We show that an n-th root of the Walsh-Hadamard transform (obtained from the Hadamard gate and a cyclic permutation of the qubits), together with two diagonal matrices, namely a local qubit-flip (for a fixed but arbitrary qubit) and a non-local phase-flip (for a fixed but arbitrary coefficient), can do universal quantum computation on n qubits. A quantum computation, making use of n qubits and based on these operations, is then a word of variable length, but whose letters are always taken from an alphabet of cardinality three. Therefore, in contrast with other universal sets, no choice of qubit lines is needed for the application of the operations described here. A quantum algorithm based on this set can be interpreted as a discrete diffusion of a quantum particle on a de Bruijn graph, corrected on-the-fly by auxiliary modifications of the phases associated to the arcs.
Suppose we can apply a given 2-qubit Hamiltonian H to any (ordered) pair of qubits. We say H is n-universal if it can be used to approximate any unitary operation on n qubits. While it is well known that almost any 2-qubit Hamiltonian is 2-universal (Deutsch, Barenco, Ekert 1995; Lloyd 1995), an explicit characterization of the set of non-universal 2-qubit Hamiltonians has been elusive. Our main result is a complete characterization of 2-non-universal 2-qubit Hamiltonians. In particular, there are three ways that a 2-qubit Hamiltonian H can fail to be universal: (1) H shares an eigenvector wit…
Superconducting quantum circuit is a promising system for building quantum computer. With this system we demonstrate the universal quantum computations, including the preparing of initial states, the single-qubit operations, the two-qubit universal gate operations between arbitrary qubits, the multiple pairs of two-qubit gate operations in parallel, the coupling operations on a group of qubits in parallel, the coupling operations on multiple groups of qubits in parallel, the coupling operations on multiple pairs and multiple groups of qubits in parallel. Within available technology, a universa…
It is shown that efficient and robust universal quantum computation is possible using the stimulated Raman adiabatic passage with a qubit chain as a pointer register.
Nielsen [quant-ph/0108020] showed that universal quantum computation is possible given quantum memory and the ability to perform projective measurements on up to 4-qubits. We describe an improved method that requires only 2-qubit measurements, which are both sufficient and necessary. We present a method to partially collapse the $C_k$-hierarchy in the indirect construction of unitary gates [Gottesman and Chuang, Nature, {\bf 402} 309 (1999)], and apply the method to find discrete universal sets of 2-qubit measurements.
We consider two-qubit undergoing local dissipation and subject to local driving. We then determine the optimal Markovian feedback action to preserve initial entanglement as well as to create stationary entanglement with the help of an XY interaction Hamiltonian. Such feedback actions are worked out in a way not depending on the initial two-qubit state, whence called universal.
We show how to control and perform universal three-qubit quantum computation with trapped electron quantum states. The three qubits are the electron spin, and the first two quantum states of the cyclotron and axial harmonic oscillators. We explicitly show how the universal gates can be performed. As an example of a non-trivial quantum algorithm, we outline the implementation of the Deutsch-Jozsa algorithm in this system.
To generate arbitrary one- and two-qubit gates, the universal decompositions are usually used in quantum computing, and the universality of these decompositions has been demonstrated. However, in realistic experiments, gate errors may affect the universality of the universal decompositions. Here, we focus on the single-qubit-gate decomposition scheme and study the coherent-error effects on universality. We prove that, in the parameter space which we studied, some kinds of coherent errors will not affect the original universality, but some others will destroy it. We provide the definition and a…
We present a finite set of projective measurements that, together with quantum memory and preparation of the |0> state, suffice for universal quantum computation. This extends work of Nielsen [quant-ph/0108020], who proposed a scheme in which an arbitrary unitary operation on n qubits can be simulated using only projective measurements on at most 2n qubits. All measurements in our set involve two qubits, except two measurements which involve three qubits. Thus we improve by one the upper bound, implied by Nielsen's results, on the maximum number of qubits needed to participate in any single me…
A field configuration utilizing local static and oscillating fields is constructed to achieve universal (but low-order) protection of two-qubit states. That is, two-qubit states can be protected against arbitrary system-environment coupling if the driving field frequency, as compared with the cutoff frequency of the environment, is sufficiently large. Equally important, we show that it is possible to construct driving fields to protect two-qubit entangling gates against decoherence, without assuming any particular form of system-environment coupling. Using a non-Markovian master equation, we f…
We demonstrate that in a coupled two-qubit system any single-qubit gate can be decomposed into two conditional two-qubit gates and that any conditional two-qubit gate can be implemented by a manipulation analogous to that used for a controlled two-qubit gate. Based on this we present a unified approach to implement universal single-qubit and two-qubit gates in a coupled two-qubit system with fixed always-on coupling. This approach requires neither supplementary circuit or additional physical qubits to control the coupling nor extra hardware to adjust the energy level structure. The feasibility…
We show that there does not exist any universal quantum cloning machine that can broadcast an arbitrary mixed qubit with a constant fidelity. Based on this result, we investigate the dependent quantum cloner in the sense that some parameter of the input qubit $ρ_s(θ,ω,λ)$ is regarded as constant in the fidelity. For the case of constant $ω$, we establish the $1\to2$ optimal symmetric dependent cloner with a fidelity 1/2. It is also shown that the $1\to M$ optimal quantum cloning machine for pure qubits is also optimal for mixed qubits, when $λ$ is the unique parameter in the fidelity. For gene…
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.
Reliable quantum information processing requires high-fidelity universal manipulation of quantum systems within the characteristic coherence times. Non-adiabatic holonomic quantum computation offers a promising approach to implement fast, universal, and robust quantum logic gates particularly useful in nano-fabricated solid-state architectures, which typically have short coherence times. Here, we propose an experimentally feasible scheme to realize high-speed universal geometric quantum gates in nano-engineered pseudo-spin charge qubits. We use a system of three coupled quantum dots containing…
We present a universal set of quantum gate operations based on exchange-only spin qubits in a double quantum dot, where each qubit is obtained by three electrons in the (2,1) filling. Gate operations are addressed by modulating electrostatically the tunneling barrier and the energy offset between the two dots, singly and doubly occupied respectively. We propose explicit gate sequences of single qubit operations for Hadamard gate and $π$/8 gate, and the two-qubit controlled NOT (CNOT) gate, to complete the universal set. The unswitchable interaction between the two electrons of the doubly occup…
We propose a scheme to realize $1\to 2$ universal quantum cloning machine (UQCM) with superconducting quantum interference device (SQUID) qubits, embeded in a high-Q cavity. CNOT operations are derived to present our scheme, and the two-photon Raman resonance processes are used to increase the operation rate. Compared with previous works, our scheme has advantages in the experimental realization and further utilization.
We review our recent work on the universal (i.e. input state independent) optimal quantum copying (cloning) of qubits. We present unitary transformations which describe the optimal cloning of a qubit and we present the corresponding quantum logical network. We also present network for an optimal quantum copying ``machine'' (transformation) which produces N+1 identical copies from the original qubit. Here again the quality (fidelity) of the copies does not depend on the state of the original and is only a function of the number of copies, N. In addition, we present the machine which universaly …
Quantum control of systems plays important roles in modern science and technology. The ultimate goal of quantum control is to achieve high fidelity universal control in the time-optimal way. Although high fidelity universal control has been reported in various quantum systems, experimental implementation of time-optimal universal control remains elusive. Here we report the experimental realization of time-optimal universal control of spin qubits in diamond. By generalizing a recent method for solving quantum brachistochrone equations [X. Wang, et al., Phys. Rev. Lett. 114, 170501 (2015)], we o…
We consider the implementation of two-qubit unitary transformations by means of CNOT gates and single-qubit unitary gates. We show, by means of an explicit quantum circuit, that together with local gates three CNOT gates are necessary and sufficient in order to implement an arbitrary unitary transformation of two qubits. We also identify the subset of two-qubit gates that can be performed with only two CNOT gates.
We describe a general framework to study covariant symmetric broadcasting maps for mixed qubit states. We explicitly derive the optimal N to M superbroadcasting maps, achieving optimal purification of the single-site output copy, in both the universal and the phase covariant cases. We also study the bipartite entanglement properties of the superbroadcast states.
Uhrig's dynamical decoupling pulse sequence has emerged as one universal and highly promising approach to decoherence suppression. So far both the theoretical and experimental studies have examined single-qubit decoherence only. This work extends Uhrig's universal dynamical decoupling from one-qubit to two-qubit systems and even to general multi-level quantum systems. In particular, we show that by designing appropriate control Hamiltonians for a two-qubit or a multi-level system, Uhrig's pulse sequence can also preserve a generalized quantum coherence measure to the order of $1+O(T^{N+1})$, w…
In this paper, we show that the ability to switch globally between two 2-local Hamiltonians on n qubits is sufficient for achieving universal unitary dynamics on those n qubits. Of the two Hamiltonians used in the construction, one is comprised of nearest-neighbour two-qubit interactions on a one-dimensional chain, the other is comprised of single-qubit interactions. We describe a scheme for choosing the switching times in order to generate arbitrary one- and two-qubit gates on the n qubits. However the switching scheme is inefficient, and we leave as an open problem the question of whether th…
Decoherence-induced leakage errors can couple a physical or encoded qubit to other levels, thus potentially damaging the qubit. They can therefore be very detrimental in quantum computation and require special attention. Here we present a general method for removing such errors by using simple decoupling and recoupling pulse sequences. The proposed gates are experimentally accessible in a variety of promising quantum computing proposals.
We study the entanglement evolution of photonic orbital angular momentum qubit states with opposite azimuthal indices $l_0$, in a weakly turbulent atmosphere. Using asymptotic methods, we deduce analytical expressions for the amplitude of turbulence-induced crosstalk between the modes $l_0$ and $-l_0$. Furthermore, we analytically establish distinct, universal entanglement decay laws for Kolmogorov's turbulence model and for two approximations thereof.
We derive the optimal curve satisfied by the reduction factors, in the case of universal disentangling machine which uses only local operations. Impossibility of constructing a better disentangling machine, by using non-local operations, is discussed.
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.
We give a careful proof that a parallelized version of adiabatic quantum computation can efficiently simulate universal gate model quantum computation. The proof specifies an explicit parameter-dependent Hamiltonian $H(λ)$ that is based on ground state quantum computation [1]. We treat both a 1-dimensional configuration in which qubits on a line undergo nearest neighbor 2-qubit gates and an all-to-all configuration in which every qubit undergoes 2-qubit gates with every other qubit in the system.
We provide an analytic way to implement any arbitrary two-qubit unitary operation, given an entangling two-qubit gate together with local gates. This is shown to provide explicit construction of a universal quantum circuit that exactly simulates arbitrary two-qubit operations in SU(4). Each block in this circuit is given in a closed form solution. We also provide a uniform upper bound of the applications of the given entangling gates, and find that exactly half of all the Controlled-Unitary gates satisfy the same upper bound as the CNOT gate. These results allow for the efficient implementatio…
Beyond the no-cloning theorem, the universal symmetric quantum cloning machine was first addressed by Buzek and Hillery. Here, we realized the one-to-two qubits Buzek-Hillery cloning machine with linear optical devices. This method relies on the representation of several qubits by a single photon. We showed that, the fidelities between the two output qubits and the original qubit are both 5/6 (which proved to be the optimal fidelity of one-to-two qubits universal cloner) for arbitrary input pure states.
We present a simple quantum circuit that allows for the universal and deterministic manipulation of the quantum state of confined harmonic oscillators. The scheme is based on the selective interactions of the referred oscillator with an auxiliary three-level system and a classical external driving source, and enables any unitary operations on Fock states, two-by-two. One circuit is equivalent to a single qubit unitary logical gate on Fock states qubits. Sequences of similar protocols allow for complete, deterministic and state-independent manipulation of the harmonic oscillator quantum state.
In this article we develop, step by step, the framework for universal dynamical control of two-level systems (TLS) or qubits experiencing amplitude- or phase-noise (AN or PN) due to coupling to a thermal bath. A comprehensive arsenal of modulation schemes is introduced and applied to either AN or PN, resulting in completely analogous formulae for the decoherence rates, thus underscoring the unified nature of this universal formalism. We then address the extension of this formalism to multipartite decoherence control, where symmetries are exploited to overcome decoherence.
The controlled-NOT gate and controlled square-root NOT gate play an important role in quantum algorithm. This article reports the experimental results of these two universal quantum logic gates (controlled square-root NOT gate and controlled-NOT gate) on a 7-qubit NMR quantum computer. Further, we propose a simple experimental method to measure and correct the error in the controlled phase-shift gate, which is helpful to construct a more perfect phase-shift gate experimentally and can also be used in more qubits discrete Fourier transformation.
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 …
We consider the entanglement manipulation capabilities of the universal covariant quantum cloner or quantum processor circuit for quantum bits. We investigate its use for cloning a member of a bipartite or a genuine tripartite entangled state of quantum bits. We find that for bipartite pure entangled states a nontrivial behavior of concurrence appears, while for GHZ entangled states a possibility of the partial extraction of bipartite entanglement can be achieved.
Using transversal gates is a straightforward and efficient technique for fault-tolerant quantum computing. Since transversal gates alone cannot be computationally universal, they must be combined with other approaches such as magic state distillation, code switching or code concatenation in order to achieve universality. In this paper we propose an alternative approach for universal fault-tolerant quantum computing mainly based on the code concatenation approach proposed in [PRL 112, 010505 (2014)] but in a non-uniform fashion. The proposed approach is described based on non-uniform concatenat…
We present a protocol for transferring arbitrary continuous-variable quantum states into a few discrete-variable qubits and back. The protocol is deterministic and utilizes only two-mode Rabi-type interactions which are readily available in trapped-ion and superconducting circuit platforms. The inevitable errors caused by transferring an infinite-dimensional state into a finite-dimensional register are suppressed exponentially with the number of qubits. Furthermore, the encoded states exhibit robustness against noise, such as dephasing and amplitude damping, acting on the qubits. Our protocol …
A challenge for constructing large circuits of superconducting qubits is to balance addressability, coherence and coupling strength. High coherence can be attained by building circuits from fixed-frequency qubits, however, leading techniques cannot couple qubits that are far detuned. Here we introduce a method based on a tunable bus which allows for the coupling of two fixed-frequency qubits even at large detunings. By parametrically oscillating the bus at the qubit-qubit detuning we enable a resonant exchange (XX+YY) interaction. We use this interaction to implement a 183ns two-qubit iSWAP ga…
We present some deterministic schemes to construct universal quantum gates, that is, controlled- NOT, three-qubit Toffoli, and Fredkin gates, between flying photon qubits and stationary electron-spin qubits assisted by quantum dots inside double-sided optical microcavities. The control qubit of our gates is encoded on the polarization of the moving single photon and the target qubits are encoded on the confined electron spins in quantum dots inside optical microcavities. Our schemes for these universal quantum gates on a hybrid system have some advantages. First, all the gates are accomplished…
We model repetitive quantum error correction (QEC) with the single-error-correcting five-qubit code on a network of individually-controlled qubits with always-on Ising couplings, using our previously designed universal set of quantum gates based on sequences of shaped decoupling pulses. In addition to serving as accurate quantum gates, the sequences also provide dynamical decoupling (DD) of low-frequency phase noise. The simulation involves integrating unitary dynamics of six qubits over the duration of tens of thousands of control pulses, using classical stochastic phase noise as a source of …
We investigate the decay properties of the quantumness including quantum entanglement, quantum discord and quantum coherence for two photonic qubits, which are partially entangled in their orbital angular momenta, through Kolmogorov turbulent atmosphere. It is found that the decay of quantum coherence and quantum discord may be qualitatively different from that of quantum entanglement when the initial state of two photons is not maximally entangled. We also derive two universal decay laws for quantum coherence and quantum discord, respectively, and show that the decay of quantum coherence is m…
We propose a method of compiling that permits to identify quantum circuits able to simulate arbitrary $n$-qubit unitary operations via the adjustment of angles in single-qubit gates therein. The method of compiling itself extends older quantum control techniques and stays computationally tractable for several qubits. As an application we identify compiling universal circuits for $3$, $4$ and $5$ qubits consisting of $16$, $64$ and $ 256$ CNOTs respectively.
We analyze various scenarios for entangling two initially unentangled qubits. In particular, we propose an optimal universal entangler which entangles a qubit in unknown state $|Ψ>$ with a qubit in a reference (known) state $|0>$. That is, our entangler generates the output state which is as close as possible to the pure (symmetrized) state $(|Ψ>|0> +|0>|Ψ>)$. The most attractive feature of this entangling machine, is that the fidelity of its performance (i.e. the distance between the output and the ideally entangled -- symmetrized state) does not depend on the input and takes the constant val…
We experimentally demonstrate that the nonlocal nature of time-bin entangled photonic qubits persists when one or two qubits of the pair are converted to polarization qubits. This is possible by implementing a novel Universal Time-Bin Qubit Analyzer (UTBA), which, for the first time, allows analyzing time-bin qubits in any basis. We reveal the nonlocal nature of the emitted light by violating the Clauser-Horne-Shimony-Holt inequality with measurement bases exploring all the dimensions of the Bloch sphere. Moreover, we conducted experiments where one qubit is transmitted over a 12.4 km undergro…
Entanglement is an important evidence that a quantum device can potentially solve problems intractable for classical computers. In this paper, we prepare connected graph states involving 8 to 16 qubits on ibmqx5, a 16-qubit superconducting quantum processor accessible via IBM cloud,using low-depth circuits. We demonstrate that the prepared state is fully entangled, i.e. the state is inseparable with respect to any fixed partition.
We propose a teleportation-based scheme to implement a universal set of quantum gates with a four-component cat code, assisted by appropriate entangled resource states and photon number resolving detection. The four-component cat code features the ability to recover from single photon loss. Here, we propose a concrete procedure to correct the single photon loss, including detecting the single photon loss event and recovering the initial states. By concatenating with standard qubit error correcting codes, we estimate the loss threshold for fault-tolerant quantum computation and obtain a signifi…
We find the optimal universal way of manipulating a single qubit, |psi(theta,phi)>, such that (theta,phi)->(theta-k,phi-l). Such optimal transformations fall into two classes. For 0 =< k =< pi/2 the optimal map is the identity and the fidelity varies monotonically from 1 (for k=0) to 1/2 (for k=pi/2). For pi/2 =< k =< pi the optimal map is the universal-NOT gate and the fidelity varies monotonically from 1/2 (for k=pi/2) to 2/3 (for k=pi). The fidelity 2/3 is equal to the fidelity of measurement. It is therefore rather surprising that for some values of k the fidelity is lower than 2/3.
Qubits are neither fermions nor bosons. A Fock space description of qubits leads to a mapping from qubits to parafermions: particles with a hybrid boson-fermion quantum statistics. We study this mapping in detail, and use it to provide a classification of the algebras of operators acting on qubits. These algebras in turn classify the universality of different classes of physically relevant qubit-qubit interaction Hamiltonians. The mapping is further used to elucidate the connections between qubits, bosons, and fermions. These connections allow us to share universality results between the diffe…
Impurities hosted in semiconducting solid matrices represent an extensively studied platform for quantum computing applications. In this scenario, the so-called flip-flop qubit emerges as a convenient choice for scalable implementations in silicon. Flip-flop qubits are realized implanting phosphorous donor in isotopically purified silicon, and encoding the logical states in the donor nuclear spin and in its bound electron. Electrically modulating the hyperfine interaction by applying a vertical electric field causes an Electron Dipole Spin Resonance (EDSR) transition between the states with an…
The Zeno effect occurs in quantum systems when a very strong measurement is applied, which can alter the dynamics in non-trivial ways. Despite being dissipative, the dynamics stay coherent within any degenerate subspaces of the measurement. Here we show that such a measurement can turn a single-qubit operation into a two- or multi-qubit entangling gate, even in a non-interacting system. We demonstrate this gate between two effectively non-interacting transmon qubits. Our Zeno gate works by imparting a geometric phase on the system, conditioned on it lying within a particular non-local subspace…
We show how to construct a universal set of quantum logic gates using control over exchange interactions and single- and two-spin measurements only. Single-spin unitary operations are teleported instead of being executed directly, thus eliminating a major difficulty in the construction of several of the most promising proposals for solid-state quantum computation, such as spin-coupled quantum dots, donor-atom nuclear spins in silicon, and electrons on helium. Contrary to previous proposals dealing with this difficulty, our scheme requires no encoding redundancy. We also discuss an application …
We construct a single observable measurement of which mean value on four copies of an {\it unknown} two-qubit state is sufficient for unambiguous decision whether the state is separable or entangled. In other words, there exists a universal collective entanglement witness detecting all two-qubit entanglement. The test is directly linked to a function which characterizes to some extent the entanglement quantitatively. This function is an entanglement monotone under so--called local pure operations and classical communication (pLOCC) which preserve local dimensions. Moreover it provides tight up…
The key to realizing fault-tolerant quantum computation for singlet-triplet (ST) qubits in semiconductor double quantum dot (DQD) is to operate both the single- and two-qubit gates with high fidelity. The feasible way includes operating the qubit near the transverse sweet spot (TSS) to reduce the leading order of the noise, as well as adopting the proper pulse sequences which are immune to noise. The single-qubit gates can be achieved by introducing an AC drive on the detuning near the TSS. The large dipole moment of the DQDs at the TSS has enabled strong coupling between the qubits and the ca…
We characterise a model of universal quantum computation where the register (computational) qubits are controlled by ancillary qubits, using only a single fixed interaction between register and ancillary qubits. No additional access is required to the computational register and the dynamics of both the register and ancilla are unitary. This scheme is inspired by the measurement-based ancilla-driven quantum computation of Anders et al. [PRA 82, 020301(R), 2010], but does not require measurements of the ancillas, and in this respect is similar to the original gate based model of quantum computat…
We prove that universal quantum computation is possible using only (i) the physically natural measurement on two qubits which distinguishes the singlet from the triplet subspace, and (ii) qubits prepared in almost any three different (potentially highly mixed) states. In some sense this measurement is a `more universal' dynamical element than a universal 2-qubit unitary gate, since the latter must be supplemented by measurement. Because of the rotational invariance of the measurement used, our scheme is robust to collective decoherence in a manner very different to previous proposals - in effe…
Any residual coupling of a quantum computer to the environment results in computational errors. Encoding quantum information in a so-called decoherence-free subspace provides means to avoid these errors. Despite tremendous progress in employing this technique to extend memory storage times by orders of magnitude, computation within such subspaces has been scarce. Here, we demonstrate the realization of a universal set of quantum gates acting on decoherence-free ion qubits. We combine these gates to realize the first controlled-NOT gate within a decoherence-free, scalable quantum computer.
We show that every quantum computation can be described by Bayesian update of a probability distribution on a finite state space. When applied to the model of quantum computation with magic states, the size of this state space only depends on the number of magic states used in the quantum computation, and not on the length of the gate and measurement sequence.
We develop a scheme for generating a universal qubit cluster state using probabilistic Bell measurements without the need for feed-forward or long-time quantum memories. Borrowing ideas from percolation theory we numerically show that using unambiguous Bell measurements that succeed with 75% success probability, one could build a cluster state with an underlying pyrochlore geometry such that the probability of having a spanning cluster in a chosen direction approaches unity in the limit of an infinite lattice size. The initial resources required for the generation of a universal state in our p…
