The cluster state model for quantum computation has paved the way for schemes that allow scalable quantum computing, even when using non-deterministic quantum gates. Here the initial step is to prepare a large entangled state using non-deterministic gates. A key question in this context is the relative efficiencies of different `strategies', i.e. in what order should the non-deterministic gates be applied, in order to maximize the size of the resulting cluster states? In this paper we consider this issue in the context of `large' cluster states. Specifically, we assume an unlimited resource of qubits and ask what the steady state rate at which `large' clusters are prepared from this resource is, given an entangling gate with particular characteristics. We measure this rate in terms of the number of entangling gate operations that are applied. Our approach works for a variety of different entangling gate types, with arbitrary failure probability. Our results indicate that strategies whereby one preferentially bonds together identical qubits are considerably more efficient than those in which one does not. Additionally, compared to earlier analytic results, our numerical study offers substantially improved resource scaling.
Cavity-optomechanics is an ideal platform for the generation non-Gaussian quantum states due to the anharmonic interaction between the light field and the mechanical oscillator; but exactly this interaction also impedes the preparation in pure states of the light field. In this paper we derive a driving protocol that helps to exploit the anharmonic interaction for state preparation, and that ensures that the state of the light field remains close-to-pure. This shall enable the deterministic preparation of photon Fock states or coherent superpositions thereof.
We propose a deterministic remote state preparation scheme for photon polarization qubit states, where entanglement, local operations and classical communication are used. By consuming one maximally entangled state and two classical bits, an arbitrary (either pure or mixed) qubit state can be prepared deterministically at a remote location. We experimentally demonstrate the scheme by remotely preparing 12 pure states and 6 mixed states. The fidelities between the desired and achieved states are all higher than 0.99 and have an average of 0.9947.
We characterize the long-time projective behavior of the stochastic master equation describing a continuous, collective spin measurement of an atomic ensemble both analytically and numerically. By adding state based feedback, we show that it is possible to prepare highly entangled Dicke states deterministically.
Quantum error correction and fault-tolerant quantum computation are two fundamental concepts which make quantum computing feasible. While providing a theoretical means with which to ensure the arbitrary accuracy of any quantum circuit, fault-tolerant error correction is predicated upon the robust preparation of logical states. An optimal direct circuit and a more complex fault-tolerant circuit for the preparation of the [[7,1,3]] Steane logical-zero are simulated in the presence of discrete quantum errors to quantify the regime within which fault-tolerant preparation of logical states is prefe…
We consider the two-step method [A. R. Kuzmak and V. M. Tkachuk, Phys. Lett. A 378 (2014) 1469] for preparation of an arbitrary quantum gate on two spins with anisotropic Heisenberg interaction. At the first step, the system evolves during some period of time. At the second step, we apply pulsed magnetic field individually to each spin. We obtain the conditions for realization of SWAP, iSWAP, $\sqrt{SWAP}$ and entangled gates. Finally, we consider the implementation of this method on the physical system of ultracold atoms in optical lattice.
Fault-tolerant quantum computation using quantum error-correcting codes requires fault-tolerant constructions of nontransversal gates. Shor proposed a fault-tolerant construction of a nontransversal gate, i.e., the Toffoli gate for a family of the Calderbank-Shor-Steane codes which has even-weight stabilizer generators and odd-weight logical operators. In fact, as shown in this paper, error propagations in the ancilla preparation of Shor's construction lead to logical errors. This work provides a solution to this problem through the insertion of bit flip error correction. Finally, error rates …
We propose a class of preparation schemes for orbital angular momentum and polarisation qubits carried by single photons or classical states of light based on coherent feedback control by an ancillary degree of freedom of light. The preparation methods use linear optics and include the transcription of an arbitrary polarisation state onto a two-level OAM system (swap) for arbitrary OAM values plus/minus "l" within a light beam, i.e. without spatial interferometer. The preparations can be carried out with unit efficiency independent from the potentially unknown initial state of the system. More…
We propose a non-Gaussian continuous variable (CV) gate which is able to conditionally produce superposition of two "copies" of an arbitrary input state well separated in the coordinate and momentum plane - a Schrödinger cate state. The gate uses cubic phase state of an ancillary oscillator as a non-Gaussian resource, an entangling Gaussian gate, and homodyne measurement which provides nonunique information about the target system canonical variables, which is a key feature of the scheme. We show that this nonuniqueness manifests problems which may arise by extension of the Heisenberg picture …
A scheme is presented for realizing a quantum phase gate with three-level atoms, solid-state qubits--often called artificial atoms, or ions that share a quantum data bus such as a single mode field in cavity QED system or a collective vibrational state of trapped ions. In this scheme, the conditional phase shift is tunable and controllable via the total effective interaction time. Furthermore, we show that the method can be used for effective preparation of graph-state entanglement, which are important resources for quantum computation, quantum error correction, studies of multiparticle entang…
We propose a scheme to perform basic gates of quantum computing and prepare entangled states in a system with cold trapped ions located in a single mode optical cavity. General quantum computing can be made with both motional state of the trapped ion and cavity state being qubits. We can also generate different kinds of entangled states in such a system without state reduction, and can transfer quantum states from the ion in one trap to the ion in another trap. Experimental requirement for achieving our scheme is discussed.
A key task in quantum computation is the application of a sequence of gates implementing a specific unitary operation. However, the decomposition of an arbitrary unitary operation into simpler quantum gates is a nontrivial problem. Here we propose a general and robust protocol to decompose any target unitary into a sequence of Pauli rotations. The procedure involves identifying a commuting subset of Pauli operators having a high trace overlap with the target unitary, followed by a numerical optimization of their corresponding rotation angles. The protocol is demonstrated by decomposing several…
We report a scheme for deterministic preparation of non-Gaussian quantum states on-demand. In contrast to probabilistic approaches for preparation of non-Gaussian quantum states, conditioned on photon subtraction or addition, we present a scheme that can prepare non-Gaussian quantum states on-demand, by applying a unitary transformation which removes the Gaussianity of measurement statistics of field quadratures, namely a quadrature rotation via transmission through a beam-splitter, using a two-mode photon-number squeezed state as input. The resulting state exhibits a quantum vortex structure …
In quantum computation every unitary operation can be decomposed into quantum circuits-a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-NOT (CNOT) gates. Two measures are important when judging the complexity of the circuit: the total number of CNOT gates needed to implement it and the depth of the circuit, measured by the minimal number of computation steps needed to perform it. Here we give an explicit and simple quantum circuit scheme for preparation of arbitrary quantum states, which can directly utilize any decomposition scheme for arbitr…
We implement all single-qubit operations with fidelities significantly above the minimum threshold required for fault-tolerant quantum computing, using a trapped-ion qubit stored in hyperfine "atomic clock" states of $^{43}$Ca$^+$. We measure a combined qubit state preparation and single-shot readout fidelity of 99.93%, a memory coherence time of $T^*_2=50$ seconds, and an average single-qubit gate fidelity of 99.9999%. These results are achieved in a room-temperature microfabricated surface trap, without the use of magnetic field shielding or dynamic decoupling techniques to overcome technica…
We present a two-step exact remote state preparation protocol of an arbitrary qubit with the aid of a three-particle Greenberger-Horne-Zeilinger state. Generalization of this protocol for higher-dimensional Hilbert space systems among three parties is also given. We show that only single-particle von Neumann measurement, local operation and classical communication are necessary. Moreover, since the overall information of the quantum state can be divided into two different parts, which may be at different locations, this protocol may be useful in the quantum information field.
A scheme for the deterministic joint remote preparation of a four- qubit cluster-type state using only two Greenberger-Horne-Zeilinger (GHZ) states as quantum channels is presented. In this scheme, the first sender per- forms a two-qubit projective measurement according to the real coefficient of the desired state. Then, the other sender utilizes the measurement result and the complex coefficient to perform another projective measurement. To obtain the desired state, the receiver applies appropriate unitary operations to his/her own two qubits and two CNOT operations to the two ancillary ones.…
We propose a deterministic remote state preparation (RSP) scheme for preparing an arbitrary (including pure and mixed) qubit, where a partially entangled state and finite classical communication are used. To our knowledge, our scheme is the first RSP scheme that fits into this category. One other RSP scheme proposed by Berry shares close features, but can only be used to prepare an arbitrary pure qubit. Even so, our scheme saves classical communication by approximate 1 bit per prepared qubit under equal conditions. When using a maximally entangled state, the classical communication for our sch…
Several physical architectures allow for measurement-based quantum computing using sequential preparation of cluster states by means of probabilistic quantum gates. In such an approach, the order in which partial resources are combined to form the final cluster state turns out to be crucially important. We determine the influence of this classical decision process on the expected size of the final cluster. Extending earlier work, we consider different quantum gates operating at various probabilites of success. For finite resources, we employ a computer algebra system to obtain the provably opt…
We perform optimal-control-theory calculations to determine the minimum number of two-qubit CNOT gates needed to perform quantum state preparation and unitary operator synthesis for few-qubit systems. By considering all possible gate configurations, we determine the maximum achievable fidelity as a function of quantum circuit size. This information allows us to identify the minimum circuit size needed for a specific target operation and enumerate the different gate configurations that allow a perfect implementation of the operation. We find that there are a large number of configurations that …
We introduce a Bayesian method for the estimation of single qubit errors in quantum devices, and use it to characterize these errors on three 27-qubit superconducting qubit devices. We self-consistently estimate up to seven parameters of each qubit's state preparation, readout, and gate errors, analyze the stability of these errors as a function of time, and demonstrate easily implemented approaches for mitigating different errors before a quantum computation experiment. On the investigated devices we find non-negligible qubit reset errors that cannot be parametrized as a diagonal mixed state,…
The preparation stage of optical qubits is an essential task in all the experimental setups employed for the test and demonstration of Quantum Optics principles. We consider a deterministic protocol for the preparation of qubits as a superposition of vacuum and one photon number states, which has the advantage to reduce the amount of resources required via phase-sensitive measurements using a local oscillator ('dyne detection'). We investigate the performances of the protocol using different phase measurement schemes: homodyne, heterodyne, and adaptive dyne detection (involving a feedback loop…
State preparation is a process encoding the classical data into the quantum systems. Based on quantum phase estimation, we propose the specific quantum circuits for a deterministic state preparation algorithm and a probabilistic state preparation algorithm. To discuss the gate complexity in these algorithms, we decompose the diagonal unitary operators included in the phase estimation algorithms into the basic gates. Thus, we associate the state preparation problem with the decomposition problem of the diagonal unitary operators. We analyse the fidelities in the two algorithms and discuss the s…
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…
Scalable high-fidelity and near-deterministic preparation of large photon-number states
College of Physics, Nanjing University of Aeronautics and Astronautics（南京航空航天大学物理学院）；China Mobile (Suzhou) Software Technology Co., Ltd.（中国移动（苏州）软件技术有限公司）
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…
Magic state distillation is one of the leading candidates for implementing universal fault-tolerant logical gates. However, the distillation circuits themselves are not fault-tolerant, so there is additional cost to first implement encoded Clifford gates with negligible error. In this paper we present a scheme to fault-tolerantly and directly prepare magic states using flag qubits. One of these schemes uses a single extra ancilla, even with noisy Clifford gates. We compare the physical qubit and gate cost of this scheme to the magic state distillation protocol of Meier, Eastin, and Knill, whic…
We obtain a simple formula for the average gate fidelity of a linear map acting on qudits. It is given in terms of minimal sets of pure state preparations alone, which may be interesting from the experimental point of view. These preparations can be seen as the outcomes of certain minimal positive operator valued measures. The connection of our results with these generalized measurements is briefly discussed.
Harmonic oscillators count among the most fundamental quantum systems with important applications in molecular physics, nanoparticle trapping, and quantum information processing. Their equidistant energy level spacing is often a desired feature, but at the same time a challenge if the goal is to deterministically populate specific eigenstates. Here, we show how interference in the transition amplitudes in a bichromatic laser field can suppress the sequential climbing of harmonic oscillator states (Kapitza-Dirac blockade) and achieve selective excitation of energy eigenstates, Schrödinger cats …
The high degree of control available over individual atoms enables precision tests of fundamental physical concepts. In this Letter, we experimentally study how precision measurements can be improved by preparing entangled states immune to the dominant source of decoherence. Using \Ca ions, we explicitly demonstrate the advantage from entanglement on a precision test of local Lorentz invariance for the electron. Reaching the quantum projection noise limit set by quantum mechanics, we observe for bipartite entangled states the expected gain of a factor of two in the precision. Under specific co…
We show how to prepare any graph state of up to 12 qubits with: (a) the minimum number of controlled-Z gates, and (b) the minimum preparation depth. We assume only one-qubit and controlled-Z gates. The method exploits the fact that any graph state belongs to an equivalence class under local Clifford operations. We extend up to 12 qubits the classification of graph states according to their entanglement properties, and identify each class using only a reduced set of invariants. For any state, we provide a circuit with both properties (a) and (b), if it does exist, or, if it does not, one circui…
We show how techniques from machine learning and optimization can be used to find circuits of photonic quantum computers that perform a desired transformation between input and output states. In the simplest case of a single input state, our method discovers circuits for preparing a desired quantum state. In the more general case of several input and output relations, our method obtains circuits that reproduce the action of a target unitary transformation. We use a continuous-variable quantum neural network as the circuit architecture. The network is composed of several layers of optical gates…
Quantum state preparation is an important class of quantum algorithms that is employed as a black-box subroutine in many algorithms, or used by itself to generate arbitrary probability distributions. We present a novel state preparation method that utilizes less quantum computing resource than the existing methods. Two variants of the algorithm with different emphases are introduced. One variant uses fewer qubits and no controlled gates, while the other variant potentially requires fewer gates overall. A general analysis is given to estimate the number of qubits necessary to achieve a desired …
Deterministic preparation of squeezed and non-Gaussian states in coupled qubit-boson systems
East China Normal University（华东师范大学）；Huzhou Normal University（湖州师范学院）；New York University Shanghai（纽约大学上海分校）；NYU-ECNU Institute of Physics at NYU Shanghai（纽约大学上海-华东师范大学物理研究所）；New York University Abu Dhabi（纽约大学阿布扎比分校）；New York University（纽约大学）
We propose a deterministic SWAP gate for spatially encoded qubits. The gate is constructed from waveguide crossings, Mach Zender Interferometers and phase shifters providing the gate reconfigurability. Through manipulating the phase of the phase shifters, we can apply either the SWAP or identity gates. As an essential element of nearest neighbor qubit networks, the SWAP gate has a simple structure and presents minimal overhead, making it viable for universal quantum computation.
We theoretically propose an alternative method to realize a deterministic SWAP gate using shortcuts to adiabatic passage based on the approach of Lewis- Riesenfeld invariants in cavity quantum electronic dynamics (QED). By combining Lewis-Riesenfeld invariants with quantum Zeno dynamics, the SWAP gate can be achieved deterministically. The strict numerical results show that our scheme is a fast and robust approach to achieve SWAP gate.
As one of the most prominent subfields of quantum communication research, remote state preparation (RSP) plays a crucial role in quantum networks. Here we present a deterministic remote state preparation scheme to prepare an arbitrary two-qubit state via a seven-qubit entangled channel created from Borras \emph{et al.} state. Quantum noises are inherent to each and every protocol for quantum communication that is currently in use, putting the integrity of quantum communication systems and their dependability at risk. The initial state of the system was a pure quantum state, but as soon as ther…
We establish bounds to the necessary resource consumption when building up cluster states for one-way computing using probabilistic gates. Emphasis is put on state preparation with linear optical gates, as the probabilistic character is unavoidable here. We identify rigorous general bounds to the necessary consumption of initially available maximally entangled pairs when building up one-dimensional cluster states with individually acting linear optical quantum gates, entangled pairs and vacuum modes. As the known linear optics gates have a limited maximum success probability, as we show, this …
We discuss techniques for producing, manipulating and measureing qubits encoded optically as vacuum and single photon states. We show that a universal set of non-deterministic gates can be constructed using linear optics and photon counting. We investigate the efficacy of a test gate given realistic detector efficiencies.
We theoretically present a method to realize a deterministic photon-photon (SWAP)^{1/2} gate using a three-level lambda system interacting with single photons in reflection geometry. The lambda system is used completely passively as a temporary memory for a photonic qubit; the initial state of the lambda system may be arbitrary, and active control by auxiliary fields is unnecessary throughout the gate operations. These distinct merits make this entangling gate suitable for deterministic and scalable quantum computation.
Compared with a qubit, a qudit (i.e., $d$-level or $d$-state quantum system) provides a larger Hilbert space to store and process information. On the other hand, qudit-based hybrid quantum computing usually requires performing hybrid quantum gates with qudits different in their nature or in their encoding format. In this work, we consider the qutrit case, i.e., the case for a qudit with $d$=3. We propose a simple method to realize a hybrid quantum controlled-SUM gate with one superconducting (SC) qutrit and a cat-state qutrit. This gate plus single-qutrit gates form a universal set of ternary …
We propose deterministic realizations of nonlinear phase gates by repeating non-commuting Rabi interactions feasible between a harmonic oscillator and {\em only} a single two-level ancillary qubit. We show explicitly that the key nonclassical features of the states after the ideal cubic phase gate and the quartic phase gate are reproduced faithfully by the engineered operators. This theoretical proposal completes the universal set of operators in continuous variable quantum computation.
We theoretically study operations with a four-level superconducting circuit as a two-qubit system. Using a mapping on a two-qubit system, we show how to implement iSWAP gates and Hadamard gates through pulses on transitions between particular pairs of energy levels. Our approach allows one to prepare pure two-qubit entangled states with desired form of reduced density matrices of the same purity and, in particular, arbitrary identical reduced states of qubits. We propose using schemes for the Hadamard gate and two-qubit entangled states with identical reduced density matrices in order to verif…
