An explicit algorithm for calculating the optimized Euler angles for both qubit state transfer and gate engineering given two arbitrary fixed Hamiltonians is presented. It is shown how the algorithm enables us to efficiently implement single qubit gates even if the control is severely restricted and the experimentally accessible Hamiltonians are far from orthogonal. It is further shown that using the optimized Euler angles can significantly improve the fidelity of quantum operations even for systems where the experimentally accessible Hamiltonians are nearly orthogonal. Unlike schemes such as composite pulses, the proposed scheme does not significantly increase the number of local operations or gate operation times.
An explicit algorithm for calculating the optimized Euler angles for both qubit state transfer and gate engineering given two arbitrary fixed Hamiltonians is presented. It is shown how the algorithm enables us to efficiently implement single qubit gates even if the control is severely restricted and the experimentally accessible Hamiltonians are far from orthogonal. It is further shown that using the optimized Euler angles can significantly improve the fidelity of quantum operations even for systems where the experimentally accessible Hamiltonians are nearly orthogonal. Unlike schemes such as composite pulses, the proposed scheme does not significantly increase the number of local operations or gate operation times.
An explicit algorithm for calculating the optimized Euler angles for both qubit state transfer and gate engineering given two arbitary fixed Hamiltonians is presented. It is shown how the algorithm enables us to efficiently implement single qubit gates even if the control is severely restricted and the experimentally accessible Hamiltonians are far from orthogonal. It is further shown that using the optimized Euler angles can significantly improve the fidelity of quantum operations even for systems where the experimentally accessible Hamiltonians are nearly orthogonal. Unlike schemes such as composite pulses, the proposed scheme does not significantly increase the number of local operations or gate operation times.
Recently, the development of quantum chips has made great progress-- the number of qubits is increasing and the fidelity is getting higher. However, qubits of these chips are not always fully connected, which sets additional barriers for implementing quantum algorithms and programming quantum programs. In this paper, we introduce a general circuit optimizing scheme, which can efficiently adjust and optimize quantum circuits according to arbitrary given qubits' layout by adding additional quantum gates, exchanging qubits and merging single-qubit gates. Compared with the optimizing algorithm of IBM's QISKit, the quantum gates consumed by our scheme is 74.7%, and the execution time is only 12.9% on average.
We propose a novel method to sequentially optimize arbitrary single-qubit gates in parameterized quantum circuits for simulating real and imaginary time evolution. Unlike previously-known methods, the proposed method fully utilizes all parameters of single-qubit gates and therefore can potentially obtain better performance. Specifically, the proposed method simultaneously optimizes both the axis and the angle of a single-qubit gate, while the known methods either optimize the angle with the axis fixed, or vice versa. The proposed method is shown to generalize the known methods and results in a sinusoidal cost function parameterized by the axis and angle of rotation. Furthermore, we demonstrate how the proposed method can be extended to optimize a set of parameterized two-qubit gates with excitation-conservation constraints, which includes the Hop and the Reconfigurable Beam Splitter gates. We perform numerical experiments showing the power of the proposed method to find ground states of typical Hamiltonians with quantum imaginary time evolution using parameterized quantum circuits.
The set of quantum logic gates that can be easily implemented is fundamental to the performance of quantum computers, as it governs the accuracy of basic quantum operations and dictates the complexity of implementing quantum algorithms. Traditional approaches to extending gate sets often require operating devices outside the ideal parameter regimes used to realize qubits, leading to increased control complexity while offering only a limited set of gates. Here we experimentally demonstrate a unified and versatile gate scheme capable of generating arbitrary two-qubit gates using only an exchange interaction and qubit driving on a superconducting quantum processor. We achieve high fidelities averaging 99.38% across a wide range of commonly used two-qubit unitaries, enabling precise multipartite entangled state preparation. Furthermore, we successfully produce a B gate, which efficiently synthesizes the entire family of two-qubit gates. Our results establish that fully exploiting the capabilities of the exchange interaction can yield a comprehensive and highly accurate gate set. With maximum expressivity, optimal gate time, demonstrated high fidelity and easy adaption to other quantum platforms, our unified control scheme offers the prospect of improved performance in quantum hardware and algorithm development. The efficiency of a quantum computer depends on which basic operations it can implement. Now a scheme that can implement any two-qubit logic gate has been demonstrated on a superconducting architecture.
We introduce a scheme for realizing arbitrary controlled-unitary operations in a two-qubit system. If the $2\ifmmode\times\else\texttimes\fi{}2$ unitary matrix is special unitary (has unit determinant), the controlled-unitary gate operation can be realized in a single pulse operation. The pulse in our scheme will constitute varying one of the parameters of the system between an arbitrarily maximum and a ``calculated'' minimum value. This parameter will constitute the variable parameter of the system while the other parameters, which include the coupling between the two qubits, will be treated as fixed parameters. The values of the parameters are what we solve for using our approach in order to realize an arbitrary controlled-unitary operation. We further show that the computational complexity of the operation is no greater than that required for a controlled-NOT (CNOT) gate. Since conventional schemes realize a controlled-unitary operation by breaking it into a sequence of single-qubit and CNOT gate operations, our method is an improvement because we not only require less time duration, but also fewer control lines to implement the same operation. To demonstrate improvement over other schemes, we show, as examples, how two controlled-unitary operations, one being the controlled-Hadamard gate, can be realized in a single pulse operation using our scheme. Furthermore, our method can be applied to a wide range of coupling schemes and can be used to realize gate operations between two qubits coupled via Ising, Heisenberg, and anisotropic interactions.
Electron spins trapped in quantum dots have recently proven to be a promising technology for the implementation of qubits, already demonstrating high fidelity single- and two-qubits gates. The next step towards fault-tolerant quantum computing is to increase the number of so-called spin qubits on the processor. However, this poses several challenges, one of which being how to implement single-qubit gates in multi-qubit systems, with high fidelity. This work focused on two aspects. The first one was to identify the physical phenomena and limitations that hinder the realisation of high fidelity single-qubit gates in multi-qubit environments. The second objective was to investigate, implement and optimise methods in order to minimise the impact of these perturbing phenomena. The identified perturbing effects include unwanted driving between a pulse and the neighbouring qubits, as well as frequency shifts induced by drive-spin coupling and non-ideal pulse in experimental setups. Crosstalk was addressed using pulse shaping (i.e. amplitude or phase modulation of the driving pulse to tailor its spectral characteristics and reduce the energy transmitted at unwanted frequencies). The performance of shapes taken from both NMR and signal processing literature was investigated, for various pulse parameters, through an extensive grid search. In addition, a frequency correction algorithm was devised: off-resonant drive frequencies are selected so that the shifted qubits are resonantly driven. It currently accounts for two phenomena: the AC Stark and Bloch-Siegert shifts. The algorithm furthermore tracks the changes caused by the time-dependent characteristics of the shaped pulses. The proposed frequency correction algorithm was shown to almost entirely negate the effects of the considered shifts, leading to unitary fidelity improvements by up to 55%. In addition, pulse shaping was demonstrated to noticeably improve the fidelity of simultaneous single-qubit rotations compared to unshaped driving. Rotations with fidelities as high as 99.98% were obtained for pi/2 rotations on two-qubits systems. Moreover, shapes whose Fourier transform is narrow and sharp, associated with low Rabi frequencies, were demonstrated to generally provide the highest fidelities of the tested configurations. Lastly, the trends and guidelines highlighted by these results were shown to scale to systems with larger numbers of qubits. The correction techniques investigated in this work have proven promising for the implementation of high fidelity single-qubit gates in multi-qubit systems. In particular, the guidelines for selecting a well-performing pulse shape should also be useful for the design of optimised driving schemes, regardless of the number of qubits involved. Additionally, the proposed frequency shift correction algorithm is expected to be able to handle arbitrary shifts, and so to be easily adaptable to use in experiments.