The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. Hence, an arbitrarily long quantum computation can be performed reliably, provided that the average probability of error per quantum gate is less than a certain critical value, the accuracy threshold. A quantum computer storing about 10^6 qubits, with a probability of error per quantum gate of order 10^{-6}, would be a formidable factoring engine. Even a smaller, less accurate quantum computer would be able to perform many useful tasks. (This paper is based on a talk presented at the ITP Conference on Quantum Coherence and Decoherence, 15-18 December 1996.)
Multigrid has become a popular method for solving some of the most challenging real-world computational problems, such as computational fluid dynamics (CFD). The reason for this is the very good scaling properties of multigrid, which is often linear, or close to linear, with respect to problem size. In this paper a method is presented, which can be used to implement a quantum version of the multigrid algorithm. The method relies upon a quantum state that is maintained in a equal superposition throughout the calculation, and where information is encoded digitally in the qubits in a way more sim…
We revisit the question of universality in quantum computing and propose a new paradigm. Instead of forcing a physical system to enact a predetermined set of universal gates (e.g., single-qubit operations and CNOT), we focus on the intrinsic ability of a system to act as a universal quantum computer using only its naturally available interactions. A key element of this approach is the realization that the fungible nature of quantum information allows for universal manipulations using quantum information encoded in a subspace of the full system Hilbert space, as an alternative to using physical…
The requirement of performing both single-qubit and two-qubit operations in the implementation of universal quantum logic often leads to very demanding constraints on quantum computer design. We show here how to eliminate the need for single-qubit operations in a large subset of quantum computer proposals: those governed by isotropic and XXZ,XY-type anisotropic exchange interactions. Our method employs an encoding of one logical qubit into two physical qubits, while logic operations are performed using an analogue of the NMR selective recoupling method.
We propose an effective realization of the universal set of elementary quantum gates in solid state quantum computer based on macroscopic (or mesoscopic) resonance systems - multi-atomic coherent ensembles, squids or quantum dots in quantum electrodynamic cavity. We exploit an encoding of logical qubits by the pairs of the macroscopic two- or three-level atoms that is working in a Hilbert subspace of all states inherent to these atomic systems. In this subspace, logical single qubit gates are realized by the controlled reversible transfer of single atomic excitation in the pair via the exchang…
We investigate the problem of Bayesian updating of a probability distribution encoded in the quantum state of n qubits. The updating procedure takes the form of a quantum algorithm that prepares the quantum register in the state representing the posterior distribution. Depending on how the prior distribution is given, we describe two implementations, one probabilistic and one deterministic, of such an algorithm in the standard model of a quantum computer.
Aiming the construction of quantum computers and quantum communication systems based on optical devices, in this work we present possible implementations of quantum and classical CNOTs gates, as well an optical setup for generation and distribution of bipartite entangled states, using linear optical devices and photon number quantum non-demolition measurement.
Large-scale universal quantum computing requires the implementation of quantum error correction (QEC). While the implementation of QEC has already been demonstrated for quantum memories, reliable quantum computing requires also the application of nontrivial logical gate operations to the encoded qubits. Here, we present examples of such operations by implementing, in addition to the identity operation, the NOT and the Hadamard gate to a logical qubit encoded in a five qubit system that allows correction of arbitrary single qubit errors. We perform quantum process tomography of the encoded gate…
Recently a scheme has been proposed for constructing quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. One of the difficult steps in this scheme is the preparation of the encoded states. We show how these states can be generated by coupling a continuous quantum variable to a single qubit. An ion trap quantum computer provides a natural setting for a continuous system coupled to a qubit. We discuss how encoded states may be generated in an ion trap.
I revisit the ideas underlying dynamical decoupling methods within the framework of quantum information processing, and examine their potential for direct implementations in terms of encoded rather than physical degrees of freedom. The usefulness of encoded decoupling schemes as a tool for engineering both closed- and open-system encoded evolutions is investigated based on simple examples.
Quantum computing promises to provide exponential speed-ups to certain classes of problems. In many such algorithms, a classical vector $\mathbf{b}$ is encoded in the amplitudes of a quantum state $\left |b \right >$. However, efficiently preparing $\left |b \right >$ is known to be a difficult problem because an arbitrary state of $Q$ qubits generally requires approximately $2^Q$ entangling gates, which results in significant decoherence on today's Noisy Intermediate Scale Quantum (NISQ) computers. We present a deterministic (nonvariational) algorithm that allows one to flexibly reduce the qu…
We propose an effective set of elementary quantum gates which provide an encoded universality and demonstrate the physical feasibility of these gates for the solid-state quantum computer based on the multi-atomic systems in the QED cavity. We use the two-qubit encoding and swapping-based operations to simplify a physical realization of universal quantum computing and add the immunity to a number of errors. This approach allows to implement any encoded single-qubit operation by three elementary gates and the encoded controlled- NOT operation can be performed in a single step. The considerable a…
We propose a deterministic yet fully passive scheme to transfer the quantum state from a frequency-encoded photon to the spin of a quantum-dot mediated by a nanophotonic waveguide. We assess the quality of the state transfer by studying the effects of all relevant experimental imperfections on the state-transfer fidelity. We show that a transfer fidelity exceeding 95% is achievable for experimentally realistic parameters. Our work sets the stage for deterministic solid-state quantum networks tailored to frequency-encoded photonic qubits.
Hypothesis elimination is a special case of Bayesian updating, where each piece of new data rules out a set of prior hypotheses. We describe how to use Grover's algorithm to perform hypothesis elimination for a class of probability distributions encoded on a register of qubits, and establish a lower bound on the required computational resources.
In this work, we present active and passive linear optical setups for error correction in quantum communication systems that employ polarization of single-photon and mesoscopic coherent states. Applications in quantum communication systems are described.
We investigate effective noise channels for encoded quantum systems with and without active error correction. Noise acting on physical qubits forming a logical qubit is thereby described as a logical noise channel acting on the logical qubits, which leads to a significant decrease of the effective system dimension. This provides us with a powerful tool to study entanglement features of encoded quantum systems. We demonstrate this framework by calculating lower bounds on the lifetime of distillable entanglement and the negativity for encoded multipartite qubit states with different encodings. A…
We present a linear optics quantum computation scheme with a greatly reduced cost in resources compared to KLM. The scheme makes use of elements from cluster state computation and achieves comparable resource usage to those schemes while retaining the circuit based approach of KLM.
We present a hybrid scheme for quantum computation that combines the modular structure of elementary building blocks used in the circuit model with the advantages of a measurement-based approach to quantum computation. We show how to construct optimal resource states of minimal size to implement elementary building blocks for encoded quantum computation in a measurement-based way, including states for error correction and encoded gates. The performance of the scheme is determined by the quality of the resource states, where within this error model we find a threshold of the order of 10% local …
In order to eliminate disturbing effects of decoherence, encoding of quantum information in decoherence-free subspaces has been suggested. We analyze the benefits of this concept for a quantum register that is realized in a spin chain in contact with a common bosonic bath. Within a dissipation-less model we provide explicit analytical results for the average fidelity of plain and encoded quantum registers. For the investigation of dissipative spin-boson couplings we employ a master equation of Bloch-Redfield type.
Quantum state transfer and teleportation, with qubits encoded in internal states of the atoms in cavities, among spatially separated nodes of a quantum network in decoherence-free subspace are proposed, based on a cavity-assisted interaction by single-photon pulses. We show in details the implementation of a logic-qubit Hadamard gate and a two-logic-qubit conditional gate, and discuss the experimental feasibility of our scheme.
A recently developed theory for eliminating decoherence and design constraints in quantum computers, ``encoded recoupling and decoupling'', is shown to be fully compatible with a promising proposal for an architecture enabling scalable ion-trap quantum computation [D. Kielpinski et al., Nature 417, 709 (2002)]. Logical qubits are encoded into pairs of ions. Logic gates are implemented using the Sorensen-Molmer (SM) scheme applied to pairs of ions at a time. The encoding offers continuous protection against collective dephasing. Decoupling pulses, that are also implemented using the SM scheme d…
Transversal gates play an important role in the theory of fault-tolerant quantum computation due to their simplicity and robustness to noise. By definition, transversal operators do not couple physical subsystems within the same code block. Consequently, such operators do not spread errors within code blocks and are, therefore, fault tolerant. Nonetheless, other methods of ensuring fault tolerance are required, as it is invariably the case that some encoded gates cannot be implemented transversally. This observation has led to a long-standing conjecture that transversal encoded gate sets canno…
Polarizations of single-photon pulses have been controlled with long-term stability of more than 10 hours by using an active feedback technique for auto-compensation of unpredictable polarization scrambling in long-distance fiber. Experimental tests of long-term operations in 50, 75 and 100 km fibers demonstrated that such a single-photon polarization control supported stable polarization encoding in long-distance fibers to facilitate stable one-way fiber system for polarization-encoded quantum key distribution, providing quantum bit error rates below the absolute security threshold.
Quantum optical metrology aims to identify ultimate sensitivity bounds for the estimation of parameters encoded into quantum states of the electromagnetic field. In many practical applications, including imaging, microscopy, and remote sensing, the parameter of interest is not only encoded in the quantum state of the field, but also in its spatio-temporal distribution, i.e. in its mode structure. In this mode-encoded parameter estimation setting, we derive an analytical expression for the quantum Fisher information valid for arbitrary multimode Gaussian fields. To illustrate the power of our a…
We show how to carry out quantum logical operations (controlled-not and Toffoli gates) on encoded qubits for several encodings which protect against various 1-bit errors. This improves the reliability of these operations by allowing one to correct for one bit errors which either preexisted or occurred in course of operation. The logical operations we consider allow one to cary out the vast majority of the steps in the quantum factoring algorithm. Thus, our results help bring quantum factoring and other quantum computations closer to reality
We briefly review what a quantum computer is, what it promises to do for us, and why it is so hard to build one. Among the first applications anticipated to bear fruit is quantum simulation of quantum systems. While most quantum computation is an extension of classical digital computation, quantum simulation differs fundamentally in how the data is encoded in the quantum computer. To perform a quantum simulation, the Hilbert space of the system to be simulated is mapped directly onto the Hilbert space of the (logical) qubits in the quantum computer. This type of direct correspondence is how da…
A major milestone of quantum error correction is to achieve the fault-tolerance threshold beyond which quantum computers can be made arbitrarily accurate. This requires extraordinary resources and engineering efforts. We show that even without achieving full fault tolerance, quantum error detection is already useful on the current generation of quantum hardware. We demonstrate this experimentally by executing an end-to-end chemical calculation for the hydrogen molecule encoded in the [[4, 2, 2]] quantum error-detecting code. The encoded calculation with logical qubits significantly improves th…
A class of architectures is advanced for cluster state quantum computation using quantum dots. These architectures include using single and multiple dots as logical qubits. Special attention is given to the supercoherent qubits introduced by Bacon, Brown, and Whaley [Phys. Rev. Lett. {\bf 87}, 247902 (2001)] for which we discuss the effects of various errors, and present means of error protection.
In this paper we present Quanrum Encoded Quantum Evolutionary Algorithm (QEQEA) and compare its performance against a a classical GPU accelerated Genetic Algorithm (GPUGA). The proposed QEQEA differs from existing quantum evolutionary algorithms in several points: representation of candidates circuits is using qubits and qutrits and the proposed evolutionary operators can in theory be implemented on quantum computer provided a classical control exists. The synthesized circuits are obtained by a set of measurements performed on the encoding units of quantum representation. Both algorithms are a…
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…
We present a paradigm for constructing approximate quantum circuits from reversible classical circuits that operate on many possible encodings of an input and send almost all encodings of that input to an encoding of the correct output. We introduce oblivious carry runways, which use piecewise addition circuits to perform approximate encoded additions and reduce the asymptotic depth of addition to $O(\lg \lg n)$. We show that the coset representation of modular integers (Zalka 2006) is an approximate encoded modular addition, and that it can be used in combination with oblivious carry runways.…
We present a novel one-way quantum key distribution protocol based on 3-dimensional quantum state, a qutrit, that encodes two qubits in its 2-dimensional subspaces. The qubits hold the classical bit information that has to be shared between the legitimate users. Alice sends such a qutrit to Bob where he decodes one of the qubit and measures it along the random Pauli basis. This scheme has higher secure key rate at longer transmission distance than the standard BB84 protocol.
Quantum key distribution (QKD) protocols based on high-dimensional quantum states have shown the route to increase the key rate generation while benefiting of enhanced error tolerance, thus overcoming the limitations of two-dimensional QKD protocols. Nonetheless, the reliable transmission through fiber links of high-dimensional quantum states remains an open challenge that must be addressed to boost their application. Here, we demonstrate the reliable transmission over a 2 km long multicore fiber of path-encoded high-dimensional quantum states. Leveraging on a phase-locked loop system, a stabl…
We propose an effective realization of a complete set of elementary quantum gates in the solid-state quantum computer based on the multi-atomic coherent (MAC-) ensembles in the QED cavity. Here, we use the two-ensemble qubit encoding and swapping-based operations that together provide implementation of any encoded single-qubit operation by three elementary gates and the encoded controlled-NOT operation is performed in a single step. This approach simplifies a physical realization of universal quantum computing and adds the immunity to a number of errors. We also demonstrate that the proposed a…
Quantum secure data transfer is an important topic for quantum cyber security. We propose a scheme to realize quantum secure data transfer in the basis of quantum secure direct communication (QSDC). In this proposal, the transmitted data is encoded in the pulse shape of a single optical qubit, which is emitted from a trapped atom owned by the sender and received by the receiver with another trapped atom. The encoding process can be implemented with high fidelity by controlling the time-dependent driving pulse on the trapped atom to manipulate the Rabi frequency in accordance with the target pu…
The generation of entanglement between distant atoms via single photons is the basis for networked quantum computing, a promising route to large-scale trapped-ion and trapped-atom processors. Locating the emitter within an optical cavity provides an efficient matter-light interface, but mirror-induced birefringence within the cavity introduces time-dependence to the polarisation of the photons produced. We show that such `polarisation oscillation' effects can lead to severe loss of fidelity in the context of two-photon, polarisation encoded measurement-based remote entanglement schemes. It is …
We consider the cloning of sequences of qubits prepared in the states used in the BB84 or 6-state quantum cryptography protocol, and show that the single-qubit fidelity is unaffected even if entire sequences of qubits are prepared in the same basis. This result is of great importance for practical quantum cryptosystems because it reduces the need for high-speed random number generation without impairing on the security against finite-size attacks.
In the context of multiparameter quantum estimation theory, we investigate the construction of linear schemes in order to infer two classical parameters that are encoded in the quadratures of two quantum coherent states. The optimality of the scheme built on two phase-conjugate coherent states is proven with the saturation of the quantum Cramér--Rao bound under some global energy constraint. In a more general setting, we consider and analyze a variety of $n$-mode schemes that can be used to encode $n$ classical parameters into $n$ quantum coherent states and then estimate all parameters optima…
Free-space time-bin encoded quantum key distribution from near- to mid-infrared wavelengths
QTI s.r.l.（QTI有限公司）；CNR - Istituto Nazionale di Ottica (CNR-INO)（意大利国家研究委员会光学研究所）；LENS - European Laboratory for Non-Linear Spectroscopy（欧洲非线性光谱学实验室）；Università degli Studi di Firenze（佛罗伦萨大学）
Quantum cryptographic protocols based on complementarity are nonsecure against attacks in which complementarity is imitated with classical resources. The Kochen-Specker (KS) theorem provides protection against these attacks, without requiring entanglement or spatially separated composite systems. We analyze the maximum tolerated noise to guarantee the security of a KS-protected cryptographic scheme against these attacks, and describe a photonic realization of this scheme using hybrid ququarts defined by the polarization and orbital angular momentum of single photons.
We propose and demonstrate a quantum key distribution scheme in higher-order $d$-dimensional alphabets using spatial degrees of freedom of photons. Our implementation allows for the transmission of 4.56 bits per sifted photon, while providing improved security: an intercept-resend attack on all photons would induce an error rate of 0.47. Using our system, it should be possible to send more than a byte of information per sifted photon.
Quantum computation can be performed by encoding logical qubits into the states of two or more physical qubits, and controlling a single effective exchange interaction and possibly a global magnetic field. This "encoded universality" paradigm offers potential simplifications in quantum computer design since it does away with the need to perform single-qubit rotations. Here we show that encoded universality schemes can be combined with quantum error correction. In particular, we show explicitly how to perform fault-tolerant leakage correction, thus overcoming the main obstacle to fault-tolerant…
In this paper we demonstrate an active polarization drift compensation scheme for optical fibres employed in a quantum key distribution experiment with polarization encoded qubits. The quantum signals are wavelength multiplexed in one fibre along with two classical optical side channels that provide the control information for the polarization compensation scheme. This set-up allows us to continuously track any polarization change without the need to interrupt the key exchange. The results obtained show that fast polarization rotations of the order of 40*pi rad/s are effectively compensated fo…
Recently, Lechner, Hauke and Zoller [Science Advances, 1(9)e1500838, (2015)] have proposed a quantum annealing architecture, in which a classical spin glass with all-to-all connectivity is simulated by a spin glass with geometrically local interactions. We interpret this architecture as a classical error-correcting code, which is highly robust against weakly correlated bit-flip noise, and we analyze the code's performance using a belief-propagation decoding algorithm. Our observations may also apply to more general encoding schemes and noise models.
Quantum bits are more robust to noise when they are encoded non-locally. In such an encoding, errors affecting the underlying physical system can then be detected and corrected before they corrupt the encoded information. In 2001, Gottesman, Kitaev and Preskill (GKP) proposed a hardware-efficient instance of such a qubit, which is delocalised in the phase-space of a single oscillator. However, implementing measurements that reveal error syndromes of the oscillator while preserving the encoded information has proved experimentally challenging: the only realisation so far relied on post-selectio…
We investigate secret key rates for the quantum repeater using encoding [L. Jiang et al., Phys. Rev. A 79, 032325 (2009)] and compare them to the standard repeater scheme by Briegel, Dür, Cirac, and Zoller. The former scheme has the advantage of a minimal consumption of classical communication. We analyze the trade-off in the secret key rate between the communication time and the required resources. For this purpose, we introduce an error model for the repeater using encoding which allows for input Bell states with a fidelity smaller than one, in contrast to the model given in [L. Jiang et al.…
Decoherence-induced leakage errors can couple a physical or encoded qubit to other levels, thus potentially damaging the qubit. They can therefore be very detrimental in quantum computation and require special attention. Here we present a general method for removing such errors by using simple decoupling and recoupling pulse sequences. The proposed gates are experimentally accessible in a variety of promising quantum computing proposals.
Quantum teleportation is considered a basic primitive in many quantum information processing tasks and has been experimentally confirmed in various photonic and matter-based setups. Here, we consider teleportation of quantum information encoded in modes of a fermionic field. In fermionic systems, superselection rules lead to a more differentiated picture of entanglement and teleportation. In particular, one is forced to distinguish between single-mode entanglement swapping, and qubit teleportation with or without authentication via Bell inequality violation, as we discuss here in detail. We fo…
