We present a study on preparing and manipulating path-like temporal-mode (TM) qubits based on third-order nonlinear interactions. Specifically, we consider the process of frequency conversion via difference frequency generation. To prepare a qubit, we aim to use Gaussian input states to a nonlinear waveguide. The coupling between the input state and a specific TM is maximized, obtaining qubits prepared with fidelities close to one. TMs evolve linearly within the medium; therefore, it is possible to define rotations around any axis contained in the $xy$ plane, allowing spanning the full Bloch sphere in two steps. Particularly, we present a method to obtain any of the Pauli quantum gates by varying geometric or user-accessible parameters in a given experimental configuration. Our study allows for experimentally feasible proposals capable of controllable arbitrary qubit transformations.
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…
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 …
This work presents a feasible design of an integrated photonic circuit performing as a device for single-qubit preparation and rotations through the third-order nonlinear process of difference frequency generation (DFG) and defined in the temporal mode basis. The first stage of our circuit includes the generation of heralded single photons by spontaneous four-wave mixing in a micro-ring cavity engineered for delivering a single-photon state in a unique temporal mode. The second stage comprises the implementation of DFG in a spiral waveguide with controlled dispersion properties for reaching co…
Quantum state preparation plays an equally important role with quantum operations and measurements in quantum information processing. The previous methods of preparing initial state for bulk quantum computation all have inevitable disadvantages, such as, requiring multiple experiments, causing loss of signals, or requiring molecules with restrictive structure. In this work, three kinds of quantum circuits are introduced to prepare the pseudo-pure states of ($n-1$) qubits in the Hilbert space of $n$ coupled spins which merely need the assist of one ancilla spin and two experiments independent o…
Verifiable blind quantum computing allows a client with poor quantum devices to delegate universal quantum computing to a remote quantum server in such a way that the client's privacy is protected and the honesty of the server is verified. In existing protocols, the client has to send single-qubit states to the server. These states might be decohered by the channel noise. Furthermore, the client hides some "trap" qubits in the server's register so that the client can detect the server's deviation. In reality, however, these trap qubits are disturbed by imperfect operations by the server, which…
Entanglement boosting: Low-volume logical Bell pair preparation for distributed fault-tolerant quantum computation
Nanofiber Quantum Technologies, Inc. (NanoQT)（纳米纤维量子技术有限公司）；Clarendon Laboratory, University of Oxford（牛津大学克拉伦登实验室）；Department of Computer Science, Graduate School of Information Science and Technology, The University of Tokyo（东京大学大学院信息理工学研究系计算机科学专业）
A theory is universal contextual if its prediction cannot be reproduced by an ontological model satisfying both preparation and measurement noncontextuality assumptions. In this report, we first generalize the logical proofs of quantum preparation and measurement contextuality for qubit system for any odd number of preparations and measurements. Based on the logical proof, we derive testable universally non-contextual inequalities violated by quantum theory. We then propose a class of two-party communication games and show that the average success probability of winning such games is solely li…
Quantum error correction is an essential component for practical quantum computing on noisy quantum hardware. However, logical operations on error-corrected qubits require a significant resource overhead, especially for high-precision and high-fidelity non-Clifford rotation gates. To address this issue, we propose a postselection-based algorithm to efficiently prepare resource states for gate teleportation. Our algorithm achieves fault tolerance, demonstrating the exponential suppression of logical errors with code distance, and it applies to any stabilizer codes. We provide analytical derivat…
Magic state distillation is a resource intensive subroutine that consumes noisy input states to produce high-fidelity resource states that are used to perform logical operations in practical quantum-computing architectures. The resource cost of magic state distillation can be reduced by improving the fidelity of the raw input states. To this end, we propose an initialization protocol that offers a quadratic improvement in the error rate of the input magic states in architectures with biased noise. This is achieved by preparing an error-detecting code which detects the dominant errors that occu…
Quantum computing potentially offers exponential speed-ups over classical computing for certain tasks. A central, outstanding challenge to making quantum computing practical is to achieve fault tolerance, meaning that computations of any length or size can be realised in the presence of noise. The Gottesman-Kitaev-Preskill code is a promising approach towards fault-tolerant quantum computing, encoding logical qubits into grid states of harmonic oscillators. However, for the code to be fault tolerant, the quality of the grid states has to be extremely high. Approximate grid states have recently…
We investigate a scheme of fault-tolerant quantum computation based on the cluster model. Logical qubits are encoded by a suitable code such as the Steane's 7-qubit code. Cluster states of logical qubits are prepared by post-selection through verification at high fidelity level, where the unsuccessful ones are discarded without recovery operation. Then, gate operations are implemented by transversal measurements on the prepared logical cluster states. The noise threshold is improved significantly by making the high fidelity preparation and transversal measurement. It is estimated to be about 3…
The use of nuclear magnetic resonance (NMR) to carry out quantum information processing (QIP) often requires the preparation, transformation, and detection of pseudopure states. In our previous work, it was shown that the use of pairs of pseudopure states (POPS) as a basis for QIP is very convenient because of the simplicity in experimental execution. It is now further demonstrated that the product of the NMR spectra corresponding to two sets of POPS that share a common pseudopure state has the same peak frequencies as those of the common (single) pseudopure state. Examples of applying two dif…
Robust quantum computation requires encoding delicate quantum information into degrees of freedom that are hard for the environment to change. Quantum encodings have been demonstrated in many physical systems by observing and correcting storage errors, but applications require not just storing information; we must accurately compute even with faulty operations. The theory of fault-tolerant quantum computing illuminates a way forward by providing a foundation and collection of techniques for limiting the spread of errors. Here we implement one of the smallest quantum codes in a five-qubit super…
We present an approach to single-shot high-fidelity preparation of an $n$-qubit state based on neighboring optimal control theory. This represents a new application of the neighboring optimal control formalism which was originally developed to produce single-shot high-fidelity quantum gates. To illustrate the approach, and to provide a proof-of-principle, we use it to prepare the two qubit Bell state $|β_{01}\rangle = (1/\sqrt{2})\left[\, |01\rangle + |10\rangle\,\right]$ with an error probability $ε\sim 10^{-6}$ ($10^{-5}$) for ideal (non-ideal) control. Using standard methods in the literatu…
Modular fault-tolerant quantum computing on a non-CSS code
Universität Innsbruck（因斯布鲁克大学）；Forschungszentrum Jülich（于利希研究中心）；RWTH Aachen University（亚琛工业大学）；Universidad Autonoma de Madrid（马德里自治大学）；Alpine Quantum Technologies GmbH（阿尔卑斯量子技术公司）
Extremely Low-Cost Magic State Preparation toward Fault-Tolerant Quantum Computing
School of Physics, Peking University（北京大学物理学院）；Center on Frontiers of Computing Studies, School of Computer Science, Peking University（北京大学前沿交叉学科研究院计算机学院）
In this paper we propose and analyze a feasible scheme where the detection of a single scattered photon from two trapped atoms or ions performs a conditional unitary operation on two qubits. As examples we consider the preparation of all four Bell states, the reverse operation that is a Bell measurement, and a CNOT gate. We study the effect of atomic motion and multiple scattering, by evaluating Bell inequalities violations, and by calculating the CNOT gate fidelity.
We begin by discussing the history of quantum logic, dividing it into three eras or lives. The first life has to do with Birkhoff and von Neumann's algebraic approach in the 1930's. The second life has to do with attempt to understand quantum logic as logic that began in the late 1950's and blossomed in the 1970's. And the third life has to do with recent developments in quantum logic coming from its connections to quantum computation. We discuss our own work connecting quantum logic to quantum computation (viewing quantum logic as the logic of quantum registers storing qubits), and make some …
In fault-tolerant quantum computing schemes, the overhead is often dominated by the cost of preparing codewords reliably. This cost generally increases quadratically with the block size of the underlying quantum error-correcting code. In consequence, large codes that are otherwise very efficient have found limited fault-tolerance applications. Fault-tolerant preparation circuits therefore are an important target for optimization. We study the Golay code, a 23-qubit quantum error-correcting code that protects the logical qubit to a distance of seven. In simulations, even using a naive ancilla p…
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…
Quantum error correction protects fragile quantum information by encoding it into a larger quantum system. These extra degrees of freedom enable the detection and correction of errors, but also increase the operational complexity of the encoded logical qubit. Fault-tolerant circuits contain the spread of errors while operating the logical qubit, and are essential for realizing error suppression in practice. While fault-tolerant design works in principle, it has not previously been demonstrated in an error-corrected physical system with native noise characteristics. In this work, we experimenta…
Spin systems such as silicon or nitrogen vacancy centers in diamond, quantum dots and quantum dot molecules coupled to optical cavities appear as key elements for creating quantum networks as not only constituting the nodes of the network, but also assisting the creation of photonic networks. Here we study deterministic preparation of arbitrary size $W$ states with spin systems. We present an efficient operation on three qubits, two being the logical qubits and one being the ancillary qubit, where no interaction between the logical qubits are required. The proposed operation can create a $W$-t…
We present a protocol to prepare decoherence free cluster states using ultracold atoms loaded in a two dimensional superlattice. The superlattice geometry leads to an array of 2*2 plaquettes, each of them holding four spin-1/2 particles that can be used for encoding a single logical qubit in the two-fold singlet subspace, insensitive to uniform magnetic field fluctuations in any direction. Dynamical manipulation of the supperlattice yields distinct inter and intra plaquette interactions and permits to realize one qubit and two qubit gates with high fidelity, leading to the generation of univer…
We find the minimal number of independent preparations and measurements certifying the dimension of a classical or quantum system limited to $d$ states, optionally reduced to the real subspace. As a dimension certificate, we use the linear independence tested by a determinant. We find the sets of preparations and measurements that maximize the chance to detect larger space if the extra contribution is very small. We discuss the practical application of the test to certify the space logical operations on a quantum computer.
The noisy binary linear problem (NBLP) is known as a computationally hard problem, and therefore, it offers primitives for post-quantum cryptography. An efficient quantum NBLP algorithm that exhibits a polynomial quantum sample and time complexities has recently been proposed. However, the algorithm requires a large number of samples to be loaded in a highly entangled state and it is unclear whether such a precondition on the quantum speedup can be obtained efficiently. Here, we present a complete analysis of the quantum solvability of the NBLP by considering the entire algorithm process, name…
Polyatomic molecular ions contain many desirable attributes of a useful quantum system, including rich internal degrees of freedom and highly controllable coupling to the environment. To date, the vast majority of state-specific experimental work on molecular ions has concentrated on diatomic species. The ability to prepare and readout polyatomic molecules in single quantum states would enable diverse experimental avenues not available with diatomics, including new applications in precision measurement, sensitive chemical and chiral analysis at the single molecule level, and precise studies of…
The preparation procedure, an undefined notion in quantum theory, has not had the relevance that it deserves in the interpretation of quantum mechanical formalism. Here we utilize the concepts of identical and similar preparation procedures to show the conceptual differences and mutual interconnections between the statistical and the conventional interpretation of quantum formalism. Although the statistical understanding, and its final logical consequence, hidden variables theories (this connexion being explained in the text), have a great intuitive appeal due to its fewer ontological difficul…
We present schemes to prepare two-dimensional cluster states [H. J. Briegel and R. Raussendorf, Phys. Rev. Lett. {\bf 86}, 910 (2001)] with atomic ions confined in a micro-structured linear ion trap and coupled by an engineered spin-spin interaction. In particular, we show how to prepare a $n \times 2$ cluster state by creating a linear cluster state and adding third-neighbor entanglement using selective recoupling techniques. The scheme is based on the capabilities provided by segmented linear Paul traps to confine ions in local potential wells and to separate and transport ions between these…
Due to their rich level structure, molecules are well-suited for probing time variation of fundamental constants, precisely measuring parity violation and time-reversal non-invariance effects, studying quantum mechanical aspects of chemical reactions, and implementing scalable quantum information processing architectures. Molecular ions are particularly attractive for these applications due to their long storage times and the near-perfect isolation from environment that result in long coherence times required to achieve high measurement precision and reduce systematic errors. However, the cont…
