Using nuclear magnetic resonance techniques, we experimentally investigated the effects of applying a two bit phase error detection code to preserve quantum information in nuclear spin systems. Input states were stored with and without coding, and the resulting output states were compared with the originals and with each other. The theoretically expected result, net reduction of distortion and conditional error probabilities to second order, was indeed observed, despite imperfect coding operations which increased the error probabilities by approximately 5%. Systematic study of the deviations from the ideal behavior provided quantitative measures of different sources of error, and good agreement was found with a numerical model. Theoretical questions in quantum error correction in bulk nuclear spin systems including fidelity measures, signal strength and syndrome measurements are discussed.
We demonstrate a five-bit nuclear-magnetic-resonance quantum computer that distinguishes among various functions on four bits, making use of quantum parallelism. Its construction draws on the recognition of the sufficiency of linear coupling along a chain of nuclear spins, the synthesis of a suitably coupled molecule, and the use of a multi-channel spectrometer.
In the present article, the robustness of entanglement in two qubits maximally entangled mixed states (MEME) have been studied under quantum decoherence channels. Here we consider bit flip, phase flip, bit-phase-flip, amplitude damping, phase damping and depolarization channels. To quantify the entanglement, the concurrence has been used as an entanglement measure. During this study interesting results have been found for sudden death and birth of entanglement under bit flip and bit-phase-flip channels. While amplitude damping channel produces entanglement sudden death and does not allow re-bi…
Traditional quantum error correction involves the redundant encoding of k quantum bits using n quantum bits to allow the detection and correction of any t bit error. The smallest general t=1 code requires n=5 for k=1. However, the dominant error process in a physical system is often well known, thus inviting the question: given a specific error model, can more efficient codes be devised? We demonstrate new codes which correct just amplitude damping errors which allow, for example, a t=1, k=1 code using effectively n=4.6. Our scheme is based on using bosonic states of photons in a finite number…
Collective decoherence is possible if the departure between quantum bits is smaller than the effective wave length of the noise field. Collectivity in the decoherence helps us to devise more efficient quantum codes. We present a class of optimal quantum codes for preventing collective amplitude damping to a reservoir at zero temperature. It is shown that two qubits are enough to protect one bit quantum information, and approximately $L+ 1/2 \log_2((πL)/2)$ qubits are enough to protect $L$ qubit information when $L$ is large. For preventing collective amplitude damping, these codes are much mor…
We experimentally demonstrate a single-qubit decohering quantum channel using linear optics. We implement the channel, whose special cases include both the amplitude-damping channel and the bit-flip channel, using a single, static optical setup. Following a recent theoretical result [M. Piani et al., Phys. Rev. A, 84, 032304 (2011)], we realize the channel in an optimal way, maximizing the probability of success, i.e., the probability for the photonic qubit to remain in its encoding. Using a two-photon entangled resource, we characterize the channel using ancilla-assisted process tomography an…
We study the dynamics of coherence-induced state ordering under incoherent channels, particularly four specific Markovian channels: $-$ amplitude damping channel, phase damping channel, depolarizing channel and bit flit channel for single-qubit states. We show that the amplitude damping channel, phase damping channel, and depolarizing channel do not change the coherence-induced state ordering by $l_1$ norm of coherence, relative entropy of coherence, geometric measure of coherence, and Tsallis relative $α$-entropies, while the bit flit channel does change for some special cases.
We construct generally applicable short-time perturbative expansions for some fidelities, such as the input-output fidelity, the entanglement fidelity, and the average fidelity. Successive terms of these expansions yield characteristic times for the damping of the fidelities involving successive powers of the Hamiltonian. The second-order results, which represent the damping rates of the fidelities, are extensively discussed. As an interesting application of these expansions, we use them to study the spatially-correlated dissipation of quantum bits. Spatial correlations in the dissipation are …
A scheme is proposed for protecting quantum states from both independent decoherence and cooperative decoherence. The scheme operates by pairing each qubit (two-state quantum system) with an ancilla qubit and by encoding the states of the qubits into the corresponding coherence-preserving states of the qubit-pairs. In this scheme, the amplitude damping (loss of energy) is prevented as well as the phase damping (dephasing) by a strategy called the free-Hamiltonian-elimination We further extend the scheme to include quantum gate operations and show that loss and decoherence during the gate opera…
To overcome the difficulty of realizing large-scale quantum Fourier transform (QFT) within existing technology, this paper presents a resource-saving method, namely t-bit semiclassical QFT over (Z_(2^n)), which could realize large-scale QFT using arbitrary-scale quantum register. Using our method, the scale of quantum register can be determined flexibility according to the scale of quantum system, enabling the quantum resource and speed of realizing QFT to be optimal. By developing a feasible method to realize the control quantum gate R_k, we experimentally demonstrate the 2-bit semiclassical …
Compared with classical search algorithms, Grover quantum algorithm [ Phys. Rev. Lett., 79, 325(1997)] achieves quadratic speedup and Bruschweiler hybrid quantum algorithm [Phys. Rev. Lett., 85, 4815(2000)] achieves an exponential speedup. In this paper, we report the experimental realization of the Bruschweiler$ algorithm in a 3-qubit NMR ensemble system. The pulse sequences are used for the algorithms and the measurement method used here is improved on that used by Bruschweiler, namely, instead of quantitatively measuring the spin projection of the ancilla bit, we utilize the shape of the an…
Randomness expansion where one generates a longer sequence of random numbers from a short one is viable in quantum mechanics but not allowed classically. Device-independent quantum randomness expansion provides a randomness resource of the highest security level. Here, we report the first experimental realization of device-independent quantum randomness expansion secure against quantum side information established through quantum probability estimation. We generate $5.47\times10^8$ quantum-proof random bits while consuming $4.39\times10^8$ bits of entropy, expanding our store of randomness by …
We investigate the system-environment information flow from the point of view ofcomplete complementarity relations. We consider some commonly used noisy quantum channels:Amplitude damping, phase damping, bit flip, bit-phase flip, phase flip, depolarizing, and correlatedamplitude damping. By starting with an entangled bipartite pure quantum state, with the linearentropy being the quantifier of entanglement, we study how entanglement is redistributed and turnedinto general correlations between the degrees of freedom of the whole system. For instance, it ispossible to express the entanglement ent…
We show how macroscopically distinct quantum superposition states (Schroedinger cat states) may be used as logical qubit encodings for the correction of spontaneous emission errors. Spontaneous emission causes a bit flip error which is easily corrected by a standard error correction circuit. The method works arbitrarily well as the distance between the amplitudes of the superposed coherent states increases.
We construct two simple error correction schemes adapted to amplitude damping noise for Bacon-Shor codes and investigate their prospects for fault-tolerant implementation. Both consist solely of Clifford gates and require far fewer qubits, relative to the standard method, to achieve correction to a desired order in the damping rate. The first, employing one-bit teleportation and single-qubit measurements, needs only one fourth as many physical qubits, while the second, using just stabilizer measurements and Pauli corrections, needs only half. We show that existing fault-tolerance methods can b…
Quantum random walk finds application in efficient quantum algorithms as well as in quantum network theory. Here we study the mixing time of a discrete quantum walk over a square lattice in presence percolation and decoherence. We consider bit-flip and phase damping noise, and evaluate the instantaneous mixing time for both the cases. Using numerical analysis we show that in case of phase damping noise probability distribution of walker's position is sufficiently close to the uniform distribution after infinite time. However, during the action of bit-flip noise, even after infinite time the to…
We address the system-reservoir dynamics of classical and quantum correlations in the decoherence phenomenon, regarding a two qubit composite system interacting with two independent environments. The most common noise channels (amplitude damping, phase damping, bit flip, bit-phase flip, and phase flip) was studied. By analytical and numerical analysis we found that, contrary to what is usually stated in the literature, decoherence may occurs without entanglement between the system and the environment. We also found that, in some cases, the bipartite quantum correlation initially presented in t…
Encoding schemes and error-correcting codes are widely used in information technology to improve the reliability of data transmission over real-world communication channels. Quantum information protocols can further enhance the performance in data transmission by encoding a message in quantum states, however, most proposals to date have focused on the regime of a large number of uses of the noisy channel, which is unfeasible with current quantum technology. We experimentally demonstrate quantum enhanced communication over an amplitude damping noisy channel with only two uses of the channel per…
An error prevention procedure based on two-particle encoding is proposed for protecting an arbitrary unknown quantum state from dissipation, such as phase damping and amplitude damping. The schemes, which exhibits manifestation of the quantum Zeno effect, is effective whether quantum bits are decohered independently or cooperatively. We derive the working condition of the scheme and argue that this procedure has feasible practical implementation.
We report experimental implementation of discrete Fourier transformation(DFT) on a nuclear magnetic resonance(NMR) quantum computer. Experimental results agree with theoretical results. Using the pulse sequences we introduced, DFT can be realized on any L-bit quantum number in principle.
In contexts where relevant problems can easily attain configuration spaces of enormous sizes, solving Linear Differential Equations (LDEs) can become a hard achievement for classical computers; on the other hand, the rise of quantum hardware can conceptually enable such high-dimensional problems to be solved with a foreseeable number of qubits, whilst also yielding quantum advantage in terms of time complexity. Nevertheless, in order to bridge towards experimental realizations with several qubits and harvest such potential in a short-term basis, one must dispose of efficient quantum algorithms…
We present a strategy to engineer a simple cavity-QED two-bit universal quantum gate using mesoscopic distinct quantum superposition states. The dissipative effect on decoherence and amplitude damping of the quantum bits are analyzed and the critical parameters are presented.
The relaxation of a quantum field stored in a high-$Q$ superconducting cavity is monitored by non-resonant Rydberg atoms. The field, subjected to repetitive quantum non-demolition (QND) photon counting, undergoes jumps between photon number states. We select ensembles of field realizations evolving from a given Fock state and reconstruct the subsequent evolution of their photon number distributions. We realize in this way a tomography of the photon number relaxation process yielding all the jump rates between Fock states. The damping rates of the $n$ photon states ($0\leq n \leq 7$) are found …
We present an n-bit Toffoli gate quantum circuit based on the realization proposed by Barenco, where some of the Toffoli gates in their construction are replaced with Peres gates. This results in a significant cost reduction. Our main contribution is a quantum circuit which simulates the (m+1)-bit Toffoli gate with 32m-96 elementary quantum gates and one garbage bit which is passed unchanged. This paper is a corrected and expanded version of our recent journal publication.
Decoherence and loss will limit the practicality of quantum cryptography and computing unless successful error correction techniques are developed. To this end, we have discovered a new scheme for perfectly detecting and rejecting the error caused by loss (amplitude damping to a reservoir at T=0), based on using a dual-rail representation of a quantum bit. This is possible because (1) balanced loss does not perform a ``which-path'' measurement in an interferometer, and (2) balanced quantum nondemolition measurement of the ``total'' photon number can be used to detect loss-induced quantum jumps…
The Fredkin three-bit gate is universal for computational logic, and is reversible. Classically, it is impossible to do universal computation using reversible two-bit gates only. Here we construct the Fredkin gate using a combination of six two-body reversible (quantum) operators.
Quantum secure communication brings a new direction for information security. As an important component of quantum secure communication, deterministic joint remote state preparation (DJRSP) could securely transmit a quantum state with 100\% success probability. In this paper, we study how the efficiency of DJRSP is affected when qubits involved in the protocol are subjected to noise or decoherence. Taking a GHZ based DJRSP scheme as an example, we study all types of noise usually encountered in real-world implementations of quantum communication protocols, i.e., the bit-flip, phase-flip (phase…
We reckon the behaviour of spin squeezing in tripartite unsqueezed maximally entangled Green- berger-Horne-Zeilinger (GHZ) and W states under various decoherence channels with Kitagawa- Ueda (KU) criteria. In order to search spin squeezing sudden death (SSSD) and signatures of spin squeezing production we use bit flip, phase flip, bit-phase-flip, amplitude damping, phase damping and depolarization channels in the present study. In literature, the influence of decoherence has been studied as a destroying element. On the contrary here we investigate the positive aspect of decoherence, which prod…
We propose a prepare-and-measure scheme for quantum key distribution with 2-bit quantum codes. The protocol is unconditionally secure under whatever type of intercept-and-resend attack. Given the symmetric and independent errors to the transmitted qubits, our scheme can tolerate a bit error rate up to 26% in 4-state protocol and 30% in 6-state protocol, respectively. These values are higher than all currently known threshold values for prepare-and-measure protocols. A specific realization with linear optics is given.
Quantum secure communication provides a new way for protecting the security of information. As an important component of quantum secure communication, remote state preparation (RSP) can securely transmit a quantum state from a sender to a remote receiver. The existence of quantum noise severely affects the security and reliability of quantum communication system. In this paper, we study the method for improving the efficiency of joint RSP (JRSP) subjected to noise with the help of weak measurement and its reversal measurement. Taking a GHZ based deterministic JRSP as an example, we utilize the…
The correlation dynamics is investigated for various bi-partitions of a composite system consisting of two qubits, and two independent and non-identical noisy environments. The two qubits have no direct interaction with each other and locally interact with their environments. Classical and quantum correlations including entanglement are initially prepared only between the two qubits. We find that, contrary to the identical noisy environment case, the entanglement and quantum correlation transfer directions can be controlled by combining different noisy environments. The amplitude damping envir…
Dissipation-driven quantum state engineering uses the environment to steer the state of quantum systems and preserve quantum coherence in the steady state. We show that modulating the damping rate of a microwave resonator generates a vacuum squeezed state of arbitrary squeezing strength, thereby constituting a mechanism allowing perfect squeezing. Given the recent experimental realizations in circuit QED of a microwave resonator with a tunable damping rate [Yin et al., Phys. Rev. Lett. 110, 107001 (2013)], superconducting circuits are an ideal playground to implement this technique. By dispers…
We describe the first experimental realization of the Deutsch-Jozsa quantum algorithm to evaluate the properties of a 2-bit boolean function in the framework of one-way quantum computation. For this purpose a novel two-photon six-qubit cluster state was engineered. Its peculiar topological structure is the basis of the original measurement pattern allowing the algorithm realization. The good agreement of the experimental results with the theoretical predictions, obtained at $\sim$1kHz success rate, demonstrate the correct implementation of the algorithm.
United Nation (UN) security council has fifteen members, out of which five permanent members of the council can use their veto power against any unfavorable decision taken by the council. In certain situation, a member using right to veto may prefer to remain anonymous. This need leads to the requirement of the protocols for anonymous veto which can be viewed as a special type of voting. Recently, a few protocols for quantum anonymous veto have been designed which clearly show quantum advantages in ensuring anonymity of the veto. However, none of the efficient protocols for quantum anonymous v…
The effect of entanglement and correlated noise in a four-player quantum Minority game is investigated. Different time correlated quantum memory channels are considered to analyze the Nash equilibrium payoff of the 1st player. It is seen that the Nash equilibrium payoff is substantially enhanced due to the presence of correlated noise. The behaviour of damping channels (amplitude damping and phase damping) is approximately similar. However, bit-phase flip channel heavily influences the minority game as compared to other channels in the presence of correlated noise. On the other hand, phase fli…
We study the effects of decoherence on the entanglement generated by Unruh effect in noninertial frames by using bit flip, phase damping and depolarizing channels. It is shown that decoherence strongly influences the initial state entanglement. The entanglement sudden death can happens irrespective of the acceleration of the noninertial frame under the action of phase flip and phase damping channels. It is investigated that an early sudden death happens for large acceleration under the depolarizing environment. Moreover, the entanglement increases for a highly decohered phase flip channel.
The first optical proposal for the realization of the two-bit version of the Deutsch-Jozsa algorithm [D. Deutsch and R. Jozsa, Proc. R. Soc. London A {\bf 493}, 553 (1992)] is presented. The proposal uses Stark shifts in an ensemble of atoms and degenerate sources of photons. The photons interact dispersively with an atomic ensemble, leading to an effective Hamiltonian in atom-field basis, which is useful for performing the required two-qubit operations. Combining these with a set of one-qubit operations, the algorithm can be implemented. A discussion of the experimental feasibility of the pro…
We report the realization of a nuclear magnetic resonance (NMR) quantum computer which combines the quantum Fourier transform (QFT) with exponentiated permutations, demonstrating a quantum algorithm for order-finding. This algorithm has the same structure as Shor's algorithm and its speed-up over classical algorithms scales exponentially. The implementation uses a particularly well-suited five quantum bit molecule and was made possible by a new state initialization procedure and several quantum control techniques.
Efficient teleportation is a crucial step for quantum computation and quantum networking. In the case of qubits, four different entangled Bell states have to be distinguished. We have realized a probabilistic, but in principle deterministic, Bell-state analyzer for two photonic quantum bits by the use of a nondestructive controlled-NOT gate based on entirely linear optical elements. This gate was capable of distinguishing between all of the Bell states with higher than 75% fidelity without any noise substraction due to utilizing quantum interference effects.
We discuss the realization of quantum advantage in a system without quantum entanglement but with non-zero quantum discord. We propose an optical realization of symmetric two-qubit $X$-states with controllable anti-diagonal elements. This approach does not requires initially entangled states, and it can generate states that have quantum discord, with or without entanglement. We discuss how quantum advantage can be attained in the context of a two-qubit game. We show that when entanglement is not present, the maximum quantum advantage is 1/3 bit. A comparable quantum advantage, 0.311 bit, can b…
The construction of large, coherent quantum systems necessary for quantum computation remains an entreating but elusive goal, due to the ubiquitous nature of decoherence. Recent progress in quantum error correction schemes have given new hope to this field, but thus far, the codes presented in the literature assume a restricted number of errors and error free encoding, decoding, and measurement. We investigate a specific scenario without these assumptions; in particular, we evaluate a scheme to preserve a single quantum bit against phase damping using a three-qubit encoding based on Shor. By a…
We report the experimental realization of the ''active'' quantum teleportation (QST) of a one-particle entangled qubit. This demonstration completes the original QST protocol and renders it available for actual implementation in quantum computation networks. It is accomplished by implementing a 8m optical delay line and a single-photon triggered fast Electro-Optic Pockels cell. A large value of teleportation ''fidelity'' was attained: F = (90 +/- 2)%. Our work follows the line recently suggested by H. W. Lee and J. Kim, Phys. Rev. A 63, 012305 (2000) and E.Knill, R.Laflamme and G.Milburn Natur…
In a recent paper ([1]=quant-ph/0606035) it is shown how the optimal recovery operation in an error correction scheme can be considered as a semidefinite program. As a possible future improvement it is noted that still better error correction might be obtained by optimizing the encoding as well. In this note we present the result of such an improvement, specifically for the four-bit correction of an amplitude damping channel considered in [1]. We get a strict improvement for almost all values of the damping parameter. The method (and the computer code) is taken from our earlier study of such c…
Quantum key distribution using three states in equiangular configuration combines a security threshold comparable with the one of the Bennett-Brassard 1984 protocol and a quantum bit error rate (QBER) estimation that does not need to reveal part of the key. We implement an entanglement-based version of the Renes 2004 protocol, using only passive optic elements in a linear scheme for the measurement POVM, generating an asymptotic secure key rate of more than 10 kbit/s, with a mean QBER of 1.6%. We then demonstrate its security in the case of finite key and evaluate the key rate for both collect…
The quantum bit error rate is a key quantity in quantum communications. If the quantum channel is the atmosphere, the information is usually encoded in the polarization of a photon. A link budget is required, which takes into account the depolarization of the photon after its interaction with the atmosphere as well as absorption, scattering and atmospheric emissions. An experimental setup for the reproduction of a simple model of the atmosphere is used to evaluate the quantum bit error rate in a BB84 protocol and the results are presented. This result represents a first step toward the realiza…
We report upon a novel principle for realization of a fast nondeterministic random number generator whose randomness relies on intrinsic randomness of the quantum physical processes of photonic emission in semiconductors and subsequent detection by the photoelectric effect. Timing information of detected photons is used to generate binary random digits-bits. The bit extraction method based on restartable clock theoretically eliminates both bias and autocorrelation while reaching efficiency of almost 0.5 bits per random event. A prototype has been built and statistically tested.
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 dec…
The number of steps any classical computer requires in order to find the prime factors of an $l$-digit integer $N$ increases exponentially with $l$, at least using algorithms known at present. Factoring large integers is therefore conjectured to be intractable classically, an observation underlying the security of widely used cryptographic codes. Quantum computers, however, could factor integers in only polynomial time, using Shor's quantum factoring algorithm. Although important for the study of quantum computers, experimental demonstration of this algorithm has proved elusive. Here we report…
We study the occurrence of errors in a continuously decoupled two-qubit state during a $\sqrt{SWAP}$ quantum operation under decoherence. We consider a realization of this quantum gate based on the Heisenberg exchange interaction, which alone suffices for achieving universal quantum computation. Furthermore, we introduce a continuous-dynamical-decoupling scheme that commutes with the Heisenberg Hamiltonian to protect it from the amplitude damping and dephasing errors caused by the system-environment interaction. We consider two error-protection settings. One protects the qubits from both ampli…
We propose a scheme for scalable and universal quantum computation using diatomic bits with conditional dipole-dipole interaction, trapped within an optical lattice. The qubit states are encoded by the scattering state and the bound heteronuclear molecular state of two ultracold atoms per site. The conditional dipole-dipole interaction appears between neighboring bits when they both occupy the molecular state. The realization of a universal set of quantum logic gates, which is composed of single-bit operations and a two-bit controlled-NOT gate, is presented. The readout method is also discusse…
To build a general-purpose quantum computer, it is crucial for the quantum devices to implement classical boolean logic. A straightforward realization of quantum boolean logic is to use auxiliary qubits as intermediate storage. This inefficient implementation causes a large number of auxiliary qubits to be used. In this paper, we have derived a systematic way of realizing any general m-to-n bit combinational boolean logic using elementary quantum gates. Our approach transforms the m-to-n bit classical mapping into a t-bit unitary quantum operation with minimum number of auxiliary qubits, then …
Experimental realization of quantum Zeno dynamics for robust quantum metrology
Shenzhen University（深圳大学）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心（广东））；China Jiliang University（中国计量大学）；Southern University of Science and Technology（南方科技大学）
A scenario for realization of a quantum computer is proposed consisting of spatially distributed q-bits fabricated in a host structure where nuclear spin-spin coupling is mediated by laser pulse controlled electron-nuclear transferred hyperfine (superhyperfine) Fermi contact interaction. Operations illustrating entanglement, nonlocality, and quantum control logic operations are presented and discussed. The notion of universality of quantum computation is introduced and the irreducible conditions are presented. It is demonstrated that the proposed generic scenario for realization of a quantum c…
