Single-qubit Gates Research Articles

A mechanical qubit

Although strong nonlinear interactions between quantized excitations are an important resource for quantum technologies based on bosonic oscillator modes, most electromagnetic and mechanical nonlinearities are far too weak to allow for nonlinear effects to be observed at the single-quantum level. This limitation has been overcome in electromagnetic resonators by coupling them to other strongly nonlinear quantum systems such as atoms and superconducting qubits. We demonstrate the realization of the single-phonon nonlinear regime in a solid-state mechanical system. The single-phonon anharmonicity in our system exceeds the decoherence rate by a factor of 6.8, allowing us to use it as a mechanical qubit and demonstrate initialization, readout, and single-qubit gates. Our approach provides a powerful quantum acoustics platform for quantum simulations, sensing, and information processing.

In situ mixer calibration for superconducting quantum circuits

Mixers play a crucial role in superconducting quantum computing, primarily by facilitating frequency conversion of signals to enable precise control and readout of quantum states. However, imperfections, particularly local oscillator leakage and unwanted sideband signal, can significantly compromise control fidelity. To mitigate these defects, regular and precise mixer calibrations are indispensable, yet they pose a formidable challenge in large-scale quantum control. Here, we introduce an in situ and scalable mixer calibration scheme using superconducting qubits. Our method leverages the qubit's response to imperfect signals, allowing for calibration without modifying the wiring configuration. We experimentally validate the efficacy of this technique by benchmarking single-qubit gate error and qubit coherence time.

Pursuing high-fidelity control of spin qubits in natural Si/SiGe quantum dot

Electron spins in silicon quantum dots are a promising platform for fault-tolerant quantum computing. Low-frequency noise, including nuclear spin fluctuations and charge noise, is a primary factor limiting gate fidelities. Suppressing this noise is crucial for high-fidelity qubit operations. Here, we report on a two-qubit quantum device in natural silicon with universal qubit control, designed to investigate the upper limits of gate fidelities in a non-purified Si/SiGe quantum dot device. By employing advanced device structures, qubit manipulation techniques, and optimization methods, we have achieved single-qubit gate fidelities exceeding 99% and a two-qubit controlled-Z (CZ) gate fidelity of 91%. Decoupled CZ gates are used to prepare Bell states with an average fidelity of 91%, typically exceeding previously reported values in natural silicon devices. These results underscore that even natural silicon has the potential to achieve high-fidelity gate operations, particularly with further optimization methods to suppress low-frequency noise.

Time-optimal control of a solid-state spin amidst dynamical quantum wind

Time-optimal control holds promise across the full spectrum of quantum technologies, where the rapid generation of unitary gates and state transformations is crucial to mitigate decoherence effects. In practical scenarios, quantum systems are always immersed in an external time-dependent field or potential, either owing to the inevitable influence of the environment or as a sought-after effect for enhanced coherence. The challenge then lies in finding the time-optimal approach to navigate quantum systems amidst dynamical ambient Hamiltonians, a pursuit that has proven elusive thus far. We showcase the implementation of arbitrary quantum state transformations and a universal set of single-qubit gates under a background Landau-Zener Hamiltonian. Leveraging the favorable coherence properties of timedomain Rabi oscillations, we achieve velocities surpassing the Mandelstam-Tamm quantum speed limit and significantly lower energy costs than those incurred by conventional quantum control techniques. These findings highlight a promising pathway to expedite and economize high-fidelity quantum operations.

Implementation of controlled unitary gates and its application in a remote-controlled quantum gate

Recently, remote-controlled quantum information processing has been proposed for its applications in secure quantum processing protocols and distributed quantum networks. For remote-controlled quantum gates, the experimental realization of controlled unitary (CU) gates between any quantum gates is an essential task. Here, we propose and experimentally demonstrate a scheme for implementing CU gates between any pair of unitary gates using the polarization and time-bin degrees of freedom of single photons. Then, we experimentally implement remote-controlled single-qubit unitary gates by controlling either the state preparation or measurement of the control qubit with high process fidelities. We believe the proposed remote-controlled quantum gate model can pave the way for secure and efficient quantum information processing.

Universal control of four singlet-triplet qubits.

The coherent control of interacting spins in semiconductor quantum dots is of strong interest for quantum information processing and for studying quantum magnetism from the bottom up. Here we present a 2 × 4 germanium quantum dot array with full and controllable interactions between nearest-neighbour spins. As a demonstration of the level of control, we define four singlet-triplet qubits in this system and show two-axis single-qubit control of each qubit and SWAP-style two-qubit gates between all neighbouring qubit pairs, yielding average single-qubit gate fidelities of 99.49(8)-99.84(1)% and Bell state fidelities of 73(1)-90(1)%. Combining these operations, we experimentally implement a circuit designed to generate and distribute entanglement across the array. A remote Bell state with a fidelity of 75(2)% and concurrence of 22(4)% is achieved. These results highlight the potential of singlet-triplet qubits as a competing platform for quantum computing and indicate that scaling up the control of quantum dot spins in extended bilinear arrays can be feasible.

Procedure for reducing cross-resonance gate errors using pulse-level control

Abstract Current implementations of superconducting qubits are often limited by the low fidelities of multiqubit gates. We present a reproducible and runtime-efficient pulse-level approach for calibrating an improved cross-resonance gate CR(θ) for arbitrary θ. This CR(θ) gate can be used to produce a wide range of other two-qubit gates via the application of standard single-qubit gates. By performing an interleaved randomised benchmarking sequence, we demonstrate that our approach leads to significantly lower incoherent errors than the circuit-level approach currently used by IBM. Hence, our procedure provides a genuine improvement for applications where noise remains a limiting factor.

Multi-objective simulated annealing-based quantum circuit cutting for distributed quantum computation

In the current noisy intermediate-scale quantum (NISQ) era, the number of qubits and the depth of quantum circuits in a quantum computer are limited because of complex operation among increasing number of qubits, low-fidelity quantum gates under noise, and short coherence time of physical qubits. However, with distributed quantum computation (DQC) in which multiple small-scale quantum computers cooperate, large-scale quantum circuits can be implemented. In DQC, it is a key step to decompose large-scale quantum circuits into several small-scale subcircuits equivalently. In this paper, we propose a quantum circuit cutting scheme for the circuits consisting of only single-qubit gates and two-qubit gates. In the scheme, the number of non-local gates and the rounds of subcircuits operation are minimized by using the multi-objective simulated annealing (MOSA) algorithm to cluster the gates and to choose the cutting positions whilst using non-local gates. A reconstruction process is also proposed to calculate the probability distribution of output states of the original circuit. As an example, the 7-qubit circuit of Shor algorithm factoring 15 is used to verify the algorithm. Five cutting schemes are recommended, which can be selected according to practical requirements. Compared with the results of the mixing integer programming (MIP) algorithm, the number of execution rounds is efficiently reduced by slightly increasing the number of nonlocal gates.

CONTENTS OF TRAINING IN CONSTRUCTING CONTROLLED QUANTUM GATES

The article makes a selection and subsequent structuring of the content of training in the construction of controlled quantum gates using twelve decompositions of single-qubit quantum gates (Z-Y, Z-X, X-Y, Y-Z, X-Z, Y-X; Z-Y-X, Z-X-Y, X-Y-Z, X-Z-Y, Y-X-Z, Y-Z-X) used in the process of teaching the section “Quantum Computing and Programming in the QCL Language” of the training course “Applied Programming in High-Level Languages” to students of the Institute of Information Technology and Technological Education (3rd year, Herzen State Pedagogical University of Russia).

Mitigating noise in digital and digital–analog quantum computation

Noisy Intermediate-Scale Quantum (NISQ) devices lack error correction, limiting scalability for quantum algorithms. In this context, digital-analog quantum computing (DAQC) offers a more resilient alternative quantum computing paradigm that outperforms digital quantum computation by combining the flexibility of single-qubit gates with the robustness of analog simulations. This work explores the impact of noise on both digital and DAQC paradigms and demonstrates DAQC’s effectiveness in error mitigation. We compare the quantum Fourier transform and quantum phase estimation algorithms under a wide range of single and two-qubit noise sources in superconducting processors. DAQC consistently surpasses digital approaches in fidelity, particularly as processor size increases. Moreover, zero-noise extrapolation further enhances DAQC by mitigating decoherence and intrinsic errors, achieving fidelities above 0.95 for 8 qubits, and reducing computation errors to the order of 10−3. These results establish DAQC as a viable alternative for quantum computing in the NISQ era.

X, Y, and Z Subgroups of the Unitary Group

The subgroups XU(2), YU(2), and ZU(2) of the unitary group U(2) allow to find twenty-four different decompositions of an arbitrary [Formula: see text] unitary matrix. Because the group YU(2) has not been considered before, 20 out of the 24 decompositions are new. Introducing this YU(2) group allows to highlight, within quantum circuit design, a symmetry similar to the threefold symmetry of the Pauli matrices of spin systems. Similar subgroups of the unitary group U([Formula: see text]) lead to various new decompositions of an arbitrary [Formula: see text] unitary matrix. Whereas for [Formula: see text] equal 2, this leads to the synthesis of single-qubit quantum gates, for [Formula: see text] equal a power of 2, this leads to new design methods for multiple-qubit circuits.

Investigating and improving student understanding of the basics of quantum computing

Quantum information science and engineering (QISE) is a rapidly developing field that leverages the skills of experts from many disciplines to utilize the potential of quantum systems in a variety of applications. It requires talent from a wide variety of traditional fields, including physics, engineering, chemistry, and computer science, to name a few. To prepare students for such opportunities, it is important to give them a strong foundation in the basics of QISE, in which quantum computing plays a central role. In this study, we discuss the development, validation, and evaluation of a Quantum Interactive Learning Tutorial, on the basics and applications of quantum computing. These include an overview of key quantum mechanical concepts relevant to quantum computation (including ways a quantum computer is different from a classical computer), properties of single- and multiqubit systems, and the basics of single-qubit quantum gates. The tutorial uses guided inquiry-based teaching-learning sequences. Its development and validation involved conducting cognitive task analysis from both expert and student perspectives and using common student difficulties as a guide. For example, before engaging with the tutorial, after traditional lecture-based instruction, one reasoning primitive that was common in student responses is that a major difference between an N-bit classical and N-qubit quantum computer is that various things associated with a number N for a classical computer should be replaced with the number 2N for a quantum computer (e.g., 2N qubits must be initialized and 2N bits of information are obtained as the output of the computation on the quantum computer). This type of reasoning primitive also led many students to incorrectly think that there are only N distinctly different states available when computation takes place on a classical computer. Research suggests that this type of reasoning primitive has its origins in students learning that quantum computers can provide exponential advantage for certain problems, e.g., Shor’s algorithm for factoring products of large prime numbers, and that the quantum state during the computation can be in a superposition of 2N linearly independent states. The inquiry-based learning sequences in the tutorial provide scaffolding support to help students develop a functional understanding. The final version of the validated tutorial was implemented in two distinct courses offered by the physics department with slightly different student populations and broader course goals. Students’ understanding was evaluated after traditional lecture-based instruction on the requisite concepts and again after engaging with the tutorial. We analyze and discuss their improvement in performance on concepts covered in the tutorial. Published by the American Physical Society 2024

Robust control of single-qubit gates at the quantum speed limit

Robust control of single-qubit gates at the quantum speed limit

In situ characterization of qubit-drive phase distortions

Reducing errors in quantum gates is critical to the development of quantum computers. To do so, any distortions in the control signals should be identified; however, conventional tools are not always applicable when part of the system is under high vacuum, cryogenic, or microscopic. Here, we demonstrate a method to detect and compensate for amplitude-dependent phase changes, using the qubit itself as a probe. The technique is implemented using a microwave-driven trapped-ion qubit, where correcting phase distortions leads to a threefold improvement in the error of single-qubit gates implemented with pulses of different amplitudes, to attain state-of-the-art performance benchmarked at 1.6(4)×10−6 error per Clifford gate. Published by the American Physical Society 2024

Operating semiconductor quantum processors with hopping spins.

Qubits that can be efficiently controlled are essential for the development of scalable quantum hardware. Although resonant control is used to execute high-fidelity quantum gates, the scalability is challenged by the integration of high-frequency oscillating signals, qubit cross-talk, and heating. Here, we show that by engineering the hopping of spins between quantum dots with a site-dependent spin quantization axis, quantum control can be established with discrete signals. We demonstrate hopping-based quantum logic and obtain single-qubit gate fidelities of 99.97%, coherent shuttling fidelities of 99.992% per hop, and a two-qubit gate fidelity of 99.3%, corresponding to error rates that have been predicted to allow for quantum error correction. We also show that hopping spins constitute a tuning method by statistically mapping the coherence of a 10-quantum dot system. Our results show that dense quantum dot arrays with sparse occupation could be developed for efficient and high-connectivity qubit registers.

Polylogarithmic-depth controlled-NOT gates without ancilla qubits

Controlled operations are fundamental building blocks of quantum algorithms. Decomposing n-control-NOT gates (Cn(X)) into arbitrary single-qubit and CNOT gates, is a crucial but non-trivial task. This study introduces Cn(X) circuits outperforming previous methods in the asymptotic and non-asymptotic regimes. Three distinct decompositions are presented: an exact one using one borrowed ancilla with a circuit depth Θ(log(n)3)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Theta (\\log {(n)}^{3})$$\\end{document}, an approximating one without ancilla qubits with a circuit depth O(log(n)3log(1/ϵ))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{{\\mathcal{O}}}}}}}}(\\log {(n)}^{3}\\log (1/\\epsilon ))$$\\end{document} and an exact one with an adjustable-depth circuit which decreases with the number m≤n of ancilla qubits available as O(log(n/⌊m/2⌋)3+log(⌊m/2⌋))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{{\\mathcal{O}}}}}}}}(\\log {(n/\\lfloor m/2\\rfloor )}^{3}+\\log (\\lfloor m/2\\rfloor ))$$\\end{document}. The resulting exponential speedup is likely to have a substantial impact on fault-tolerant quantum computing by improving the complexities of countless quantum algorithms with applications ranging from quantum chemistry to physics, finance and quantum machine learning.

Quanto: optimizing quantum circuits with automatic generation of circuit identities

Existing quantum compilers focus on mapping a logical quantum circuit to a quantum device and its native quantum gates. Only simple circuit identities are used to optimize the quantum circuit during the compilation process. This approach misses more complex circuit identities, which could be used to optimize the quantum circuit further. We propose Quanto, the first quantum optimizer that automatically generates circuit identities. Quanto takes as input a gate set and generates provably correct circuit identities for the gate set. Quanto’s automatic generation of circuit identities includes single-qubit and two-qubit gates, which leads to a new database of circuit identities, some of which are novel to the best of our knowledge. In addition to the generation of new circuit identities, Quanto’s optimizer applies such circuit identities to quantum circuits and finds optimized quantum circuits that have not been discovered by other quantum compilers, including IBM Qiskit and Cambridge Quantum Computing Tket. Quanto’s database of circuit identities could be applied to improve existing quantum compilers and Quanto can be used to generate identity databases for new gate sets.

Decay-protected superconducting qubit with fast control enabled by integrated on-chip filters

Achieving fast gates and long coherence times for superconducting qubits presents challenges, typically requiring either a stronger coupling of the drive line or an excessively strong microwave signal to the qubit. To address this, we introduce on-chip filters of the qubit drive exhibiting a stopband at the qubit frequency, thus enabling long coherence times and strong coupling at the subharmonic frequency, facilitating fast single-qubit gates, and reduced thermal load. The filters exhibit an extrinsic relaxation time of a few seconds while enabling sub-10-ns gates with subharmonic control. Here we show up to 200-fold improvement in the measured relaxation time at the stopband. Furthermore, we implement subharmonic driving of Rabi oscillations with a π pulse duration of 12 ns. Our demonstration of on-chip filters and efficient subharmonic driving in a two-dimensional quantum processor paves the way for a scalable qubit architecture with reduced thermal load and noise from the control line.

Correction of microwave pulse reflection by digital filters in superconducting quantum circuits

Abstract Reducing the control error is vital for high-fidelity digital and analog quantum operations. In superconducting circuits, one disagreeable error arises from the reflection of microwave signals due to impedance mismatch in the control chain. Here, we demonstrate a reflection cancelation method when considering that there are two reflection nodes on the control line. We propose to generate the pre-distortion pulse by passing the envelopes of the microwave signal through digital filters, which enables real-time reflection correction when integrated into the field-programmable gate array (FPGA). We achieve a reduction of single-qubit gate infidelity from 0.67% to 0.11% after eliminating microwave reflection. Real-time correction of microwave reflection paves the way for precise control and manipulation of the qubit state and would ultimately enhance the performance of algorithms and simulations executed on quantum processors.

Multimode physics of the unimon circuit

We consider a superconducting half-wavelength resonator that is grounded at its both ends and contains a single Josephson junction. Previously this circuit was considered as a unimon qubit in the single-mode approximation where dc-phase-biasing the junction to π leads to increased anharmonicity and 99.9% experimentally observed single-qubit gate fidelity. Inspired by the promising first experimental results, we develop here a theoretical and numerical model for the detailed understanding of the multimode physics of the unimon circuit. To this end, first, we consider the high-frequency modes of the unimon circuit and find that even though these modes are at their ground state, they imply a significant renormalization to the Josephson energy. We introduce an efficient method to fully account for the relevant modes and show that unexcited high-lying modes lead to corrections in the qubit energy and anharmonicity. Interestingly, provided that the junction is offset from the middle of the circuit, we find strong cross-Kerr coupling strengths between a few low-lying modes. This observation paves the way for the utilization of the multimode structure, for example, as several qubits embedded into a single unimon circuit. Published by the American Physical Society 2024