Abstract: We present a new algorithm for classical simulation of quantum circuits over the Clifford+T gate set. The runtime of the algorithm is polynomial in the number of qubits and the number of Clifford gates in the circuit but exponential in the number of T gates. The exponential scaling is sufficiently mild that the algorithm can be used in practice to simulate medium-sized quantum circuits dominated by Clifford gates. The first demonstrations of fault-tolerant quantum circuits based on 2D topological codes are likely to be dominated by Clifford gates due to a high implementation cost associated with logical T gates. Thus our algorithm may serve as a verification tool for near-term quantum computers which cannot in practice be simulated by other means. To demonstrate the power of the new method, we performed a classical simulation of a hidden shift quantum algorithm with 40 qubits, a few hundred Clifford gates, and nearly 50 T gates.

Abstract: To enable two photons to interact, a single atom in an optical resonator is used to build a universal photon–photon quantum gate; this could lead to applications in long-distance quantum communication and scalable quantum computing that require the processing of optical quantum information. Two beams of light sharing the same space tend not to interact with one another. Yet if purely photonic technologies such as quantum communication and scalable quantum computing are to be developed — which require components such as switches and logic gates — it will be important to find conditions that facilitate controllable interactions between two photons. To that end, various single-photon quantum devices have been demonstrated in recent years, typically involving interactions between photons and atoms in a resonator. Here Stephan Ritter and colleagues employ such a system to make a logic component for quantum operations — a universal controlled phase flip photon–photon quantum gate — that involves interaction between two individual input photons mediated by a single atom. That two photons pass each other undisturbed in free space is ideal for the faithful transmission of information, but prohibits an interaction between the photons. Such an interaction is, however, required for a plethora of applications in optical quantum information processing1. The long-standing challenge here is to realize a deterministic photon–photon gate, that is, a mutually controlled logic operation on the quantum states of the photons. This requires an interaction so strong that each of the two photons can shift the other’s phase by π radians. For polarization qubits, this amounts to the conditional flipping of one photon’s polarization to an orthogonal state. So far, only probabilistic gates2 based on linear optics and photon detectors have been realized3, because “no known or foreseen material has an optical nonlinearity strong enough to implement this conditional phase shift”4. Meanwhile, tremendous progress in the development of quantum-nonlinear systems has opened up new possibilities for single-photon experiments5. Platforms range from Rydberg blockade in atomic ensembles6 to single-atom cavity quantum electrodynamics7. Applications such as single-photon switches8 and transistors9,10, two-photon gateways11, nondestructive photon detectors12, photon routers13 and nonlinear phase shifters14,15,16,17,18 have been demonstrated, but none of them with the ideal information carriers: optical qubits in discriminable modes. Here we use the strong light–matter coupling provided by a single atom in a high-finesse optical resonator to realize the Duan–Kimble protocol19 of a universal controlled phase flip (π phase shift) photon–photon quantum gate. We achieve an average gate fidelity of (76.2 ± 3.6) per cent and specifically demonstrate the capability of conditional polarization flipping as well as entanglement generation between independent input photons. This photon–photon quantum gate is a universal quantum logic element, and therefore could perform most existing two-photon operations. The demonstrated feasibility of deterministic protocols for the optical processing of quantum information could lead to new applications in which photons are essential, especially long-distance quantum communication and scalable quantum computing.

Abstract: We present quantum circuits to implement an exhaustive key search for the Advanced Encryption Standard AES and analyze the quantum resources required to carry out such an attack. We consider the overall circuit size, the number of qubits, and the circuit depth as measures for the cost of the presented quantum algorithms. Throughout, we focus on Clifford$$+T$$ gates as the underlying fault-tolerant logical quantum gate set. In particular, for all three variants of AES key size 128, 192, and 256i¾źbit that are standardized in FIPS-PUB 197, we establish precise bounds for the number of qubits and the number of elementary logical quantum gates that are needed to implement Grover's quantum algorithm to extract the key from a small number of AES plaintext-ciphertext pairs.

Abstract: The physical implementation of quantum information processing relies on individual modules-qubits-and operations that modify such modules either individually or in groups-quantum gates. Two examples of gates that entangle pairs of qubits are the controlled NOT-gate (CNOT) gate, which flips the state of one qubit depending on the state of another, and the gate that brings a two-qubit product state into a superposition involving partially swapping the qubit states. Here we show that through supramolecular chemistry a single simple module, molecular {Cr7Ni} rings, which act as the qubits, can be assembled into structures suitable for either the CNOT or gate by choice of linker, and we characterize these structures by electron spin resonance spectroscopy. We introduce two schemes for implementing such gates with these supramolecular assemblies and perform detailed simulations, based on the measured parameters including decoherence, to demonstrate how the gates would operate.

Abstract: With improved gate calibrations reducing unitary errors, we achieve a benchmarked single-qubit gate fidelity of $0.9995\ifmmode\pm\else\textpm\fi{}0.0002$ with superconducting qubits in a circuit quantum electrodynamics system. We present a method for distinguishing between unitary and nonunitary errors in quantum gates by interleaving repetitions of a target gate within a randomized benchmarking sequence. The benchmarking fidelity decays quadratically with the number of interleaved gates for unitary errors but linearly for nonunitary errors, allowing us to separate systematic coherent errors from decoherent effects. With this protocol, we show that the fidelity of the gates is not limited by unitary errors.

Abstract: Ensuring nearest neighbor compliance of quantum circuits by inserting SWAP gates has heavily been considered in the past. Here, quantum gates are considered which work on non-adjacent qubits. SWAP gates are applied in order to “move” these qubits onto adjacent positions. However, a decision how exactly the SWAPs are “moved” has mainly been made without considering the effect a “movement” of qubits may have on the remaining circuit. In this work, we propose a methodology for nearest neighbor optimization which addresses this problem by means of a look-ahead scheme. To this end, two representative implementations are presented and discussed in detail. Experimental evaluations show that, in the best case, reductions in the number of SWAP gates of 56% (compared to the state-of-the-art methods) can be achieved following the proposed methodology.

Abstract: We theoretically show that a nonlinear oscillator network with controllable parameters can be used for universal quantum computation. The initialization is achieved by a quantum-mechanical bifurcation based on quantum adiabatic evolution, which yields a Schr\"odinger cat state. All the elementary quantum gates are also achieved by quantum adiabatic evolution, in which dynamical phases accompanying the adiabatic evolutions are controlled by the system parameters. Numerical simulation results indicate that high gate fidelities can be achieved, where no dissipation is assumed.

Abstract: Extracting weak signals from quantum systems is often a test of quantum control. Classical signal-processing techniques are adapted to allow the systematic and efficient design of composite quantum gates for such tasks.

Abstract: A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer.

Abstract: Quantum information protected by the topology of the storage medium is expected to exhibit long coherence times. Another feature are topologically protected gates generated through braiding of Majorana bound states. However, braiding requires structures with branched topological segments which have inherent difficulties in the semiconductor-superconductor heterostructures now believed to host Majorana bound states. In this paper, we construct quantum bits taking advantage of the topological protection and non-local properties of Majorana bound states in a network of parallel wires, but without relying on braiding for quantum gates. The elementary unit is made from three topological wires, two wires coupled by a trivial superconductor and the third acting as an interference arm. Coulomb blockade of the combined wires spawns a fractionalized spin, non-locally addressable by quantum dots used for single-qubit readout, initialization, and manipulation. We describe how the same tools allow for measurement-based implementation of the Clifford gates, in total making the architecture universal. Proof-of-principle demonstration of topologically protected qubits using existing techniques is therefore within reach.

Abstract: Nonadiabatic holonomic quantum computation provides the means to perform fast and robust quantum gates by utilizing the resilience of non-Abelian geometric phases to fluctuations of the path in state space. While the original scheme [E. Sj\"oqvist et al., New J. Phys. 14, 103035 (2012)] needs two loops in the Grassmann manifold (i.e., the space of computational subspaces of the full state space) to generate an arbitrary holonomic one-qubit gate, we propose single-loop one-qubit gates that constitute an efficient universal set of holonomic gates when combined with an entangling holonomic two-qubit gate. Our one-qubit gate is realized by dividing the loop into path segments, each of which is generated by a $\mathrm{\ensuremath{\Lambda}}$-type Hamiltonian. We demonstrate that two path segments are sufficient to realize arbitrary single-loop holonomic one-qubit gates. We describe how our scheme can be implemented experimentally in a generic atomic system exhibiting a three-level $\mathrm{\ensuremath{\Lambda}}$-coupling structure by utilizing carefully chosen laser pulses.

Abstract: We propose an effective, scalable, hyperparallel photonic quantum computation scheme in which photonic qubits are hyperencoded both in the spatial degrees of freedom (DOF) and the polarization DOF of each photon. The deterministic hyper-controlled-not (hyper-cnot) gate on a two-photon system is attainable with our interesting interface between the polarized photon and the collective spin wave (magnon) of an atomic ensemble embedded in a double-sided optical cavity, and it doubles the operations in the conventional quantum cnot gate. Moreover, we present a compact hyper-cnot${}^{N}$ gate on $N+1$ hyperencoded photons with only two auxiliary cavity-magnon systems, not more, and it can be faithfully constituted with current experimental techniques. Our proposal enables various applications with the hyperencoded photons in quantum computing and quantum networks.

Abstract: Three-qubit quantum gates are key ingredients for quantum error correction and quantum-information processing. We generate quantum-control procedures to design three types of three-qubit gates, namely Toffoli, controlled-NOT-NOT, and Fredkin gates. The design procedures are applicable to a system comprising three nearest-neighbor-coupled superconducting artificial atoms. For each three-qubit gate, the numerical simulation of the proposed scheme achieves 99.9% fidelity, which is an accepted threshold fidelity for fault-tolerant quantum computing. We test our procedure in the presence of decoherence-induced noise and show its robustness against random external noise generated by the control electronics. The three-qubit gates are designed via the machine-learning algorithm called subspace-selective self-adaptive differential evolution.

Abstract: The implementation of holonomic quantum computation on superconducting quantum circuits is challenging due to the general requirement of controllable complicated coupling between multilevel systems. Here we solve this problem by proposing a scalable circuit QED lattice with simple realization of a universal set of nonadiabatic holonomic quantum gates. Compared with the existing proposals, we can achieve both the single and two logical qubit gates in a tunable and all-resonant way through a hybrid transmon--transmission-line encoding of the logical qubits in the decoherence-free subspaces. This distinct advantage thus leads to quantum gates with very fast speeds and consequently very high fidelities. Therefore, our scheme paves a promising way towards the practical realization of high-fidelity nonadiabatic holonomic quantum computation.

Abstract: We propose a novel scheme for high fidelity photonic controlled phase gates using Rydberg blockade in an ensemble of atoms in an optical cavity. The gate operation is obtained by first storing a photonic pulse in the ensemble and then scattering a second pulse from the cavity, resulting in a phase change depending on whether the first pulse contained a single photon. We show that the combination of Rydberg blockade and optical cavities effectively enhances the optical non-linearity created by the strong Rydberg interaction and thereby reduces the requirements for photonic quantum gates. The resulting gate can be implemented with cavities of moderate finesse which allows for highly efficient processing of quantum information encoded in photons. As a particular example of this, we show how the gate can be employed to increase the communication rate of quantum repeaters based on atomic ensembles.

Abstract: We propose genetic algorithms, which are robust optimization techniques inspired by natural selection, to enhance the versatility of digital quantum simulations. In this sense, we show that genetic algorithms can be employed to increase the fidelity and optimize the resource requirements of digital quantum simulation protocols while adapting naturally to the experimental constraints. Furthermore, this method allows us to reduce not only digital errors but also experimental errors in quantum gates. Indeed, by adding ancillary qubits, we design a modular gate made out of imperfect gates, whose fidelity is larger than the fidelity of any of the constituent gates. Finally, we prove that the proposed modular gates are resilient against different gate errors.

Abstract: Quantum computing architectures are on the verge of scalability, a key requirement for the implementation of a universal quantum computer. The next stage in this quest is the realization of quantum error correction codes, which will mitigate the impact of faulty quantum information on a quantum computer. Architectures with ten or more quantum bits (qubits) have been realized using trapped ions and superconducting circuits. While these implementations are potentially scalable, true scalability will require systems engineering to combine quantum and classical hardware. One technology demanding imminent efforts is the realization of a suitable wiring method for the control and measurement of a large number of qubits. In this work, we introduce an interconnect solution for solid-state qubits: The quantum socket. The quantum socket fully exploits the third dimension to connect classical electronics to qubits with higher density and better performance than two-dimensional methods based on wire bonding. The quantum socket is based on spring-mounted micro wires the three-dimensional wires that push directly on a micro-fabricated chip, making electrical contact. A small wire cross section (~1 mmm), nearly non-magnetic components, and functionality at low temperatures make the quantum socket ideal to operate solid-state qubits. The wires have a coaxial geometry and operate over a frequency range from DC to 8 GHz, with a contact resistance of ~150 mohm, an impedance mismatch of ~10 ohm, and minimal crosstalk. As a proof of principle, we fabricated and used a quantum socket to measure superconducting resonators at a temperature of ~10 mK.

Abstract: A universal quantum computer requires a full set of basic quantum gates. With Majorana bound states one can form all necessary quantum gates in a topologically protected way, bar one. In this paper, we present a scheme that achieves the missing, so-called, π/8 magic phase gate without the need of fine-tuning for distinct physical realizations. The scheme is based on the manipulation of geometric phases described by a universal protocol and converges exponentially with the number of steps in the geometric path. Furthermore, our magic gate proposal relies on the most basic hardware previously suggested for topologically protected gates, and can be extended to an any-phase gate, where π/8 is substituted by any α.

Abstract: With recent interest in reversible and quantum computation, research in synthesis of reversible and quantum circuits has increased in momentum. With additional requirements of neighborhood interactions among qubits (with two basis states) being a necessity in some physical realizations, several works on obtaining nearest neighbor quantum gate realization by inserting SWAP gates have been reported. These methods are based on two broad optimization approaches, one based on global ordering, where qubits are ordered over the whole netlist, and the other based on local ordering for minimizing SWAP gate insertions on smaller segments of netlists. Further reductions in cost are possible by using multi-valued qudits that have more than two basis states. The present paper considers a quantum circuit based on the NCV library, and proposes a better SWAP gate insertion method based on local ordering that uses an $N$ -gate lookahead approach to reduce cost. Experimental results on benchmark circuits and comparison against published works confirm the benefits of the proposed approach, with improvements over reported works obtained in the range of 27%–43% on the average and 54%–63% in the best case. The method is also scalable for larger circuits, with the longest runtime observed as 10 minutes.

Abstract: In the early days of quantum mechanics, it was believed that the time energy uncertainty principle (TEUP) bounds the efficiency of energy measurements, relating the duration ($\Delta t$) of the measurement, and its accuracy error ($\Delta E$) by $\Delta t\Delta E \ge$ 1/2. In 1961 Y. Aharonov and Bohm gave a counterexample, whereas Aharonov, Massar and Popescu [2002] showed that under certain conditions the principle holds. Can we classify when and to what extent the TEUP is violated? Our main theorem asserts that such violations are in one to one correspondence with the ability to "fast forward" the associated Hamiltonian, namely, to simulate its evolution for time $t$ using much less than $t$ quantum gates. This intriguingly links precision measurements with quantum algorithms. Our theorem is stated in terms of a modified TEUP, which we call the computational TEUP (cTEUP). In this principle the time duration ($\Delta t$) is replaced by the number of quantum gates required to perform the measurement, and we argue why this is more suitable to study if one is to understand the totality of physical resources required to perform an accurate measurement. The inspiration for this result is a family of Hamiltonians we construct, based on Shor's algorithm, which exponentially violate the cTEUP (and the TEUP), thus allowing exponential fast forwarding. We further show that commuting local Hamiltonians and quadratic Hamiltonians of fermions (e.g., Anderson localization model), can be fast forwarded. The work raises the question of finding a physical criterion for fast forwarding, in particular, can many body localization systems be fast forwarded? We rule out a general fast-forwarding method for all physically realizable Hamiltonians (unless BQP=PSPACE). Connections to quantum metrology and to Susskind's complexification of a wormhole's length are discussed.

Abstract: Single electron sources enable electron quantum optics experiments where single electrons emitted in a ballistic electronic interferometer plays the role of a single photons emitted in an optical medium in Quantum Optics. A qualitative step has been made with the recent generation of single charge levitons obtained by applying Lorentzian voltage pulse on the contact of the quantum conductor. Simple to realize and operate, the source emits electrons in the form of striking minimal excitation states called levitons. We review the striking properties of levitons and their possible applications in quantum physics to electron interferometry and entanglement. W Schematic generation of time resolved single charges called levitons using Lorentzian voltage pulses applied on a contact. A Quantum Point Contact is used to partition the levitons for further analysis. Injecting levitons on opposite contacts with a delay $\\tau$ enables to probe electronic like Hong Ou Mandel correlations. Copyright line will be provided by the publisher 1 Single electron sources In this introduction, we will distinguish single charge sources from coherent single electrons sources. The former have been developed for quantum metrology where the goal is to transfer an integer charge at high frequency f through a conductor with good accuracy to realize a quantized current source whose current I = ef shows metrological accuracy. The latter, the coherent single electrons source, aims at emitting (injecting) a single electron whose wave-function is well defined and controlled to realize further single electron coherent manipulation via quantum gates. The gates are provided by electronic beam-splitters made with Quantum Point Contacts or provided by electronic Mach-Zehnder and Fabry-Prot interferometers. Here it is important that the injected single electron is the only excitation created in the conductor. The frequency f of injection is not chosen to have a large current, as current accuracy is not the goal, but only to get sufficient statistics on the electron transfer events to extract physical information. 1.1 single charge sources for current standards The first manipulation of single charges trace back to the early 90's where physicists took advantage of charge quan-tization of a submicronic metallic island nearly isolated from leads by tunnel barriers. The finite energy E C = e 2 /2C to charge the small capacitor C with a single charge being larger than temperature (typically one kelvin for

Abstract: This paper studies fault-tolerant quantum computation with gapped boundaries. We first introduce gapped boundaries of Kitaev's quantum double models for Dijkgraaf-Witten theories using their Hamiltonian realizations. We classify the elementary excitations on the boundary, and systematically describe the bulk-to-boundary condensation procedure. We also provide a commuting Hamiltonian to realize defects between boundaries in any quantum double model. Next, we present the algebraic/categorical structure of gapped boundaries and boundary defects, which will be used to describe topologically protected operations and obtain quantum gates. To demonstrate a potential physical realization, we provide quantum circuits for surface codes that can perform all basic operations on gapped boundaries. Finally, we show how gapped boundaries of the abelian theory $\mathfrak{D}(\mathbb{Z}_3)$ can be used to perform universal quantum computation.

Abstract: Reversible arithmetic units such as adders, subtractors and comparators form the essential components of any hardware implementation of quantum algorithms such as Shor's factoring algorithm. Further, the synthesis methods proposed in the existing literature for reversible circuits target combinational and sequential circuits in general and are not suitable for synthesis of reversible arithmetic units. In this paper, we present several design methodologies for reversible subtractor and reversible adder-subtractor circuits, and a framework for synthesizing reversible arithmetic circuits. Three different design methodologies are proposed for the design of reversible ripple borrow subtractor that vary in terms of optimization of metrics such as ancilla inputs, garbage outputs, quantum cost and delay. The first approach follows the traditional ripple carry approach while the other two use the properties that the subtraction operation can be defined as $$a-b$$ = $$\overline{\bar{a}+b}$$ and $$a-b$$ = $${a+\bar{b}+1}$$, respectively. Next, we derive methodologies adapting the subtractor to also perform addition as selected with a control signal. Finally, a new synthesis framework for automatic generation of reversible arithmetic circuits optimizing the metrics of ancilla inputs, garbage outputs, quantum cost and the delay is presented that integrates the various methodologies described in our work.

Abstract: Photonic quantum information processing system has been widely used in communication, metrology and lithography. The recent emphasis on the miniaturized photonic platform is thus motivated by the urgent need for realizing large-scale information processing and computing. Although the integrated quantum logic gates and quantum algorithms based on path encoding have been successfully demonstrated, the technology for handling another commonly used polarization-encoded qubits has yet to be fully developed. Here, we show the implementation of a polarization-dependent beam-splitter in the hybrid waveguide system. With precisely design, the polarization-encoded controlled-NOT gate can be implemented using only single such polarization-dependent beam-splitter with the significant size reduction of the overall device footprint to 14 × 14 μm(2). The experimental demonstration of the highly integrated controlled-NOT gate sets the stage to develop large-scale quantum information processing system. Our hybrid design also establishes the new capabilities in controlling the polarization modes in integrated photonic circuits.

Abstract: 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 that while the level-1 pseudothreshold for the concatenated scheme is limited by the logical Hadamard gate, the error suppression of the logical cnot gates allows for the asymptotic threshold to increase by orders of magnitude at higher levels. We establish a lower bound of 1.28×10^{-3} for the asymptotic threshold of this code, which is competitive with known concatenated models and does not rely on ancillary magic state preparation for universal computation.

Abstract: This paper is concerned with the physical design of quantum logic circuits. More precisely, it addresses the problem of minimizing the number of required qubit reorderings (achieved by inserting explicit SWAP gates) when mapping a quantum circuit into a linear nearest neighbor quantum archi-tecture. First, an interaction graph that captures the interaction distances among various qubits in the quantum circuit is constructed. The interaction graph is utilized to partition the quantum circuit into a set of subcircuits such that the number of required qubit reoderings within each subcircuit is provably no more than a given threshold. Next, a Minimum Linear Arrangement problem for each subcircuit is formulated and solved to achieve the minimum number of internal qubit reorderings and determine the subcircuit input and output qubit orderings. Finally, a bubble sort algorithm is repeatedly employed to minimize the number of qubit reorderings that are required between the consecutive subcircuits. Experiments done on various quantum Fourier transform circuits as well as various reversible logic circuits demonstrate the effectiveness of the proposed approach.