We consider two apparently separated problems: in the first part of the paper we study the concept of a scalable (approximate) programmable quantum gate (SPQG). These are special (approximate) programmable quantum gates, with nice properties that could have implications on the theory of universal computation. Unfortunately, as we prove, such objects do not exist in the domain of usual quantum theory. In the second part the problem of noisy dense coding (and generalizations) is addressed. We observe that the additivity problem for the classical capacity obtained is of apparently greater generality than for the usual quantum channel (completely positive maps): i.e., the latter occurs as a special case of the former, but, as we shall argue with the help of the non-existence result of the first part, the former cannot be reduced to an instance of the latter. We conclude by suggesting that the additivity problem for the classical capacity of quantum channels, as posed until now, may conceptually not be in its appropriate generality.
We show how to construct quantum gate arrays that can be programmed to perform different unitary operations on a data register, depending on the input to some program register. It is shown that a universal quantum gate array - a gate array which can be programmed to perform any unitary operation - exists only if one allows the gate array to operate in a probabilistic fashion. The universal quantum gate array we construct requires an exponentially smaller number of gates than a classical universal gate array.
We experimentally demonstrate a programmable single-qubit quantum gate. This device applies a unitary phase shift operation to a data qubit with the value of the phase shift being fully determined by the state of a program qubit. Our linear optical implementation is based on the encoding of qubits into polarization states of single photons, two-photon interference on a polarizing beam splitter, and measurement on the output program qubit. We fully characterize the programmable gate by quantum process tomography. The achieved average quantum process fidelity exceeding 97% illustrates very good …
We experimentally demonstrate a programmable quantum gate that applies a sign flip operation to data qubit in an arbitrary basis fully specified by the quantum state of a two-qubit program register. Our linear-optical implementation is inspired by teleportation-based schemes for quantum computing and relies on multiphoton interference and coincidence detection. We confirm the programmability of the gate and its high-fidelity performance by carrying out full quantum process tomography of the resulting operation on data qubit for several different programs.
We present a linear-optical scheme for a controlled-phase gate with tunable phase shift programmed by a qubit state. In contrast to all previous tunable controlled-phase gates, the phase shift is not hard-coded into the optical setup, but can be tuned to any value from 0 to pi by the state of a so-called program qubit. Our setup is feasible with current level of technology using only linear-optical components. We provide an experimental feasibility study to assess the gate's implementability. We also discuss options for increasing the success probability up to 1/12 which approaches the success…
A quantum processor to import, process, and export optical quantum states is a common core technology enabling various photonic quantum information processing. However, there has been no photonic processor which is simultaneously universal, scalable, and programmable. Here, we report on an original loop-based single-mode versatile photonic quantum processor which is designed to be universal, scalable, and programmable. Our processor can perform arbitrarily many steps of programmable quantum operations on a given single-mode optical quantum state by time-domain processing in a dynamically contr…
We show how quantum dynamics can be captured in the state of a quantum system, in such a way that the system can be used to stochastically perform, at a later time, the stored transformation perfectly on some other quantum system. Thus programmable quantum gates for quantum information processing are feasible if some probability of failure -that we show to decrease exponentially with the size of the storing resources- is allowed.
We show how quantum dynamics (a unitary transformation) can be captured in the state of a quantum system, in such a way that the system can be used to perform, at a later time, the stored transformation almost perfectly on some other quantum system. Thus programmable quantum gates for quantum information processing are feasible if some small degree of imperfection is allowed. We discuss the possibility of using this fact for securely computing a secret function on a public quantum computer. Finally, our scheme for storage of operations also allows for a new form of quantum remote control.
Quantum computation has attracted much attention, among other things, due to its potentialities to solve classical NP problems in polynomial time. For this reason, there has been a growing interest to build a quantum computer. One of the basic steps is to implement the quantum circuit able to realize a given unitary operation. This task has been solved using decomposition of unitary matrices in simpler ones till reach quantum circuits having only single-qubits and CNOTs gates. Usually the goal is to find the minimal quantum circuit able to solve a given problem. In this paper we go in a differ…
A new model of quantum computation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantum computation, e. g. in achieving the programmability of permutations of N different unitary channels with 1 use instead of N uses per channel. For this task, a new elemental resource is needed, the "quantum switch", which can be programmed to switch the order of two channels with a single use of each one.
In this paper, we proposed a design of integrated programmable controlled-phase (CPHASE) gate to be used in quantum information processing applications. This gate is capable of introducing arbitrary phase difference to target qubit in the case of control qubit being in the state of |1>. Because the desired phase difference is possible to be utilized after fabrication unlike the conventional controlled-phase gates which provide hard-coded phase shift, such an integrated gate is expected to pave the way for more versatile operations of current integrated optical circuits as well as possible new …
The universal quantum computer is a device capable of simulating any physical system and represents a major goal for the field of quantum information science. Algorithms performed on such a device are predicted to offer significant gains for some important computational tasks. In the context of quantum information, "universal" refers to the ability to perform arbitrary unitary transformations in the system's computational space. The combination of arbitrary single-quantum-bit (qubit) gates with an entangling two-qubit gate is a gate set capable of achieving universal control of any number of q…
By combining telecloning and programmable quantum gate array presented by Nielsen and Chuang [Phys.Rev.Lett. 79 :321(1997)], we propose a programmable quantum processor which can be programmed to implement restricted set of operations with several identical data outputs. The outputs are approximately-transformed versions of input data. The processor successes with certain probability.
A common approach to realize conditional-phase (CZ) gates in transmon qubits relies on flux control of the qubit frequency to make computational states interact with non-computational ones using a fast-adiabatic trajectory to minimize leakage. We develop a bipolar flux-pulsing method with two key advantages over the traditional unipolar variant. First, the action of the bipolar pulse is robust to long-timescale linear-dynamical distortions in the flux-control line, facilitating tuneup and ensuring atomic repeatability. Second, the flux symmetry of the transmon Hamiltonian makes the conditional…
We discuss the unique capabilities of programmable logic devices (PLD's) for experimental quantum optics and describe basic procedures of design and implementation. Examples of advanced applications include optical metrology and feedback control of quantum dynamical systems. As a tutorial illustration of the PLD implementation process, a field programmable gate array (FPGA) controller is used to stabilize the output of a Fabry-Perot cavity.
Superconducting circuits are at the forefront of quantum computing technology because of the unparalleled combination of good coherence, fast gates and flexibility in design parameters. The majority of experiments demonstrating small quantum algorithms in the superconducting architecture have used transmon qubits and transverse qubit-qubit coupling. However, efficient universal digital computing has remained a challenge due to the fact that majority of the state-of-art architectures rely on nearest-neighbor coupling in one or two dimensions. The limited connectivity and the availability of onl…
It was shown by M.A. Nielsen and I.L. Chuang 1997, that it is impossible to build strictly universal programmable quantum gate array, that could perform any unitary operation precisely and it was suggested to use probabilistic gate arrays instead. In present work is shown, that if to use more physical and weak condition of universality (suggested already in earliest work by D.Deutsch 1985) and to talk about simulation with arbitrary, but finite precision, then it is possible to build universal programmable gate array. But now the same no-go theorem by Nielsen and Chuang will have new interesti…
Recent achievements in the field of gate defined semiconductor quantum dots reinforce the concept of a spin-based quantum computer consisting of nodes of locally connected qubits which communicate with each other via superconducting circuit resonator photons. In this work we theoretically demonstrate a versatile set of quantum gates between adjacent spin qubits defined in semiconductor quantum dots situated within the same node of such a spin-based quantum computer. The electric dipole acquired by the spin of an electron that moves across a double quantum dot potential in a magnetic field grad…
We propose and analyze the design of a programmable photonic integrated circuit for high-fidelity quantum computation and simulation. We demonstrate that the reconfigurability of our design allows us to overcome two major impediments to quantum optics on a chip: it removes the need for a full fabrication cycle for each experiment and allows for compensation of fabrication errors using numerical optimization techniques. Under a pessimistic fabrication model for the silicon-on-insulator process, we demonstrate a dramatic fidelity improvement for the linear optics CNOT and CPHASE gates and, showi…
Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths. Here, we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully-connected set of gate operations that are nati…
We analyze and compare the optimality of approximate and probabilistic universal programmable quantum processors. We define several characteristics how to quantify the optimality and we study in detail performance of three types of programmable quantum processors based on (1) the C-NOT gate, (2) the SWAP operation, and (3) the model of the quantum information distributor - the QID processor. We show under which conditions the measurement assisted QID processor is optimal. We also investigate optimality of the so-called U-processors and we also compare the optimal approximative implementation o…
We propose a model of a programmable quantum processing device realizable with existing nanophotonic technologies and which can be viewed as a basis for new high performance hardware architectures. We present protocols and their physical implementation on the controlled photon transfer for executing basic single-qubit and multi-qubit gates. The possible operation of this quantum computer scheme is analyzed. The physical architecture is then formalized by a mathematical model of the Quantum Processing Unit (QPU), which is used as a basis for the Quantum Programming Framework that makes it possi…
Programmable arrays of hundreds of Rydberg atoms have recently enabled the exploration of remarkable phenomena in many-body quantum physics. In addition, the development of high-fidelity quantum gates are making them promising architectures for the implementation of quantum circuits. We present here \textit{Pulser}, an open-source Python library for programming neutral-atom devices at the pulse level. The low-level nature of Pulser makes it a versatile framework for quantum control both in the digital and analog settings. The library also contains simulation routines for studying and exploring…
Processing quantum information using quantum three-level systems or qutrits as the fundamental unit is an alternative to contemporary qubit-based architectures with the potential to provide significant computational advantages. We demonstrate a fully programmable two-qutrit quantum processor by utilizing the third energy eigenstates of two transmons. We develop a parametric coupler to achieve excellent connectivity in the nine-dimensional Hilbert space enabling efficient implementations of two-qutrit gates. We characterize our processor by realizing several algorithms like Deutsch-Jozsa, Berns…
Quantum computers, which take advantage of the superposition and entanglement of physical states, could outperform their classical counterparts in solving problems with technological impact, such as factoring large numbers and searching databases. A quantum processor executes algorithms by applying a programmable sequence of gates to an initialized state of qubits, which coherently evolves into a final state containing the result of the computation. Although quantum processors with a few qubits have been demonstrated on multiple quantum computing platforms, realization of solid-state programma…
An examination of the concept of using classical degrees of freedom to drive the evolution of quantum computers is given. Specifically, when externally generated, coherent states of the electromagnetic field are used to drive transitions within the qubit system, a decoherence results due to the back reaction from the qubits onto the quantum field. We derive an expression for the decoherence rate for two cases, that of the single-qubit Walsh-Hadamard transform, and for an implementation of the controlled-NOT gate. We examine the impact of this decoherence mechanism on Grover's search algorithm,…
We present a versatile rf pulse control system that has been designed for multi-qubit quantum experiments. One instrument can be scaled to provide 32 channels of rf between 10 - 450 MHz. Synchronization can be achieved across multiple instruments. By using direct digital synthesis and custom control circuitry contained within a field-programmable gate array, sequences of transform-limited pulses can be produced. These have been used to carry out quantum gates that are able to meet fault-tolerant thresholds for single- and two-qubit gate fidelities, as published elsewhere. We have also extended…
We propose a scalable scheme for optical quantum computing using measurement-induced continuous-variable quantum gates in a loop-based architecture. Here, time-bin-encoded quantum information in a single spatial mode is deterministically processed in a nested loop by an electrically programmable gate sequence. This architecture can process any input state and an arbitrary number of modes with almost minimum resources, and offers a universal gate set for both qubits and continuous variables. Furthermore, quantum computing can be performed fault-tolerantly by a known scheme for encoding a qubit …
We propose a hierarchical architecture for building "logical" Majorana zero modes using "physical" Majorana zero modes at the Y-junctions of a hexagonal network of semiconductor nanowires. Each Y-junction contains three "physical" Majoranas, which hybridize when placed in close proximity, yielding a single effective Majorana mode near zero energy. The hybridization of effective Majorana modes on neighboring Y-junctions is controlled by applied gate voltages on the links of the honeycomb network. This gives rise to a tunable tight-binding model of effective Majorana modes. We show that selectin…
A quantum processor (the programmable gate array) is a quantum network with a fixed structure. A space of states is represented as tensor product of data and program registers. Different unitary operations with the data register correspond to "loaded" programs without any changing or "tuning" of network itself. Due to such property and undesirability of entanglement between program and data registers, universality of quantum processors is subject of rather strong restrictions. By different authors was developed universal "stochastic" quantum gate arrays. It was proved also, that "deterministic…
We propose a new scheme for solid-state photonic quantum computation in which trapped photons in optical cavities are taken as a quantum bit. Quantum gates can be realized by coupling the cavities with quantum dots through waveguides. The proposed scheme allows programmable and deterministic gate operations and the system can be scaled up to many quantum bits.
We demonstrate a programmable quantum Hall circuit that implements a novel iterative voltage bisection scheme and allows obtaining any binary fraction $(k/2^n)$ of the fundamental resistance quantum $R_K/2=h/2e^2$. The circuit requires a number $n$ of bisection stages that only scales logarithmically with the precision of the fraction. The value of $k$ can be set to any integer between 1 and $2^n$ by proper gate configuration. The architecture exploits gate-controlled routing, mixing and equilibration of edge modes of robust quantum Hall states. The device does not contain {\em any} internal o…
Parametric DRAG for leakage-suppressed exchange gates in superconducting qubits
National Laboratory of Solid State Microstructures, School of Physics, Nanjing University（南京大学固体微结构物理学院）；Shishan Laboratory, Suzhou Campus of Nanjing University（南京大学苏州校区石崑实验室）；Jiangsu Key Laboratory of Quantum Information Science and Technology, Nanjing University（南京大学江苏省量子信息科学与技术重点实验室）；Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学技术大学量子信息与量子物理协同创新中心）；Hefei National Laboratory（合肥国家实验室）
A programmable gate array is a circuit whose action is controlled by input data. In this letter we describe a special--purpose quantum circuit that can be programmed to evaluate the expectation value of any operator $O$ acting on a space of states of $N$ dimensions. The circuit has a program register whose state $|Ψ(O)>_P$ encodes the operator $O$ whose expectation value is to be evaluated. The method requires knowledge of the expansion of $O$ in a basis of the space of operators. We discuss some applications of this circuit and its relation to known instances of quantum state tomography.
Generative adversarial networks are an emerging technique with wide applications in machine learning, which have achieved dramatic success in a number of challenging tasks including image and video generation. When equipped with quantum processors, their quantum counterparts--called quantum generative adversarial networks (QGANs)--may even exhibit exponential advantages in certain machine learning applications. Here, we report an experimental implementation of a QGAN using a programmable superconducting processor, in which both the generator and the discriminator are parameterized via layers o…
Simulating the topological phases of matter in synthetic quantum simulators is a topic of considerable interest. Given the universality of digital quantum simulators, the prospect of digitally simulating exotic topological phases is greatly enhanced. However, it is still an open question how to realize digital quantum simulation of topological phases of matter. Here, using common single- and two-qubit elementary quantum gates, we propose and demonstrate an approach to design topologically protected quantum circuits on the current generation of noisy quantum processors where spin-orbital coupli…
Within the unified framework of exploiting the relative entropy as a distance measure of quantum correlations, we make explicit the hierarchical structure of quantum coherence, quantum discord and quantum entanglement in multipartite systems. On this basis, we introduce a new measure of quantum coherence, the basis-free quantum coherence and prove that this quantity is exactly equivalent to quantum discord. Furthermore, since the original relative entropy of coherence is a basis-dependent quantity, we investigate the local and nonlocal unitary creation of quantum coherence, focusing on the two…
Probabilistic storage and retrieval (PSR) of unitary quantum dynamics is possible with exponentially small failure probability with respect to the number of systems used as a quantum memory [PRL 122, 170502 (2019)]. Here we study improvements due to a priori knowledge about the unitary transformation to be stored. In particular, we study $N \rightarrow 1$ PSR of qubit phase gates, i.e. qubit rotations a round $Z$ axis with an unknown angle, and show that if we access the gate only $N$-times, the optimal probability of perfect retrieving of its single use is $N/(N+1)$. We propose a quantum circ…
Quantum technologies, such as quantum communication, sensing and imaging, need a platform which is flexible, miniaturizable and works at room temperature. Integrated photonics is a promising and fast-developing platform. This requires to develop the right tools to design and fabricate arbitrary photonic quantum devices. Here we present an algorithm which, starting from a $n$-mode transformation $U$, designs a photonic device implementing $U$. Using this method we design integrated photonic devices which implement quantum gates with high fidelity. Apart from quantum computation, future applicat…
Growing interest in quantum computing for practical applications has led to a surge in the availability of programmable machines for executing quantum algorithms. Present day photonic quantum computers have been limited either to non-deterministic operation, low photon numbers and rates, or fixed random gate sequences. Here we introduce a full-stack hardware-software system for executing many-photon quantum circuits using integrated nanophotonics: a programmable chip, operating at room temperature and interfaced with a fully automated control system. It enables remote users to execute quantum …
The universality theorem in quantum computing states that any quantum computational task can be decomposed into a finite set of logic gates operating on one and two qubits. However, the process of such decomposition is generally inefficient, often leading to exponentially many gates to realize an arbitrary computational task. Practical processor designs benefit greatly from availability of multi-qubit gates that operate on more than two qubits to implement the desired circuit. In 1995, Cirac and Zoller proposed a method to realize native multi-qubit controlled-$Z$ gates in trapped ion systems,…
Searching large databases is an important problem with broad applications. The Grover search algorithm provides a powerful method for quantum computers to perform searches with a quadratic speedup in the number of required database queries over classical computers. It is an optimal search algorithm for a quantum computer, and has further applications as a subroutine for other quantum algorithms. Searches with two qubits have been demonstrated on a variety of platforms and proposed for others, but larger search spaces have only been demonstrated on a non-scalable NMR system. Here, we report res…
The implementation of a quantum computer requires the realization of a large number of N-qubit unitary operations which represent the possible oracles or which are part of the quantum algorithm. Until now there are no standard ways to uniformly generate whole classes of N-qubit gates. We have developed a method to generate arbitrary controlled phase shift operations with a single network of one-qubit and two-qubit operations. This kind of network can be adapted to various physical implementations of quantum computing and is suitable to realize the Deutsch-Jozsa algorithm as well as Grover's se…
Electrically-programmable frequency comb for compact quantum photonic circuits
Institute of Nuclear Sciences, Hacettepe University（哈杰泰普大学核科学研究所）；Department of Physics, Quaid-i-Azam University（奎德-阿扎姆大学物理系）；Department of Physics, Recep Tayyip Erdogan University（雷杰普·塔伊普·埃尔多安大学物理系）；Department of Nanoscience and Nanotechnology, Faculty of Arts and Science, Burdur Mehmet Akif Ersoy University（布尔杜尔·梅赫梅特·阿克夫·埃尔索伊大学文理学院纳米科学与纳米技术系）
