The first conjecture asserts that information leaks for a pair of substantially entangled qubits are themselves substantially positively correlated. The second conjecture asserts that in a noisy quantum computer with highly entangled qubits there will be a strong effect of error synchronization. We present more general conjectures for arbitrary noisy …
Decoherence of quantum states is a major hurdle towards scalable and reliable quantum computing. Lower decoherence (i.e., higher fidelity) can alleviate the error correction overhead and obviate the need for energy-intensive noise reduction techniques e.g., cryogenic cooling. In this paper, we performed a noise-induced decoherence analysis of single and multi-qubit quantum gates using physics-based simulations. The analysis indicates that (i) decoherence depends on the input state and the gate type. Larger number of $|1\rangle$ states worsen the decoherence; (ii) amplitude damping is more detr…
We consider the effects of decoherence on Landau-Zener crossings encountered in a large-scale adiabatic-quantum-computing setup. We analyze the dependence of the success probability, i.e. the probability for the system to end up in its new ground state, on the noise amplitude and correlation time. We determine the optimal sweep rate that is required to maximize the success probability. We then discuss the scaling of decoherence effects with increasing system size. We find that those effects can be important for large systems, even if they are small for each of the small building blocks.
Certain physical aspects of quantum error correction are discussed for a quantum computer (n-qubit register) in contact with a decohering environment. Under rather plausible assumptions upon the form of the computer-environment interaction, the efficiency of a general correcting procedure is evaluated as a function of the spontaneous-decay duration and the rank of errors covered by the procedure. It is proved that the probability of errors can be made arbitrarily small by enhancing the correction method, provided the decohering interaction is represented by a bounded operator.
The aim of this letter is to analyze the effect on decoherence of the randomness of the coupling coefficients involved in the interaction Hamiltonian. By studying the spin-bath model with computer simulations, we show that such randomness greatly improves the "efficiency" of decoherence and, then, its physical meaning deserves to be considered.
We study the decoherence of a quantum computer in an environment which is inherently correlated in time and space. We first derive the nonunitary time evolution of the computer and environment in the presence of a stabilizer error correction code, providing a general way to quantify decoherence for a quantum computer. The general theory is then applied to the spin-boson model. Our results demonstrate that effects of long-range correlations can be systematically reduced by small changes in the error correction codes.
We analyse dissipation in quantum computation and its destructive impact on efficiency of quantum algorithms. Using a general model of decoherence, we study the time evolution of a quantum register of arbitrary length coupled with an environment of arbitrary coherence length. We discuss relations between decoherence and computational complexity and show that the quantum factorization algorithm must be modified in order to be regarded as efficient and realistic.
We consider the decoherence of a single localized electron spin due to its coupling to the lattice nuclear spin bath in a semiconductor quantum computer architecture. In the presence of an external magnetic field and at low temperatures, the dominant decoherence mechanism is the spectral diffusion of the electron spin resonance frequency due to the temporally fluctuating random magnetic field associated with the dipolar interaction induced flip-flops of nuclear spin pairs. The electron spin dephasing due to this random magnetic field depends intricately on the quantum dynamics of the nuclear s…
Quantum computing gates are proposed to apply on trapped ions in decoherence-free states. As phase changes due to time evolution of components with different eigenenergies of quantum superposition are completely frozen, quantum computing based on this model would be perfect. Possible application of our scheme in future ion-trap quantum computer is discussed.
We investigate the capabilities of a quantum computer based on cold trapped ions in presence of non-dissipative decoherence. The latter is accounted by using the evolution time as a random variable and then averaging on a properly defined probability distribution. Severe bounds on computational performances are found.
The Schrödinger cat state plays a crucial role in quantum theory, and has important fundamental as well as technological implications, ranging from quantum measurement theory to quantum computers. The power of the potential implications of the cat state lies in the quantum coherence, as measured by the degree of entanglement, between its microscopic and macroscopic sectors. We show that in contrast to other cat states, it is possible to choose the states of the macroscopic sector in a way that the resulting cat state, which we term as the W-cat state, has quantum coherence that is resistant to…
Quantum enhancement of optical pulse timing accuracy is investigated in the Heisenberg picture. Effects of optical loss, group-velocity dispersion, and Kerr nonlinearity on the position and momentum of an optical pulse are studied via Heisenberg equations of motion. Using the developed formalism, the impact of decoherence by optical loss on the use of adiabatic soliton control for beating the timing standard quantum limit [Tsang, Phys. Rev. Lett. 97, 023902 (2006)] is analyzed theoretically and numerically. The analysis shows that an appreciable enhancement can be achieved using current techno…
Reducing decoherence is an essential step toward realizing general-purpose quantum computers beyond the present noisy intermediate-scale quantum (NISQ) computers. To this end, dynamical decoupling (DD) approaches in which external fields are applied to qubits are often adopted. We numerically study DD using a two-level model system (qubit) under the influence of Markovian decoherence by using quantum optimal control theory with slightly modified settings, in which the physical objective is to maximally create and maintain a specified superposition state in a specified control period. An optima…
As an ensemble scheme of solid-state NMR quantum computers the extension of Kane's many-qubits silicon scheme based on the array of 31 P donor atoms are spaced lengthwise of the strip gates is considered. The possible planar topology of such ensemble quantum computer is suggested. The estimation of the output NMR signal was performed and it was shown that for the number N>=10^5 of ensemble elements involving L~10^3 qubits each, the standard NMR methods are usable. As main mechanisms of decoherence for low temperature (<0.1K), the adiabatic processes of random modulation of qubit resonance freq…
Decoherence is the main problem to be solved before quantum computers can be built. To control decoherence, it is possible to use error correction methods, but these methods are themselves noisy quantum computation processes. In this work we study the ability of Steane's and Shor's fault-tolerant recovering methods, as well a modification of Steane's ancilla network, to correct errors in qubits. We test a way to measure correctly ancilla's fidelity for these methods, and state the possibility of carrying out an effective error correction through a noisy quantum channel, even using noisy error …
The well-known increase of the decoherence rate with the temperature, for a quantum system coupled to a linear thermal bath, holds no longer for a different bath dynamics. This is shown by means of a simple classical non-linear bath, as well as a quantum spin-boson model. The anomalous effect is due to the temperature dependence of the bath spectral profile. The decoherence reduction via the temperature increase can be relevant for the design of quantum computers.
We study how macroscopic superpositions of coherent states produced by the nondissipative dynamics of binary mixtures of ultracold atoms are affected by atom losses. We identify different decoherence scenarios for symmetric or asymmetric loss rates and interaction energies in the two modes. In the symmetric case the quantum coherence in the superposition is lost after a single loss event. By tuning appropriately the energies we show that the superposition can be protected, leading to quantum correlations useful for atom interferometry even after many loss events.
We consider charge qubits based on shallow donor electron states in silicon and coupled quantum dots in GaAs. Specifically, we study the feasibility of P$_2^+$ charge qubits in Si, focusing on single qubit properties in terms of tunnel coupling between the two phosphorus donors and qubit decoherence caused by electron-phonon interaction. By taking into consideration the multi-valley structure of the Si conduction band, we show that inter-valley quantum interference has important consequences for single-qubit operations of P$_2^+$ charge qubits. In particular, the valley interference leads to a…
High-quality-factor 3D cavities in superconducting circuits are ideal candidates for bosonic logical qubits as their fidelity is limited only by the low photon loss rate. However, the transmon qubits that are used to manipulate bosonic qubits result in the emergence of additional relaxation and dephasing channels. In this work, a numerical study is performed to elucidate the effect of the various loss channels on the performance of logical gates on a bosonic qubit. A gate error model is developed that encapsulates the loss mechanisms for arbitrary gate operations and predicts experimentally ac…
We review our recent results on short time approximations, with emphasis on applications for which the system-environment interactions involve a general non-Hermitian system operator and its conjugate. We evaluate the onset of decoherence at low temperatures in open quantum systems. The developed approach is complementary to Markovian approximations and appropriate for evaluation of quantum computing schemes. Example of a spin system coupled to a bosonic heat bath is discussed.
We show that all Macroscopic Quantum Superpositions (MQS) based on phase-covariant quantum cloning are characterized by an anomalous high resilence to the de-coherence processes. The analysis supports the results of recent MQS experiments and leads to conceive a useful conjecture regarding the realization of complex decoherence - free structures for quantum information, such as the quantum computer.
We investigate the time T a quantum computer requires to factorize a given number dependent on the number of bits L required to represent this number. We stress the fact that in most cases one has to take into account that the execution time of a single quantum gate is related to the decoherence time of the qubits that are involved in the computation. Although exhibited here only for special systems, this inter-dependence of decoherence and computation time seems to be a restriction in many current models for quantum computers and leads to the result that the computation time T scales much str…
The external control circuits of quantum gates inevitably introduce a small but finite noise to the operation of quantum computers. The complex modes of decoherence introduced by this noise are not covered by the common error models. Using the controlled-phase gate as an example, the effect of gate control noise on decoherence is investigated for different quantum computer architectures. It is shown that the decoherence rate rises faster than linearly with the length of a quantum register for most cases considered, adding to the challenge of implementing proposed error correcting and fault tol…
