Juan Carlos Garcia-Escartin, Pedro Chamorro-Posada
We show that universal quantum logic can be achieved using only linear optics and a quantum shutter device. With these elements, we design a quantum memory for any number of qubits and a CNOT gate which are the basis of a universal quantum computer. An interaction-free model for a quantum shutter is given.
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Demonstrating a universal logical gate set in error-detecting surface codes on a superconducting quantum processor
本研究针对超导系统中表面码逻辑量子比特两量子比特门缺失的问题，用处理器\textit{Wukong}在距离-2表面码上实现通用逻辑门集合，含横向CNOT与任意单量子比特旋转门，还容错制备逻辑贝尔态，证实纠缠，推动超导容错量子计算发展。
Probabilistic quantum cloning and identifying machines can be constructed via unitary-reduction processes [Duan and Guo, Phys. Rev. Lett. 80, 4999 (1998)]. Given the cloning (identifying) probabilities, we derive an explicit representation of the unitary evolution and corresponding Hamiltonian to realize probabilistic cloning (identification). The logic networks are obtained by decomposing the unitary representation into universal quantum logic operations. The robustness of the networks is also discussed. Our method is suitable for a $k$-partite system, such as quantum computer, and may be gen…
Logical qubit encoding and quantum error correction (QEC) have been experimentally demonstrated in various physical systems with multiple physical qubits, however, logical operations are challenging due to the necessary nonlocal operations. Alternatively, logical qubits with bosonic-mode-encoding are of particular interest because their QEC protection is hardware efficient, but gate operations on QEC protected logical qubits remain elusive. Here, we experimentally demonstrate full control on a single logical qubit with a binomial bosonic code, including encoding, decoding, repetitive QEC, and …
Universal quantum theory contains twisted logic
本文从理论和实验上证明海森堡不确定性原理使连续非兼容测量的逻辑推演无法串联，并指出忽视该结构会导致错误认为可单次测量区分非正交态。
We consider the model of quantum computer, which is represented as a Ising spin lattice, where qubits (spin-half systems) are separated by the isolators (two spin-half systems). In the idle mode or at the single bit operations the total spin of isolators is 0. There are no need of complicated protocols for correcting the phase and probability errors due to permanent interaction between the qubits. We present protocols for implementation of universal quantum gates with the rectangular radio-frequency pulses.
We present protocols for implementation of universal quantum gates on an arbitrary superposition of quantum states in a scalable solid-state Ising spin quantum computer. The spin chain is composed of identical spins 1/2 with the Ising interaction between the neighboring spins. The selective excitations of the spins are provided by the gradient of the external magnetic field. The protocols are built of rectangular radio-frequency pulses. The phase and probability errors caused by unwanted transitions are minimized and computed numerically.
The quantum logic gates used in the design of a quantum computer should be both universal, meaning arbitrary quantum computations can be performed, and fault-tolerant, meaning the gates keep errors from cascading out of control. A number of no-go theorems constrain the ways in which a set of fault-tolerant logic gates can be universal. These theorems are very restrictive, and conventional wisdom holds that a universal fault-tolerant logic gate set cannot be implemented natively, requiring us to use costly distillation procedures for quantum computation. Here, we present a general framework for…
In this paper, we present the experimental realization of multi-qubit gates $% Λ_n(not) $ in macroscopic ensemble of three-qubit and four-qubit molecules. Instead of depending heavily on the two-bit universal gate, which served as the basic quantum operation in quantum computing, we use pulses of well-defined frequency and length that simultaneously apply to all qubits in a quantum register. It appears that this method is experimentally convenient when this procedure is extended to more qubits on some quantum computation, and it can also be used in other physical systems.
Photon-Number Conserved Universal Quantum Logic Employing Continuous-Time Quantum Walk on Dual-Rail Qubit Arrays
利用双轨量子比特编码与连续时间量子行走的协同作用，在超导电路中实现通用量子逻辑，通过可调耦合强度实现单、双、三量子比特操作，抑制泄漏并提升保真度。
The basic principles and results of Conservative Logic introduced by Fredkin and Toffoli on the basis of a seminal paper of Landauer are extended to d-valued logics, with a special attention to three-valued logics. Different approaches to d-valued logics are examined in order to determine some possible universal sets of logic primitives. In particular, we consider the typical connectives of Lukasiewicz and Godel logics, as well as Chang's MV-algebras. As a result, some possible three-valued and d-valued universal gates are described which realize a functionally complete set of fundamental conn…
Logical blocks for fault-tolerant topological quantum computation
本文提出逻辑块框架，以时空统一方式描述拓扑逻辑门，并基于表面码与LDPC码级联及FBQC实现通用容错量子计算，验证阈值一致性并探索减少资源开销的新方案。
Categorical Universal Logic is a theory of monad-relativised hyperdoctrines (or fibred universal algebras), which in particular encompasses categorical forms of both first-order and higher-order quantum logics as well as classical, intuitionistic, and diverse substructural logics. Here we show there are those dual adjunctions that have inherent hyperdoctrine structures in their predicate functor parts. We systematically investigate into the categorical logics of dual adjunctions by utilising Johnstone-Dimov-Tholen's duality-theoretic framework. Our set-theoretical duality-based hyperdoctrines …
Quantum computers can be protected from noise by encoding the logical quantum information redundantly into multiple qubits using error correcting codes. When manipulating the logical quantum states, it is imperative that errors caused by imperfect operations do not spread uncontrollably through the quantum register. This requires that all operations on the quantum register obey a fault-tolerant circuit design which, in general, increases the complexity of the implementation. Here, we demonstrate a fault-tolerant universal set of gates on two logical qubits in a trapped-ion quantum computer. In…
A modular quantum computer based on Cornucopia codes
本文提出基于Cornucopia码的模块化量子计算机架构，通过可重复使用的组件实现通用逻辑操作，在低开销下保留超高码率量子存储器的资源优势，为低开销容错量子计算机提供了新路径。
Universal Quantum Gate Set for Gottesman-Kitaev-Preskill Logical Qubits
本研究在囚禁离子机械运动的有限能量 GKP 态上，通过动态调制自旋-运动耦合的最优控制，实验实现含单比特门和首个双比特纠缠门的通用逻辑门集合。
Many well-known and well-studied four by four universal quantum logic gates in the literature are of a specific form, the so called eight-vertex form \eqref{8vertexform} \cite{kaufman etal 05-1,kaufman etal 05-2}, or {\it similar} to it. We present a formalism for universal quantum logic gates of such a form. First, we provide explicit formulas in terms of matrix entries, which are the necessary and sufficient conditions for such a matrix to be a solution to the Yang-Baxter equation \eqref{byb}. Then, combining this with the conditions needed for being unitary \eqref{unitarycond} and being ent…
It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions including magic state distillation. Widely overlooked, however, is the possibility of non-transversal, yet still fault-tolerant, gates that work directly on small quantum codes. Here we demonstrate precisely the existence of such gates. In particular, we show how the limits of non-transversality can be overcome by performing rounds of intermediate error-correc…
Universal Weakly Fault-Tolerant Quantum Computation via Code Switching in the [[8,3,2]] Code
本文提出一种基于[[8,3,2]]码的码切换协议，通过两种不同版本的码实现通用弱故障容错计算，利用Clifford单量子门和逻辑CCZ门，通过数值模拟验证其有效性。
We present a formula for an infinite number of universal quantum logic gates, which are $4$ by $4$ unitary solutions to the Yang-Baxter (Y-B) equation. We obtain this family from a certain representation of the cyclic group of order $n$. We then show that this {\it discrete} family, parametrized by integers $n$, is in fact, a small sub-class of a larger {\it continuous} family, parametrized by real numbers $θ$, of universal quantum gates. We discuss the corresponding Yang-Baxterization and related symmetries in the concomitant Hamiltonian.
Genuine Multipartite Entanglement between Logical Qubits via Cross-Code Lattice Surgery
研究利用交叉码晶格手术在俘获离子量子处理器中实验生成并验证逻辑真正多方纠缠，介绍了通过不同码实现的通用逻辑门集，展示了多方纠缠态及单逻辑量子比特任意旋转，为容错量子计算架构提供核心构建块。
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…
A single physical interaction might not be universal for quantum computation in general. It has been shown, however, that in some cases it can generate universal quantum computation over a subspace. For example, by encoding logical qubits into arrays of multiple physical qubits, a single isotropic or anisotropic exchange interaction can generate a universal logical gate-set. Recently, encoded universality for the exchange interaction was explicitly demonstrated on three-qubit arrays, the smallest nontrivial encoding. We now present the exact specification of a discrete universal logical gate-s…
Universal logic gates for coupled period-doubling systems
本文提出了一种利用NAND和NOR门在周期倍频状态下编码的经典信息进行通用逻辑操作的通用架构，展示了通过调整耦合强度和脉冲持续时间精确控制节点状态的能力，并验证了该协议在不同系统中的通用性。
Topological measurement-based quantum computation (MBQC) enables one to carry out universal fault-tolerant quantum computation via single-qubit Pauli measurements with a family of large entangled states called cluster states as resources. Raussendorf's three-dimensional cluster states (RTCSs) based on the surface codes are mainly considered for topological MBQC. In such schemes, however, the fault-tolerant implementation of the logical Hadamard, phase ($Z^{1/2}$), and $T$ ($Z^{1/4}$) gates which are essential for building up arbitrary logical gates has not been achieved to date without using s…
Error semitransparent universal control of a bosonic logical qubit
本文提出基于动态编码子空间的框架，利用简单线性驱动实现误差半透明的通用逻辑门，通过减少光子损失导致的退相干，展示了量子纠错延长的操作寿命和非克莱因门的构造。
Complementary 3D color codes for transversal quantum logic
研究提出基于四面体三维颜色码及其哈达玛变换对应物的混合架构，二者支持互补横向非克利福德操作，结合相关变换实现几乎通用的横向逻辑门集，还通过构造逻辑受控Z门等完成通用门集。
We investigate how to carry out universal quantum computation deterministically with free electrons in decoherence-free subspace by using polarizing beam splitters, charge detectors, and single-spin rotations. Quantum information in our case is encoded in spin degrees of freedom of the electron-pairs which construct a decoherence-free subspace. We design building blocks for two noncommutable single-logic-qubit gates and a logic controlled phase gate, based on which a universal and scalable quantum information processing robust to dephasing is available in a deterministic way.
Demonstration of measurement-free universal fault-tolerant quantum computation
在囚禁离子量子处理器上实验演示了无需线路中测量的容错通用逻辑操作工具箱，并基于状态注入在八量子比特码上容错实现了Grover量子搜索算法，为无测量量子计算提供了初步步骤。
One of the limitations to the quantum computing capability of a continuous-variable system is determined by our ability to cool it to the ground state, because pure logical states, in which we accurately encode quantum information, are conventionally pure physical states that are constructed from the ground state. In this work, we present an alternative quantum computing formalism that encodes logical quantum information in mixed physical states. We introduce a class of mixed-state protocols that are based on a parity encoding, and propose an implementation of the universal logic gates by usin…
Some of the most promising proposals for scalable solid-state quantum computing, e.g., those using electron spins in quantum dots or donor electron or nuclear spins in Si, rely on a two-qubit quantum gate that is ideally generated by an isotropic exchange interaction. However, an anisotropic perturbation arising from spin-orbit coupling is inevitably present. Previous studies focused on removing the anisotropy. Here we introduce a new universal set of quantum logic gates that takes advantage of the anisotropic perturbation. The price is a constant but modest factor in additional pulses. The ga…
We show that in quantum computation almost every gate that operates on two or more bits is a universal gate. We discuss various physical considerations bearing on the proper definition of universality for computational components such as logic gates.
Recent development of mixed-state encoding (MSE) allows pure-state logical information to be encoded by a bosonic (continuous-variable) system in mixed physical state. Despite interest due to its counter-intuitiveness, the utility of the current MSE scheme is limited due to several operational drawbacks, namely redundant information carrier, probabilistic initialisation, and requirement of discrete-variable measurement. In this work, we present a simplified MSE that does not suffer from any of these drawbacks. Specifically, our protocol encodes each qubit by only one mixed-state bosonic mode, …
Although the initial proposal for ion trap quantum computation made use of an auxiliary internal level to perform logic between ions, this resource is not necessary in principle. Instead, one may perform such operations directly using sideband laser pulses, operating with an arbitrary (sufficiently small) Lamb-Dicke parameter. We explore the potential of this technique, showing how to perform logical operations between the internal state of an ion and the collective motional state and giving explicit constructions for a controlled-not gate between ions.
Quantum error correction and fault-tolerance make it possible to perform quantum computations in the presence of imprecision and imperfections of realistic devices. An important question is to find the noise rate at which errors can be arbitrarily suppressed. By concatenating the 7-qubit Steane and 15-qubit Reed-Muller codes, the 105-qubit code enables a universal set of fault-tolerant gates despite not all of them being transversal. Importantly, the CNOT gate remains transversal in both codes, and as such has increased error protection relative to the other single qubit logical gates. We show…
We propose a universal gate set for quantum computing with all-to-all connectivity and intrinsic robustness to bit-flip errors based on parity encoding. We show that logical controlled phase gate and $R_z$ rotations can be implemented in parity encoding with single-qubit operations. Together with logical $R_x$ rotations, implemented via nearest-neighbor controlled-NOT gates and an $R_x$ rotation, these form a universal gate set. As the controlled phase gate requires only single-qubit rotations, the proposed scheme has advantages for several cornerstone quantum algorithms, e.g., the quantum Fou…
Lithium niobate photonic circuits have the salutary property of permitting the generation, transmission, and processing of photons to be accommodated on a single chip. Compact photonic circuits such as these, with multiple components integrated on a single chip, are crucial for efficiently implementing quantum information processing schemes. We present a set of basic transformations that are useful for manipulating modal qubits in Ti:LiNbO$_3$ photonic quantum circuits. These include the mode analyzer, a device that separates the even and odd components of a state into two separate spatial pat…
A fundamental question in the theory of quantum computation is to understand the ultimate space-time resource costs for performing a universal set of logical quantum gates to arbitrary precision. Here we demonstrate that non-Abelian anyons in Turaev-Viro quantum error correcting codes can be moved over a distance of order the code distance, and thus braided, by a constant depth local unitary quantum circuit followed by a permutation of qubits. Our gates are protected in the sense that the length of error strings do not grow by more than a constant factor. When applied to the Fibonacci code, ou…
We present a new scheme to perform noise resilient universal adiabatic quantum computation using two-body interactions. To achieve this, we introduce a new family of error detecting subsystem codes whose gauge generators and a set of their logical operators - capable of encoding universal Hamiltonian computations - can be implemented using two-body interactions. Logical operators of the code are used to encode any given computational Hamiltonian, and the gauge operators are used to construct a penalty Hamiltonian whose ground subspace is protected against local-errors. In contrast to previous …
We report first steps towards elucidating the relationship between contextuality, measurement-based quantum computation (MBQC) and the non-classical logic of a topos associated with the computation. We show that, in a class of MBQC, classical universality requires non-classical logic, which is 'consumed' during the course of the computation, thereby pinpointing another potential quantum computational resource.
Certain quantum codes allow logic operations to be performed on the encoded data, such that a multitude of errors introduced by faulty gates can be corrected. An important class of such operations are {\em transversal}, acting bitwise between corresponding qubits in each code block, thus allowing error propagation to be carefully limited. If any quantum operation could be implemented using a set of such gates, the set would be {\em universal}; codes with such a universal, transversal gate set have been widely desired for efficient fault-tolerant quantum computation. We study the structure of G…
An important approach to the fault-tolerant quantum computation is protecting the logical information using the quantum error correction. Usually, the logical information is in the form of logical qubits, which are encoded in physical qubits using quantum error correction codes. Compared with the qubit quantum computation, the fermionic quantum computation has advantages in quantum simulations of fermionic systems, e.g. molecules. In this paper, we show that the fermionic quantum computation can be universal and fault-tolerant if we encode logical Majorana fermions in physical Majorana fermion…
Braiding defects in topological stabiliser codes has been widely studied as a promising approach to fault-tolerant quantum computing. We present a no-go theorem that places very strong limitations on the potential of such schemes for universal fault-tolerant quantum computing in any spatial dimension. In particular, we show that, for the natural encoding of quantum information in defects in topological stabiliser codes, the set of logical operators implementable by braiding defects is contained in the Clifford group. Indeed, we show that this remains true even when supplemented with locality-p…
Super-compact universal quantum logic gates with inversedesigned elements
研究通过逆向设计方法在硅芯片上实现了尺寸仅约一个真空波长的超紧凑通用量子逻辑门，并通过级联基本门构建量子电路，为大规模量子光子芯片的实现铺平了道路。
Universal quantum computation via scalable measurement-free error correction
本文提出Bacon-Shor码无测量形变协议与一次性Toffoli小装置，实现无中间测量、无前馈的容错通用量子计算，测得约0.12%的电路级退极化噪声容错阈值，适配中性原子平台。
N-qubit universal quantum logic with a photonic qudit and O(N) linear optics elements
本研究提出用单个时间箱qudit和O(N)个线性光学元件实现N量子比特通用逻辑，元件规模远低于传统方案，可构建低成本小规模量子处理器，并通过腔QED系统连接物质量子比特实现可扩展与量子互联功能。
Universal adapters between quantum LDPC codes
本文提出了一种通用的量子LDPC码适配器，用于实现联合逻辑Pauli测量和可寻址的逻辑CNOT门，通过改进的图边扩张和SkipTree算法，提高了容错计算的效率。
We present the dipole induced transparency (DIT) of a diamond nitrogen-vacancy center embedded in a photonic crystal cavity coupled to two waveguides, and it is obvious with the robust and flexible reflectance and transmittance difference of circularly polarized lights between the uncoupled and the coupled cavities even in the bad cavity regime (the Purcell regime). With this DIT, we propose two universal hyperparallel hybrid photonic quantum logic gates, including a hybrid hyper-controlled-not gate and a hybrid hyper-Toffoli gate, on photon systems in both the polarization and the spatial-mod…
A universal quantum computing scheme, with a universal set of logical gates, is proposed based on networks of 1D quantum systems. The encoding of information is in terms of universal features of gapped phases, for which effective field theories such as sine-Gordon field theory can be employed to describe a qubit. Primary logical gates are from twist, pump, glue, and shuffle operations that can be realized in principle by tuning parameters of the systems. Our scheme demonstrates the power of 1D quantum systems for robust quantum computing.
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.
Developing universal logical state-purification strategy for quantum error correcting codes
提出一种基于测量的协议，通过工程化哈密顿量时间演化、投影测量与后选择，从任意热态以单位保真度纯化量子纠错码的任意逻辑态，并验证了其鲁棒性与可行性。
This paper presents a physical mapping tool for quantum circuits, which generates the optimal Universal Logic Block (ULB) that can perform any logical fault-tolerant (FT) quantum operations with the minimum latency. The operation scheduling, placement, and qubit routing problems tackled by the quantum physical mapper are highly dependent on one another. More precisely, the scheduling solution affects the quality of the achievable placement solution due to resource pressures that may be created as a result of operation scheduling whereas the operation placement and qubit routing solutions influ…
It has been experimentally proven that realizing universal quantum gates using higher-radices logic is practically and technologically possible. We developed a Parallel Genetic Algorithm that synthesizes Boolean reversible circuits realized with a variety of quantum gates on qudits with various radices. In order to allow synthesizing circuits of medium sizes in the higher radix quantum space we performed the experiments using a GPU accelerated Genetic Algorithm. Using the accelerated GA we compare heuristic improvements to the mutation process based on cost minimization, on the adaptive cost o…
Quantum computation requires many qubits that can be coherently controlled and coupled to each other. Qubits that are defined using lithographic techniques are often argued to be promising platforms for scalability, since they can be implemented using semiconductor fabrication technology. However, leading solid-state approaches function only at temperatures below 100 mK, where cooling power is extremely limited, and this severely impacts the perspective for practical quantum computation. Recent works on spins in silicon have shown steps towards a platform that can be operated at higher tempera…
Universal fault-tolerant logic with heterogeneous holographic codes
本研究构建异构全息码，通过交替双曲铺砌张量网络组合种子码，实现通用容错非克利福德门，节省物理量子比特开销并支持多逻辑量子比特编码，强化其在实用量子计算中的应用。
Universal Logical Quantum Photonic Neural Network Processor via Cavity-Assisted Interactions
本文提出一种基于腔辅助三能级原子相互作用的量子光子神经网络架构，利用光子数选择性相位门构建通用门集，实现多模多光子态制备、玻色子纠错码逻辑操作与纠错电路，为近期集成光子硬件上的容错量子计算铺平道路。
We present a new hardware-efficient paradigm for universal quantum computation which is based on encoding, protecting and manipulating quantum information in a quantum harmonic oscillator. This proposal exploits multi-photon driven dissipative processes to encode quantum information in logical bases composed of Schrödinger cat states. More precisely, we consider two schemes. In a first scheme, a two-photon driven dissipative process is used to stabilize a logical qubit basis of two-component Schrödinger cat states. While such a scheme ensures a protection of the logical qubit against the photo…
Architectural mechanisms of a universal fault-tolerant quantum computer
本研究通过中性原子阵列实现了通用容错量子计算架构，展示了量子纠错、逻辑纠缠与量子态传输的结合，为大规模量子计算提供了基础。
A basic question in the theory of fault-tolerant quantum computation is to understand the fundamental resource costs for performing a universal logical set of gates on encoded qubits to arbitrary accuracy. Here we consider qubits encoded with constant space overhead (i.e. finite encoding rate) in the limit of arbitrarily large code distance $d$ through the use of topological codes associated to triangulations of hyperbolic surfaces. We introduce explicit protocols to demonstrate how Dehn twists of the hyperbolic surface can be implemented on the code through constant depth unitary circuits, wi…
We study quasi-exact quantum error correcting codes and quantum computation with them. A quasi-exact code is an approximate code such that it contains a finite number of scaling parameters, the tuning of which can flow it to corresponding exact codes, serving as its fixed points. The computation with a quasi-exact code cannot realize any logical gate to arbitrary accuracy. To overcome this, the notion of quasi-exact universality is proposed, which makes quasi-exact quantum computation a feasible model especially for executing moderate-size algorithms. We find that the incompatibility between u…
We consider categorical logic on the category of Hilbert spaces. More generally, in fact, any pre-Hilbert category suffices. We characterise closed subobjects, and prove that they form orthomodular lattices. This shows that quantum logic is just an incarnation of categorical logic, enabling us to establish an existential quantifier for quantum logic, and conclude that there cannot be a universal quantifier.
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