Carlo Ottaviani, David Vitali, Maurizio Artoni, Francesco Cataliotti, Paolo Tombesi
We present here an all--optical scheme for the experimental realization of a quantum phase gate. It is based on the polarization degree of freedom of two travelling single photon wave-packets and exploits giant Kerr nonlinearities that can be attained in coherently driven ultracold atomic media.
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The two-qubit interaction Hamiltonian of a given physical implementation determines whether or not a two-qubit gate such as the CNOT gate can be realized easily. It can be shown that, e.g., with the XY interaction more than one two-qubit operation is required in order to realize CNOT. Here we propose a two-qubit gate for the XY interaction which combines CNOT with the SWAP operation. By using this gate quantum circuits can be implemented efficiently, even if only nearest-neighbor coupling between the qubits is available.
We characterize single qubit Clifford gate operations with randomized benchmarking in a 2D array of neutral atom qubits, and demonstrate global and site selected gates with high fidelity. An average fidelity of $F^2=0.9983(14)$ is measured for global microwave driven gates applied to a 49 qubit array. Single site gates are implemented with a focused laser beam to Stark shift the microwaves into resonance at a selected site. At Stark selected single sites we observe $F^2=0.9923(7)$ and an average spin flip crosstalk error at other sites of $0.002(9)$.
In a large scale trapped atomic ion quantum computer, high-fidelity two-qubit gates need to be extended over all qubits with individual control. We realize and characterize high-fidelity two-qubit gates in a system with up to 4 ions using radial modes. The ions are individually addressed by two tightly focused beams steered using micro-electromechanical system (MEMS) mirrors. We deduce a gate fidelity of 99.49(7)% in a two-ion chain and 99.30(6)% in a four-ion chain by applying a sequence of up to 21 two-qubit gates and measuring the final state fidelity. We characterize the residual errors an…
Due to their strong and tunable interactions, Rydberg atoms can be used to realize fast two-qubit entangling gates. We propose a generalization of a generic two-qubit Rydberg-blockade gate to multi-qubit Rydberg-blockade gates which involve both many control qubits and many target qubits simultaneously. This is achieved by using strong microwave fields to dress nearby Rydberg states, leading to asymmetric blockade in which control-target interactions are much stronger than control-control and target-target interactions. The implementation of these multi-qubit gates can drastically simplify bot…
The prevalent approach to executing quantum algorithms on quantum computers is to break-down the algorithms to a concatenation of universal gates, typically single and two-qubit gates. However such a decomposition results in long gate sequences which are exponential in the qubit register size. Furthermore, gate fidelities tend to decrease when acting in larger qubit registers. Thus high-fidelity implementations in large qubit registers is still a prominent challenge. Here we propose and investigate multi-qubit entangling gates for trapped-ions. Our gates couple many qubits at once, allowing to…
In two-qubit gate simulations an entangling gate is used several times together with single qubit gates to simulate another two-qubit gate. We show how a two-qubit gate's simulation power is related to the simulation power of its mirror gate. And we show that an arbitrary two-qubit gate can be simulated by three applications of a super controlled gate together with single qubit gates. We also give the gates set that can be simulated by n applications of a controlled gate in a constructive way. In addition we give some gates which can be used four times to simulate an arbitrary two-qubit gate.
High-fidelity two-qubit entangling gates play an important role in many quantum information processing tasks and are a necessary building block for constructing a universal quantum computer. Such high-fidelity gates have been demonstrated on trapped-ion qubits, however, control errors and noise in gate parameters may still lead to reduced fidelity. Here we propose and demonstrate a general family of two-qubit entangling gates which are robust to different sources of noise and control errors. These gates generalize the celebrated Mølmer-Sørensen gate by using multi-tone drives. We experimentall…
The decomposition of matrices associated to two-qubit and three-qubit orthogonal gates is studied, and based on the decomposition the synthesis of these gates is investigated. The optimal synthesis of general two-qubit orthogonal gate is obtained. For two-qubit unimodular orthogonal gate, it requires at most 2 CNOT gates and 6 one-qubit Ry gates. For the general three-qubit unimodular orthogonal gate, it can be synthesized by 16 CNOT gates and 36 one-qubit Ry and Rz gates in the worst case.
We study the speed/fidelity trade-off for a two-qubit phase gate implemented in $^{43}$Ca$^+$ hyperfine trapped-ion qubits. We characterize various error sources contributing to the measured fidelity, allowing us to account for errors due to single-qubit state preparation, rotation and measurement (each at the $\sim0.1\%$ level), and to identify the leading sources of error in the two-qubit entangling operation. We achieve gate fidelities ranging between $97.1(2)\%$ (for a gate time $t_g=3.8μ$s) and $99.9(1)\%$ (for $t_g=100μ$s), representing respectively the fastest and lowest-error two-qubit…
Near-term quantum computers are limited by the decoherence of qubits to only being able to run low-depth quantum circuits with acceptable fidelity. This severely restricts what quantum algorithms can be compiled and implemented on such devices. One way to overcome these limitations is to expand the available gate set from single- and two-qubit gates to multi-qubit gates, which entangle three or more qubits in a single step. Here, we show that such multi-qubit gates can be realized by the simultaneous application of multiple two-qubit gates to a group of qubits where at least one qubit is invol…
In this work we investigate that whether one can construct single and two qubit gates for arbitrary quantum states from the principle of no signalling. We considered the problem for Pauli gates, Hadamard gate, C-Not gate.
In this paper, we propose a scheme to realize three-qubit controlled phase gate and multiqubit controlled-NOT gate of one qubit simultaneously controlling n target qubit with four level quantum system in a cavity. Adjustment of level spacing during the gates implementation is not required. Implementation time for multiqubit controlled NOT gate is independent of number of qubit. Three-qubit phase gate is generalized to n-qubit phase gate with multiple control qubit and the number of steps (complexity) reduces linearly as compare to conventional gate decomposition method. Our scheme can be appli…
In this paper, we study the optimal simulation of three-qubit unitary by using two-qubit gates. First, we give a lower bound on the two-qubit gates cost of simulating a multi-qubit gate. Secondly, we completely characterize the two-qubit gate cost of simulating a three-qubit controlled controlled gate by generalizing our result on the cost of Toffoli gate. The function of controlled controlled gate is simply a three-qubit controlled unitary gate and can be intuitively explained as follows: the gate will output the states of the two control qubit directly, and apply the given one-qubit unitary …
We propose how to realize a three-step controlled-phase gate of one superconducting qubit simultaneously controlling n qubits selected from N qubits in a cavity (1<n<N). The operation time of this gate is independent of the number n of qubits involved in the gate operation. This phase gate controlling at once n qubits is insensitive to the initial state of the cavity mode and can be used to produce an analogous CNOT gate simultaneously acting on n qubits.
We propose how to realize a three-step controlled-phase gate of one qubit simultaneously controlling $n$ qubits in a cavity or coupled to a resonator. The $n$ two-qubit controlled-phase gates, forming this multiqubit phase gate, can be performed simultaneously. The operation time of this phase gate is independent of the number $n$ of qubits. This phase gate controlling at once $n$ qubits is insensitive to the initial state of the cavity mode and can be used to produce an analogous CNOT gate simultaneously acting on $n$ qubits. We present two alternative approaches to implement this gate. One a…
We present improved circuits for the control-control-phase (Toffoli) gate and the control-swap (Fredkin) gate using three and four global two-qubit gates, respectively. This is a nearly double speed-up compared to the conventional circuits, which require five (for Toffoli) and seven (for Fredkin) conditional two-qubit gates. We apply the same approach to construct the conditional four-qubit phase gate by seven global two-qubit gates. We also present construction of the Toffoli and the Fredkin gates with five nearest-neighbour interactions. Our constructions do not employ ancilla qubits or anci…
Quantum algorithms often benefit from the ability to execute multi-qubit (>2) gates. To date such multi-qubit gates are typically decomposed into single- and two-qubit gates, particularly in superconducting qubit architectures. The ability to perform multi-qubit operations in a single step could vastly improve the fidelity and execution time of many algorithms. Here, we propose a single shot method for executing an i-Toffoli gate, a three-qubit gate gate with two control and one target qubit, using currently existing superconducting hardware. We show numerical evidence for a process fidelity o…
The three-electron configuration of gate-defined double quantum dots encodes a promising qubit for quantum information processing. I propose a two-qubit entangling gate using a pulse-gated manipulation procedure. The requirements for high-fidelity entangling operations are equivalent to the requirements for the pulse-gated single-qubit manipulations that have been successfully realized for Si QDs. This two-qubit gate completes the universal set of all-pulse-gated operations for the three-electron double-dot qubit and paves the way for a scalable setup to achieve quantum computation.
Modifying $n$-qubit controlled-$ZX$ gate to be $n$-qubit Toffoli gate
本文修改受控-$ZX$门的分解方法，仅用$2n-3$个附加单量子比特门实现$n$-量子比特Toffoli门，保持原电路深度$8n-20$且无需辅助比特，并证明其在现有物理系统中易于构建。
One of the challenges when scaling up semiconductor-based quantum processors consists in the presence of crosstalk errors caused by control operations on neighboring qubits. In previous work, crosstalk in spin qubit arrays has been investigated for non-driven single qubits near individually driven quantum gates and for two simultaneously driven single-qubit gates. Nevertheless, simultaneous gates are not restricted to single-qubit operations but also include frequently used two-qubit gates such as the CNOT gate. We analyse the impact of crosstalk drives on qubit operations, such as the CNOT an…
High-fidelity three-qubit iToffoli gate for fixed-frequency superconducting qubits
研究固定频率超导量子比特中高保真三比特 iToffoli 门的实现，基于交叉共振效应并同步施加微波脉冲，达到 98.26% 的过程保真度，为多比特门开发开辟了新路径。
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 prove that a generic three-qubit quantum logic gate can be implemented using at most 98 one-qubit rotations about the $y$- and $z$-axes and 40 CNOT gates, beating an earlier bound of 64 CNOT gates.
In this paper, we settle the long-standing open problem of the minimum cost of two-qubit gates for simulating a Toffoli gate. More precisely, we show that five two-qubit gates are necessary. Before our work, it is known that five gates are sufficient and only numerical evidences have been gathered, indicating that the five-gate implementation is necessary. The idea introduced here can also be used to solve the problem of optimal simulation of three-qubit control phase introduced by Deutsch in 1989.
A quantum algorithm can be decomposed into a sequence consisting of single qubit and 2-qubit entangling gates. To optimize the decomposition and achieve more efficient construction of the quantum circuit, we can replace multiple 2-qubit gates with a single global entangling gate. Here, we propose and implement a scalable scheme to realize the global entangling gates on multiple $\yb$ ion qubits by coupling to multiple motional modes through external fields. Such global gates require simultaneously decoupling of multiple motional modes and balancing of the coupling strengths for all the qubit-p…
Experimental demonstration of a high-fidelity virtual two-qubit gate
本研究实验演示虚拟双量子比特门，通过电路中间测量实现投影门、确定性采样减少评估次数并结合量子误差缓解，将虚拟CZ门平均保真度提至0.9938±0.0002，为少比特量子模拟及远距双比特门实现提供实用方案。
In some quantum computing (QC) architectures, entanglement of an arbitrary number of qubits can be generated in a single operation. This property has many potential applications, and may specifically be useful for quantum error correction (QEC). Stabilizer measurements can then be implemented using a single multi-qubit gate instead of several two-qubit gates, thus reducing circuit depth. In this study, the toric code is used as a benchmark to compare the performance of two-qubit and five-qubit gates within parity-check circuits. We consider trapped ion qubits that are controlled via Raman tran…
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.
Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any n-qubit gate of this type using at most 2^{n-1} - 1 controlled-NOT gates, 2^{n-1} one-qubit gates and a single diagonal n-qubit gate. The circuit is based on the so-called quantum multiplexor, for which we provide a modified construction. We illustrate the versatility of these gates by applying them to the decomposition of a general n-qubit gate and a local state preparation procedure. …
Two-qubit gates for the soft 0-π qubit
针对软0-π量子比特，提出一种无保护CZ门，利用计算态与高非计算态直接跃迁，在约160纳秒内实现约99.9%保真度，填补了双量子比特门空白。
Two-qubit gates are important components of quantum computing. However, unwanted interactions between qubits (so-called parasitic gates) can be particularly problematic and degrade the performance of quantum applications. In this work, we present two software methods to mitigate parasitic two-qubit gate errors. The first approach is built upon the KAK decomposition and keeps the original unitary decomposition for the error-free native two-qubit gate. It counteracts a parasitic two-qubit gate by only applying single-qubit rotations and therefore has no two-qubit gate overhead. We show the optim…
The three-qubit Toffoli gate plays an important role in quantum error correction and complex quantum algorithms such as Shor's factoring algorithm, motivating the search for efficient implementations of this gate. Here we introduce a Toffoli gate suitable for exchange-coupled electron spin qubits in silicon quantum dot arrays. Our protocol is a natural extension of a previously demonstrated resonantly driven CNOT gate for silicon spin qubits. It is based on a single exchange pulse combined with a resonant microwave drive, with an operation time on the order of 100 ns and fidelity exceeding 99%…
Time-optimal multi-qubit gates: Complexity, efficient heuristic and gate-time bounds
本研究证明时间最优多量子比特门合成是NP难的，给出特殊时间最优门的显式构造，提出多项式时间启发式合成算法，推导GZZ门时间上下界并推测其为O(n)标度，可实现更快更鲁棒的量子算法执行。
Optimal Construction of Two-Qubit Gates using the Symmetries of B Gate Equivalence Class
本文利用B门等价类的对称性，发现仅该等价类具有逆和镜像两种对称性，并找到一参数族可构造通用两比特量子电路，仅需两个非局部门。
Fast microwave-driven two-qubit gates between fluxonium qubits with a transmon coupler
本研究通过精心设计的微波驱动脉冲，实现了一个高保真度的回旋子量子比特间两个量子比特门，展示了快速频率选择性纠缠门的实现方法。
We construct a minimal robust controlled-NOT gate with an Ising-type interaction by which elementary two-qubit gates are implemented. It is robust against inaccuracy of the coupling strength and the obtained quantum circuits are constructed with the minimal number (N=3) of elementary two-qubit gates and several one-qubit gates. It is noteworthy that all the robust circuits can be mapped to one-qubit circuits robust against a pulse length error. We also prove that a minimal robust SWAP gate cannot be constructed with N=3, but requires N=6 elementary two-qubit gates.
In this Letter, we present two analytic expressions that most generally simulate $n$-qubit controlled-$U$ gates with standard one-qubit gates and CNOT gates using exponential and polynomial complexity respectively. Explicit circuits and general expressions of decomposition are derived. The exact numbers of basic operations in these two schemes are given using gate counting technique.
Recent investigations show that conservation laws limit the accuracy of gate operations in quantum computing. The inevitable error under the angular momentum conservation law has been evaluated so far for the CNOT, Hadamard, and NOT gates for spin 1/2 qubits, while the SWAP gate has no constraint. Here, we extend the above results to general single-qubit gates. We obtain an upper bound of the gate fidelity of arbitrary single-qubit gates implemented under arbitrary conservation laws, determined by the geometry of the conservation law and the gate operation on the Bloch sphere as well as the si…
The Heisenberg exchange interaction is a natural method to implement non-local (i.e., multi-qubit) quantum gates in quantum information processing. We consider quantum circuits comprising of $(SWAP)^α$ gates, which are realized through the exchange interaction, and single-qubit gates. A universal two-qubit quantum circuit is constructed from only three $(SWAP)^α$ gates and six single-qubit gates. We further show that three $(SWAP)^α$ gates are not only sufficient, but necessary. Since six single-qubit gates are known to be necessary, our universal two-qubit circuit is optimal in terms of the n…
High-quality two-qubit gate operations are crucial for scalable quantum information processing. Often, the gate fidelity is compromised when the system becomes more integrated. Therefore, a low-error-rate, easy-to-scale two-qubit gate scheme is highly desirable. Here, we experimentally demonstrate a new two-qubit gate scheme that exploits fixed-frequency qubits and a tunable coupler in a superconducting quantum circuit. The scheme requires less control lines, reduces crosstalk effect, simplifies calibration procedures, yet produces a controlled-Z gate in 30ns with a high fidelity of 99.5%, der…
In order to demonstrate non-trivial quantum computations experimentally, such as the synthesis of arbitrary entangled states, it will be useful to understand how to decompose a desired quantum computation into the shortest possible sequence of one-qubit and two-qubit gates. We contribute to this effort by providing a method to construct an optimal quantum circuit for a general two-qubit gate that requires at most 3 CNOT gates and 15 elementary one-qubit gates. Moreover, if the desired two-qubit gate corresponds to a purely real unitary transformation, we provide a construction that requires at…
The most general structure (in matrix form) of a single-qubit gate is presented. Subsequently, used that to obtain a set of conditions for testing (a) whether a given 2-qubit gate is genuinely a 2-qubit gate, i.e., not decomposable into two single qubit gates and (b) whether a given single qubit gate is self-inverse? Relevance of the results reported here is discussed in the context of optimization of reversible and quantum circuits, especially for the optimization of quantum cost. A systematic procedure is developed for the identification of the non-decomposable 2-qubit gates. Such a non-deco…
Constructing three-qubit unitary gates in terms of Schmidt rank and CNOT gates
本文构造了Schmidt秩从一到七的三量子比特酉门，发现Toffoli和Fredkin门秩分别为二和四，并利用CNOT及局域门实现，揭示了CNOT门数量与Schmidt秩的联系。
The number of two-qubit gates required to transform deterministically a three-qubit pure quantum state into another is discussed. We show that any state can be prepared from a product state using at most three CNOT gates, and that, starting from the GHZ state, only two suffice. As a consequence, any three-qubit state can be transformed into any other using at most four CNOT gates. Generalizations to other two-qubit gates are also discussed.
Universal quantum computation requires the implementation of arbitrary control operations on the quantum register. In most cases, this is achieved by external control fields acting selectively on each qubit to drive single-qubit operations. In combination with a drift Hamiltonian containing interactions between the qubits, this allows the implementation of any required gate operation. Here, we demonstrate an alternative scheme that does not require local control for all qubits: we implement one- and two-qubit gate operations on a set of target qubits indirectly, through a combination of gates …
Although single and two-qubit gates are sufficient for universal quantum computation, single-shot three-qubit gates greatly simplify quantum error correction schemes and algorithms. We design fast, high-fidelity three-qubit entangling gates based on microwave pulses for transmon qubits coupled through a superconducting resonator. We show that when interqubit frequency differences are comparable to single-qubit anharmonicities, errors occur primarily through a single unwanted transition. This feature enables the design of fast three-qubit gates based on simple analytical pulse shapes that are e…
High-quality-factor 3D cavities in superconducting circuits are ideal candidates for bosonic logical qubits as their fidelity is limited only by the low photon loss rate. However, the transmon qubits that are used to manipulate bosonic qubits result in the emergence of additional relaxation and dephasing channels. In this work, a numerical study is performed to elucidate the effect of the various loss channels on the performance of logical gates on a bosonic qubit. A gate error model is developed that encapsulates the loss mechanisms for arbitrary gate operations and predicts experimentally ac…
We propose how to realize a multiqubit tunable phase gate of one qubit simultaneously controlling $n$ qubits with four-level quantum systems in a cavity or coupled to a resonator. Each of the $n$ two-qubit controlled-phase (CP) gates involved in this multiqubit phase gate has a shared control qubit but a {\it different} target qubit. In this propose, the two lowest levels of each system represent the two logical states of a qubit while the two higher-energy intermediate levels are used for the gate implementation. The method presented here operates essentially by creating a single photon throu…
Non-adiabatic holonomic quantum gate in decoherence-free subspaces is of greatly practical importance due to its built-in fault tolerance, coherence stabilization virtues, and short run-time. Here we propose some compact schemes to implement two- and three-qubit controlled unitary quantum gates and Fredkin gate. For the controlled unitary quantum gates, the unitary operator acting on the target qubit is an arbitrary single-qubit gate operation. The controlled quantum gates can be directly implemented using non-adiabatic holonomy in decoherence-free subspaces and the required resource for the d…
Optimal implementation of quantum gates is crucial for designing a quantum computer. The necessary condition for optimal construction of a two-qubit unitary operation is obtained. It can be proved that the B gate is the unique gate that can construct a two-qubit universal circuit with only two applications, i.e. this condition is also sufficient in the case of two applications of the elementary two-qubit gate. It is also shown that one half of perfect entanglers can not simulate an arbitrary two-qubit gate with only 3 applications.
We present a new experimental protocol for performing universal gates in a register of superconducting qubits coupled by fixed on-chip linear reactances. The qubits have fixed, detuned Larmor frequencies and can remain, during the entire gate operation, biased at their optimal working point where decoherence due to fluctuations in control parameters is suppressed to first order. Two-qubit gates are performed by simultaneously irradiating two qubits at their respective Larmor frequencies with appropriate amplitude and phase, while one-qubit gates are performed by the usual single-qubit irradiat…
Quantum protocols based on adiabatic evolution are remarkably robust against imperfections of control pulses and system uncertainties. While adiabatic protocols have been successfully implemented for quantum operations such as quantum state transfer and single-qubit gates, their use for geometric two-qubit gates remains a challenge. In this paper, we propose a general scheme to realize robust geometric two-qubit gates in multi-level qubit systems where the interaction between the qubits is mediated by an auxiliary system (such as a bus or coupler). While our scheme utilizes Stimulated Raman Ad…
Implementing two-qubit gates at the quantum speed limit
本文利用机器学习启发的最优控制方法，在超导transmon量子比特上实验实现了接近量子速度极限的高保真度双量子比特门，并证明该方法适用于多种量子计算平台，可显著加速非原生双量子比特门。
Quantum gates with parametrically driven multi-qubit couplers
本文通过参数驱动方法，利用中心可调耦合电路实现四量子比特板中任意两量子比特（包括对角）的√iSWAP门及三量子比特门，数值模拟显示50ns内√iSWAP门保真度达99.9%。
Recent experiments have demonstrated superconducting transmon qubits with semiconductor nanowire Josephson junctions. These hybrid gatemon qubits utilize field effect tunability characteristic for semiconductors to allow complete qubit control using gate voltages, potentially a technological advantage over conventional flux-controlled transmons. Here, we present experiments with a two-qubit gatemon circuit. We characterize qubit coherence and stability and use randomized benchmarking to demonstrate single-qubit gate errors below 0.7% for all gates, including voltage-controlled $Z$ rotations. W…
Qubitization is a modern approach to estimate Hamiltonian eigenvalues without simulating its time evolution. While in this way approximation errors are avoided, its resource and gate requirements are more extensive: qubitization requires additional qubits to store information about the Hamiltonian, and Toffoli gates to probe them throughout the routine. Recently, it was shown that storing the Hamiltonian in a unary representation can alleviate the need for such gates in one of the qubitization subroutines. Building on that principle, we develop an entirely new decomposition of the entire algor…
Cat-qubit-inspired gate on cos($2θ$) qubits
针对基于电压控制半导体纳米线约瑟夫森结的 cos($2θ$) 比特，提出一种受 Kerr-cat 比特启发的单比特 Z 门。该门通过绝热改变势能实现相空间 π 旋转，始终将动力学约束在子空间内，从而在保持相干性的同时实现高保真操作，并经数值模拟验证。
A new approach to single-qubit operations using exchange interactions of single electrons in gate-defined quantum dots has recently been demonstrated: the resonant exchange qubit. We show that two-qubit operations, specifically the CPHASE gate, can be performed between resonant exchange qubits very straightforwardly, using a single exchange pulse. This is in marked contrast to the best known protocols for exchange qubits where such a gate requires many pulses so that leakage processes arising from the exchange interaction can be overcome. For resonant exchange qubits a simple two-qubit gate is…
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 study the class of two qubit gates which can be achieved using only linear optical elements (beam splitters and phase shifters) and post-selection. We are able to exactly characterize this set, and find that it is impossible to implement most two qubit gates in this way. The proof also gives rise to an algorithm for calculating the optimal success probability of those gates which are achievable.
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