Arbitrary Single-qubit Gates Research Articles

Spacetime-Efficient Low-Depth Quantum State Preparation with Applications

We propose a novel deterministic method for preparing arbitrary quantum states. When our protocol is compiled into CNOT and arbitrary single-qubit gates, it prepares an N-dimensional state in depth O(log⁡(N)) and spacetime allocation (a metric that accounts for the fact that oftentimes some ancilla qubits need not be active for the entire circuit) O(N), which are both optimal. When compiled into the {H,S,T,CNOT} gate set, we show that it requires asymptotically fewer quantum resources than previous methods. Specifically, it prepares an arbitrary state up to error ϵ with optimal depth of O(log⁡(N)+log⁡(1/ϵ)) and spacetime allocation O(Nlog⁡(log⁡(N)/ϵ)), improving over O(log⁡(N)log⁡(log⁡(N)/ϵ)) and O(Nlog⁡(N/ϵ)), respectively. We illustrate how the reduced spacetime allocation of our protocol enables rapid preparation of many disjoint states with only constant-factor ancilla overhead – O(N) ancilla qubits are reused efficiently to prepare a product state of wN-dimensional states in depth O(w+log⁡(N)) rather than O(wlog⁡(N)), achieving effectively constant depth per state. We highlight several applications where this ability would be useful, including quantum machine learning, Hamiltonian simulation, and solving linear systems of equations. We provide quantum circuit descriptions of our protocol, detailed pseudocode, and gate-level implementation examples using Braket.

Error per single-qubit gate below 10−4 in a superconducting qubit

Implementing arbitrary single-qubit gates with near perfect fidelity is among the most fundamental requirements in gate-based quantum information processing. In this work, we fabricate a transmon qubit with long coherence times and demonstrate single-qubit gates with the average gate error below 10−4, i.e. (7.42 ± 0.04) × 10−5 by randomized benchmarking (RB). To understand the error sources, we experimentally obtain an error budget, consisting of the decoherence errors lower bounded by (4.62 ± 0.04) × 10−5 and the leakage rate per gate of (1.16 ± 0.04) × 10−5. Moreover, we reconstruct the process matrices for the single-qubit gates by the gate set tomography (GST), with which we simulate RB sequences and obtain single-qubit fidelities consistent with experimental results. We also observe non-Markovian behavior in the experiment of long-sequence GST, which may provide guidance for further calibration. The demonstration extends the upper limit that the average fidelity of single-qubit gates can reach in a transmon-qubit system, and thus can be an essential step towards practical and reliable quantum computation in the near future.

Parallelizable synthesis of arbitrary single-qubit gates with linear optics and time-frequency encoding

Parallelizable synthesis of arbitrary single-qubit gates with linear optics and time-frequency encoding

Compiling arbitrary single-qubit gates via the phase shifts of microwave pulses

Applying phase shifts to qubit drives is known to give essentially perfect $Z$ rotations, but the current scheme is only compatible with a very special class of two-qubit gates. This puts unnecessary restrictions on the quantum instruction set. A proposed scheme is compatible with arbitrary two-qubit gates and is also uniquely optimal in the number of pulses needed.

Control and mitigation of microwave crosstalk effect with superconducting qubits

Improving gate performance is vital for scalable quantum computing. Universal quantum computing also requires gate fidelity to reach a high level. For a superconducting quantum processor, which operates in the microwave band, the single-qubit gates are usually realized with microwave driving. The crosstalk between microwave pulses is a non-negligible error source. In this article, we propose an error mitigation scheme to address this crosstalk issue for single-qubit gates. There are three steps in our method. First, by controlling the detuning between qubits, the microwave induced classical crosstalk error can be constrained within the computational subspace. Second, by applying the general decomposition procedure, the arbitrary single-qubit gate can be decomposed as a sequence of X and virtual Z gates. Finally, by optimizing the parameters in virtual Z gates, the error constrained in the computational space can be corrected. Using our method, no additional compensation signals are needed, arbitrary single-qubit gate time will not be prolonged, and the circuit depth containing simultaneous single-qubit gates will also not increase. The simulation results show that, in a specific regime of qubit–qubit detuning, the infidelities of simultaneous single-qubit gates can be as low as that without microwave crosstalk.

Simulating time evolution with fully optimized single-qubit gates on parametrized quantum circuits

We propose a method to sequentially optimize arbitrary single-qubit gates in parametrized quantum circuits for simulating real- and imaginary-time evolution. The method utilizes full degrees of freedom of single-qubit gates and therefore can potentially obtain better performance. Specifically, it 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. It generalizes the known methods and utilizes sinusoidal cost functions parametrized by the axis and angle of rotation. Furthermore, we demonstrate how it can be extended to optimize a set of parametrized 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 parametrized quantum circuits. In addition, we show the method can be applied to real-time evolution and discuss the tradeoff between its simulation accuracy and hardware efficiency.

Designing gate operations for single-ion quantum computing in rare-earth-ion-doped crystals

Quantum computers based on rare-earth-ion-doped crystals show promising properties in terms of scalability and connectivity if single ions can be used as qubits. Through simulations, we investigate gate operations on such qubits. We discuss how gate and system parameters affect gate errors, the required frequency bandwidth per qubit, and the risk for instantaneous spectral diffusion (ISD). Furthermore, we examine how uncertainties in the system parameters affect the gate errors, and how precisely the system needs to be known. We find gate errors for arbitrary single-qubit gates of $2.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ when ISD is not considered and $3.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ when we take heed to minimize it. Additionally, we construct two-qubit gates with errors ranging from $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\ensuremath{\rightarrow}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ over a broad range of dipole-dipole interaction strengths.

Constructing quantum circuits with global gates

There are various gate sets that can be used to describe a quantum computation. A particularly popular gate set in the literature on quantum computing consists of arbitrary single-qubit gates and two-qubit CNOT gates. A CNOT gate is however not always the natural multi-qubit interaction that can be implemented on a given physical quantum computer, necessitating a compilation step that transforms these CNOT gates to the native gate set. An especially interesting case where compilation is necessary is for ion trap quantum computers, where the natural entangling operation can act on more than two qubits and can even act globally on all qubits at once. This calls for an entirely different approach to constructing efficient circuits. In this paper we study the problem of converting a given circuit that uses two-qubit gates to one that uses global gates. Our three main contributions are as follows. First, we find an efficient algorithm for transforming an arbitrary circuit consisting of Clifford gates and arbitrary phase gates into a circuit consisting of single-qubit gates and a number of global interactions proportional to the number of non-Clifford phases present in the original circuit. Second, we find a general strategy to transform a global gate that targets all qubits into one that targets only a subset of the qubits. This approach scales linearly with the number of qubits that are not targeted, in contrast to the exponential scaling reported in (Maslov and Nam 2018 New J. Phys. 20 033018). Third, we improve on the number of global gates required to synthesise an arbitrary n-qubit Clifford circuit from the 12n − 18 reported in (Maslov and Nam 2018 New J. Phys. 20 033018) to 6n − 8.

Topological Quantum Compiling with Reinforcement Learning.

Quantum compiling, a process that decomposes the quantum algorithm into a series of hardware-compatible commands or elementary gates, is of fundamental importance for quantum computing. We introduce an efficient algorithm based on deep reinforcement learning that compiles an arbitrary single-qubit gate into a sequence of elementary gates from a finite universal set. It generates near-optimal gate sequences with given accuracy and is generally applicable to various scenarios, independent of the hardware-feasible universal set and free from using ancillary qubits. For concreteness, we apply this algorithm to the case of topological compiling of Fibonacci anyons and obtain near-optimal braiding sequences for arbitrary single-qubit unitaries. Our algorithm may carry over to other challenging quantum discrete problems, thus opening up a new avenue for intriguing applications of deep learning in quantum physics.

Flux-tunable phase shifter for microwaves

We introduce a magnetic-flux-tunable phase shifter for propagating microwave photons, based on three equidistant superconducting quantum interference devices (SQUIDs) on a transmission line. We experimentally implement the phase shifter and demonstrate that it produces a broad range of phase shifts and full transmission within the experimental uncertainty. Together with previously demonstrated beam splitters, this phase shifter can be utilized to implement arbitrary single-qubit gates for qubits based on propagating microwave photons. These results complement previous demonstrations of on-demand single-photon sources and detectors, and hence assist in the pursuit of an all-microwave quantum computer based on propagating photons.

Universal quantum control in zero-field nuclear magnetic resonance

This paper describes a general method for manipulation of nuclear spins in zero magnetic field. In the absence of magnetic fields, the spins lose the individual information on chemical shifts and inequivalent spins can only be distinguished by nuclear gyromagnetic ratios and spin-spin couplings. For spin-1/2 nuclei with different gyromagnetic ratios (i.e., different species) in zero magnetic field, we describe the scheme to realize a set of universal quantum logic gates, e.g., arbitrary single-qubit gates and two-qubit controlled-NOT gate. This method allows for universal quantum control in systems which might provide promising applications in materials science, chemistry, biology,quantum information processing and fundamental physics.

Multi-qubit non-adiabatic holonomic controlled quantum gates in decoherence-free subspaces

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 by utilizing non-adiabatic holonomy in decoherence-free subspaces and the required resource for the decoherence-free subspace encoding is minimal by using only two neighboring physical qubits undergoing collective dephasing to encode a logical qubit.

Mechanically induced two-qubit gates and maximally entangled states for single electron spins in a carbon nanotube

We theoretically analyze a system where two electrons are trapped separately in two quantum dots on a suspended carbon nanotube (CNT), subject to external ac electric driving. An indirect mechanically-induced coupling of two distant single electron spins is induced by the interaction between the spins and the mechanical motion of the CNT. We show that a two-qubit iSWAP gate and arbitrary single-qubit gates can be obtained from the intrinsic spin-orbit coupling. Combining the iSWAP gate and single-qubit gates, maximally entangled states of two spins can be generated in a single step by varying the frequency and the strength of the external electric driving field. The spin-phonon coupling can be turned off by electrostatically shifting the electron wave function on the nanotube.

Ground states of one-dimensional symmetry-protected topological phases and their utility as resource states for quantum computation

The program of classifying symmetry protected topological (SPT) phases in 1D has been recently completed and has opened the doors to study closely the properties of systems belonging to these phases. It was recently found that being able to constrain the form of ground states of SPT order based on symmetry properties also allows to explore novel resource states for processing of quantum information. In this paper, we generalize the consideration of Else et al. [Phys. Rev. Lett. {\bf 108}, 240505 (2012)] where it was shown that the ground-state form of spin-1 chains protected by $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry supports perfect operation of the identity gate, important also for long-distance transmission of quantum information. We develop a formalism to constrain the ground-state form of SPT phases protected by any arbitrary finite symmetry group and use it to examine examples of ground states of SPT phases protected by various finite groups for similar gate protections. We construct a particular Hamiltonian invariant under $A_4$ symmetry transformation which is one of the groups that allows protected identity operation and examine its ground states. We find that there is an extended region where the ground state is the AKLT state, which not only supports the identity gate but also arbitrary single-qubit gates.

Robust quantum gates for singlet-triplet spin qubits using composite pulses

We present a comprehensive theoretical treatment of SUPCODE, a method for generating dynamically corrected quantum gate operations, which are immune to random noise in the environment, by using carefully designed sequences of soft pulses. SUPCODE enables dynamical error suppression even when the control field is constrained to be positive and uniaxial, making it particularly suited to counteracting the effects of noise in systems subject to these constraints such as singlet-triplet qubits. We describe and explain in detail how to generate SUPCODE pulse sequences for arbitrary single-qubit gates and provide several explicit examples of sequences that implement commonly used gates, including the single-qubit Clifford gates. We develop sequences for noise-resistant two-qubit gates for two exchanged-coupled singlet-triplet qubits by cascading robust single-qubit gates, leading to a 35% reduction in gate time compared to previous works. This cascade approach can be scaled up to produce gates for an arbitrary-length spin qubit array, and is thus relevant to scalable quantum computing architectures. To more accurately describe real spin qubit experiments, we show how to design sequences that incorporate additional features and practical constraints such as sample-specific charge noise models and finite pulse rise times. We provide a detailed analysis based on randomized benchmarking to show how SUPCODE gates perform under realistic $1/f^\alpha$ noise and find a strong dependence of gate fidelity on the exponent $\alpha$, with best performance for $\alpha>1$. Our SUPCODE sequences can therefore be used to implement robust universal quantum computation while accommodating the fundamental constraints and experimental realities of singlet-triplet qubits.

Tunable interfaces for realizing universal quantum computation with topological qubits

We propose to implement tunable interfaces for realizing universal quantum computation with topological qubits. One interface is between the topological and superconducting qubits, which can realize an arbitrary single-qubit gate on the topological qubit. When two qubits are involved, the interface between the topological qubits and a microwave cavity can induce a nontrivial two-qubit gate, which cannot be constructed based on braiding operations. The two interfaces, being tunable via an external magnetic flux, may serve as the building blocks towards universal quantum computation with topological qubits.

Robust site-resolvable quantum gates in an optical lattice via inhomogeneous control

The power of optical lattices for quantum simulation and computation is greatly enhanced when atoms at individual lattice sites can be accessed for measurement and control. Experiments routinely use high-resolution microscopy to obtain site-resolved images in real time, and site-resolved spin flips have been implemented using microwaves resonant with frequency-shifted target atoms in focused light fields. Here we show that methods adapted from inhomogeneous control can greatly increase the performance of such resonance addressing, allowing the targeting of arbitrary single-qubit quantum gates on selected sites with minimal cross-talk to neighbouring sites and significant robustness against uncertainty in the atom position. We further demonstrate the simultaneous implementation of different gates at adjacent sites with a single global microwave pulse. Coherence is verified through two-pulse experiments, and the average gate fidelity is measured to be 95±3%. Our approach may be useful in other contexts such as ion traps and nitrogen-vacancy centres in diamond.

Optimization of the Solovay-Kitaev algorithm

The Solovay-Kitaev algorithm is the standard method used for approximating arbitrary single-qubit gates for fault-tolerant quantum computation. In this paper we introduce a technique called "search space expansion", which modifies the initial stage of the Solovay-Kitaev algorithm, increasing the length of the possible approximating sequences but without requiring an exhaustive search over all possible sequences. We show that our technique, combined with a GNAT geometric tree search outputs gate sequences that are almost an order of magnitude smaller for the same level of accuracy. This therefore significantly reduces the error correction requirements for quantum algorithms on encoded fault-tolerant hardware.

Faster quantum chemistry simulation on fault-tolerant quantum computers

Quantum computers can in principle simulate quantum physics exponentially faster than their classical counterparts, but some technical hurdles remain. We propose methods which substantially improve the performance of a particular form of simulation, ab initio quantum chemistry, on fault-tolerant quantum computers; these methods generalize readily to other quantum simulation problems. Quantum teleportation plays a key role in these improvements and is used extensively as a computing resource. To improve execution time, we examine techniques for constructing arbitrary gates which perform substantially faster than circuits based on the conventional Solovay–Kitaev algorithm (Dawson and Nielsen 2006 Quantum Inform. Comput.6 81). For a given approximation error ϵ, arbitrary single-qubit gates can be produced fault-tolerantly and using a restricted set of gates in time which is O(log ϵ) or O(log log ϵ); with sufficient parallel preparation of ancillas, constant average depth is possible using a method we call programmable ancilla rotations. Moreover, we construct and analyze efficient implementations of first- and second-quantized simulation algorithms using the fault-tolerant arbitrary gates and other techniques, such as implementing various subroutines in constant time. A specific example we analyze is the ground-state energy calculation for lithium hydride.

Constructing arbitrary steane code single logical qubit fault-tolerant gates

We present a simple method for constructing optimal fault-tolerant approximations of arbitrary unitary gates using an arbitrary discrete universal gate set. The method presented is numerical and scales exponentially with the number of gates used in the approximation. However, for the specific case of arbitrary single-qubit gates and the fault-tolerant gates permitted by the concatenated 7-qubit Steane code, we find gate sequences sufficiently long and accurate to permit the fault-tolerant factoring of numbers thousands of bits long. A general scaling law of how rapidly these fault-tolerant approximations converge to arbitrary single-qubit gates is also determined.