Set Of Gates Research Articles

Logical Blocks for Fault-Tolerant Topological Quantum Computation

Logical gates constitute the building blocks of fault-tolerant quantum computation. While quantum error-corrected memories have been extensively studied in the literature, explicit constructions and detailed analyses of thresholds and resource overheads of universal logical gate sets have so far been limited. In this paper, we present a comprehensive framework for universal fault-tolerant logic motivated by the combined need for platform-independent logical gate definitions, flexible and scalable tools for numerical analysis, and exploration of novel schemes for universal logic that improve resource overheads. Central to our framework is the description of logical gates holistically in a way which treats space and time on a similar footing. Focusing on schemes based on surface codes, we introduce explicit, but platform-independent representations of topological logic gates -- called logical blocks -- and generate new, overhead-efficient methods for universal quantum computation. As a specific example, we propose fault-tolerant schemes based on surface codes concatenated with more general low-density parity check (LDPC) codes. The logical blocks framework enables a convenient mapping from an abstract description of the logical gate to a precise set of physical instructions for both circuit-based and fusion-based quantum computation (FBQC). Using this, we numerically simulate a surface-code-based universal gate set implemented with FBQC, and verify that their thresholds are consistent with the bulk memory threshold. We find that boundaries, defects, and twists can significantly impact the logical error rate scaling, with periodic boundary conditions potentially halving the resource requirements. Motivated by the favorable logical error rates for boundaryless computation, we introduce a novel computational scheme based on the teleportation of twists that may offer further resource reductions.

On the universality and membership problems for quantum gates

We study the universality and membership problems for gate sets consisting of a finite number of quantum gates. Our approach relies on the techniques from compact Lie group theory. We also introduce an auxiliary problem called the subgroup universality problem, which helps in solving some instances of the membership problem and can be of interest on its own. The resulting theorems are mainly formulated in terms of centralizers and the adjoint representations of a given set of quantum gates.

Redundancy Attack: Breaking Logic Locking Through Oracleless Rationality Analysis

During the last decade, logic locking has been proposed to protect integrated circuits against piracy and reverse engineering threats. Functional pruning attacks, such as the Boolean satisfiability (SAT) attack, have greatly challenged the security of logic locking techniques, yet they require access to an oracle and suffer from muted efficacy on inherently SAT-hard circuits. In this article, we present a novel oracleless attack on both XOR and MUX-based logic locking by analyzing the redundancy level deviation under different keys. Our fundamental insight is that incorrect keys would produce circuits that violate universally followed design principles, prominent among which stands the minimization of logic redundancy. We leverage the redundancy-level deviation produced by individual and pairs of key bits to recover key bit values and establish pairwise equivalence, leading to an efficient nearly linear time attack algorithm. We experimentally verify that the proposed attack quickly unveils more than half of the key bits with high accuracy on 21 ISCAS’85 and MCNC circuits locked with a variety of locking techniques. To fortify logic locking in the face of this successful redundancy attack, we supplement this article with a key gate insertion methodology that smooths the deviation in redundancy level. We achieve this goal by selecting key gates that exhibit pairwise dissociation among a set of individually secure locations, which effectively breaks down correlations in arbitrary sets of key gates and, thus, imposes a consistent redundancy level throughout the key space. Experimental results confirm the strong redundancy attack resilience of the proposed defense strategy.

Complete Unitary Qutrit Control in Ultracold Atoms

Physical quantum systems are commonly composed of more than two levels and offer the capacity to encode information in higher-dimensional spaces beyond the qubit, starting with the three-level qutrit. Here, we encode neutral-atom qutrits in an ensemble of ultracold ${}^{87}\mathrm{Rb}$ and demonstrate arbitrary single-qutrit SU(3) gates. We generate a full set of gates using only two resonant microwave tones, including synthesizing a gate that effects a direct coupling between the two disconnected levels in the three-level $\mathrm{\ensuremath{\Lambda}}$-scheme. Using two different gate sets, we implement and characterize the Walsh-Hadamard Fourier transform, and find similar final-state fidelity and purity from both approaches. This work establishes the ultracold neutral-atom qutrit as a promising platform for qutrit-based quantum information processing, extensions to $d$-dimensional qudits, and explorations in multilevel quantum state manipulations with nontrivial geometric phases.

Supervised learning of random quantum circuits via scalable neural networks

Predicting the output of quantum circuits is a hard computational task that plays a pivotal role in the development of universal quantum computers. Here we investigate the supervised learning of output expectation values of random quantum circuits. Deep convolutional neural networks (CNNs) are trained to predict single-qubit and two-qubit expectation values using databases of classically simulated circuits. These circuits are built using either a universal gate set or a continuous set of rotations plus an entangling gate, and they are represented via properly designed encodings of these gates. The prediction accuracy for previously unseen circuits is analyzed, also making comparisons with small-scale quantum computers available from the free IBM Quantum program. The CNNs often outperform these quantum devices, depending on the circuit depth, on the network depth, and on the training set size. Notably, our CNNs are designed to be scalable. This allows us exploiting transfer learning and performing extrapolations to circuits larger than those included in the training set. These CNNs also demonstrate remarkable resilience against noise, namely, they remain accurate even when trained on (simulated) expectation values averaged over very few measurements.

Fidelity-based distance bounds for N -qubit approximate quantum error correction

The Eastin-Knill theorem is a central result of quantum error correction theory and states that a quantum code cannot correct errors exactly, possess continuous symmetries, and implement a universal set of gates transversely. As a way to circumvent this result, there are several approaches in which one gives up on either exact error correction or continuous symmetries. In this context, it is common to employ a complementary measure of fidelity as a way to quantify quantum state distinguishability and benchmark approximations in error correction. Despite having useful properties, evaluating fidelity measures stands as a challenging task for quantum states with a large number of entangled qubits. With that in mind, we address two distance measures based on the sub- and superfidelities as a way to bound error approximations, which in turn require a lower computational cost. We model the lack of exact error correction to be equivalent to the action of a single dephasing channel, evaluate the proposed fidelity-based distances both analytically and numerically, and obtain a closed-form expression for a general $N$-qubit quantum state. We illustrate our bounds with two paradigmatic examples, an $N$-qubit mixed GHZ state and an $N$-qubit mixed $W$ state.

Modeling of spin decoherence in a Si hole qubit perturbed by a single charge fluctuator

Spin qubits in semiconductor quantum dots are one of the promizing devices to realize a quantum processor. A better knowledge of the noise sources affecting the coherence of such a qubit is therefore of prime importance. In this work, we study the effect of telegraphic noise induced by the fluctuation of a single electric charge. We simulate as realistically as possible a hole spin qubit in a quantum dot defined electrostatically by a set of gates along a silicon nanowire channel. Calculations combining Poisson and time-dependent Schr\"odinger equations allow to simulate the relaxation and the dephasing of the hole spin as a function of time for a classical random telegraph signal. We show that dephasing time $T_2$ is well given by a two-level model in a wide range of frequency. Remarkably, in the most realistic configuration of a low frequency fluctuator, the system has a non-Gaussian behavior in which the phase coherence is lost as soon as the fluctuator has changed state. The Gaussian description becomes valid only beyond a threshold frequency $\omega_{th}$, when the two-level system reacts to the statistical distribution of the fluctuator states. We show that the dephasing time $T_{2}(\omega_{th})$ at this threshold frequency can be considerably increased by playing on the orientation of the magnetic field and the gate potentials, by running the qubit along "sweet" lines. However, $T_{2}(\omega_{th})$ remains bounded due to dephasing induced by the non-diagonal terms of the stochastic perturbation Hamiltonian. Our simulations reveal that the spin relaxation cannot be described cleanly in the two-level model because the coupling to higher energy hole levels impacts very strongly the spin decoherence. This result suggests that multi-level simulations including the coupling to phonons should be necessary to describe the relaxation phenomenon in this type of qubit.

Graph Generation for Quantum States Using Qiskit and Its Application for Quantum Neural Networks

This paper describes a practical approach to the quantum theory using the simulation and processing technology available today. The proposed project allows us to create an exploration graph so that for an initial starting configuration of the qubits, all possible states are created given a set of gates selected by the user. For each node in the graph, we can obtain various types of information such as the applied gates from the initial state (the transition route), necessary cost, representation of the quantum circuit, as well as the amplitudes of each state. The project is designed not as an end goal, but rather as a processing platform that allows users to visualize and explore diverse solutions for different quantum problems in a much easier manner. We then describe some potential applications of this project in other research fields, illustrating the way in which the states from the graph can be used as nodes in a new interpretation of a quantum neural network; the steps of a hybrid processing chain are presented for the problem of finding one or more states that verify certain conditions. These concepts can also be used in academia, with their implementation being possible with the help of the Python programming language, the NumPy library, and Qiskit—the open-source quantum framework developed by IBM.

Compressive Gate Set Tomography

Flexible characterization techniques that provide a detailed picture of the experimental imperfections under realistic assumptions are crucial to gain actionable advice in the development of quantum computers. Gate set tomography self-consistently extracts a complete tomographic description of the implementation of an entire set of quantum gates, as well as the initial state and measurement, from experimental data. It has become a standard tool for this task but comes with high requirements on the number of sequences and their design, making it already experimentally challenging for only two qubits. In this work, we show that low-rank approximations of gate sets can be obtained from significantly fewer gate sequences and that it is sufficient to draw them at random. This coherent noise characterization however still contains the crucial information for improving the implementation. To this end, we formulate the data processing problem of gate set tomography as a rank-constrained tensor completion problem. We provide an algorithm to solve this problem while respecting the usual positivity and normalization constraints of quantum mechanics. For this purpose, we combine methods from Riemannian optimization and machine learning and develop a saddle-free second-order geometrical optimization method on the complex Stiefel manifold. Besides the reduction in sequences, we numerically demonstrate that the algorithm does not rely on structured gate sets or an elaborate circuit design to robustly perform gate set tomography. Therefore, it is more flexible than traditional approaches. We also demonstrate how coherent errors in shadow estimation protocols can be mitigated using estimates from gate set tomography.5 MoreReceived 25 May 2022Revised 10 January 2023Accepted 25 January 2023DOI:https://doi.org/10.1103/PRXQuantum.4.010325Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum channelsQuantum tomographyQuantum verificationQuantum Information

Device structure and fabrication process for silicon spin qubit realizing process-variation-robust SWAP gate operation

In this study, we propose technologies for the device structure, gate fabrication process, and back-bias-assisted operation of Si spin qubits to realize the high robustness of the two-qubit SWAP gate operation against process variations. We performed quantum device simulations for MOS-type two-qubit devices and verified the benefits of these technologies on the SWAP gate fidelity. We clarified that these technologies significantly improve the robustness of the SWAP gate operation against process variations and achieve a 6σ-yield SWAP gate operation with 99% fidelity, assuming device size fluctuation of the International Roadmap for Devices and Systems (IRDS) target for 2022. The proposed technologies provide a solution for completing a universal quantum gate set for realizing universal quantum computers with silicon.

Practical computational advantage from the quantum switch on a generalized family of promise problems

The quantum switch is a quantum computational primitive that provides computational advantage by applying operations in a superposition of orders. In particular, it can reduce the number of gate queries required for solving promise problems where the goal is to discriminate between a set of properties of a given set of unitary gates. In this work, we use Complex Hadamard matrices to introduce more general promise problems, which reduce to the known Fourier and Hadamard promise problems as limiting cases. Our generalization loosens the restrictions on the size of the matrices, number of gates and dimension of the quantum systems, providing more parameters to explore. In addition, it leads to the conclusion that a continuous variable system is necessary to implement the most general promise problem. In the finite dimensional case, the family of matrices is restricted to the so-called Butson-Hadamard type, and the complexity of the matrix enters as a constraint. We introduce the “query per gate'' parameter and use it to prove that the quantum switch provides computational advantage for both the continuous and discrete cases. Our results should inspire implementations of promise problems using the quantum switch where parameters and therefore experimental setups can be chosen much more freely.

Calculable lower bounds on the efficiency of universal sets of quantum gates

Currently available quantum computers, so called Noisy Intermediate-Scale Quantum devices, are characterized by relatively low number of qubits and moderate gate fidelities. In such scenario, the implementation of quantum error correction is impossible and the performance of those devices is quite modest. In particular, the depth of circuits implementable with reasonably high fidelity is limited, and the minimization of circuit depth is required. Such depths depend on the efficiency of the universal set of gates used in computation, and can be bounded using the Solovay–Kitaev theorem. However, it is known that much better, asymptotically tight bounds of the form , can be obtained for specific . Those bounds are controlled by so called spectral gap, denoted . Yet, the computation of is not possible for general and in practice one considers spectral gap at a certain scale , denoted . This turns out to be sufficient to bound the efficiency of provided that one is interested in a physically feasible case, in which an error ϵ is bounded from below. In this paper we derive lower bounds on and, as a consequence, on the efficiency of universal sets of d-dimensional quantum gates satisfying an additional condition. The condition is naturally met for generic quantum gates, such as e.g. Haar random gates. Our bounds are explicit in the sense that all parameters can be determined by numerical calculations on existing computers, at least for small d. This is in contrast with known lower bounds on which involve parameters with ambiguous values.

Effective implementation of nonadiabatic geometric quantum gates of cat-state qubits using an auxiliary qutrit

We propose an effective protocol for the implementation of nonadiabatic geometric quantum gates of cat-state qubits in Kerr-nonlinear resonators driven by two-photon squeezing drives. Coupling the Kerr-nonlinear resonators with an auxiliary qutrit with proper coupling strengths, the selective transition of the auxiliary qutrit is realized. The selective transition can be exploited in the implementation of a set of useful quantum gates, including the phase gates, the NOT gates, the controlled-phase gates, the controlled NOT gates, and the Toffoli gates. Numerical simulations show the implementations of different types of gates are robust against systematic errors, random noise, and decoherence. Therefore, the protocol may be helpful for robust and scalable quantum computation based on cat-state qubits.

Steane code analysis by randomized benchmarking

Quantum error correction codes (QECC) play a fundamental role in protecting the information processed in today’s noisy quantum computers. To build good error correction schemes, it is essential to understand how noise affects the behavior of these codes. In this research paper, we analyze Steane code, a 7-qubit QECC, using a randomized benchmarking (RB) protocol. With RB protocols, we can partially characterize the quality of implementation of a set of quantum gates. We show a scenario where Steane code with one logical qubit is advantageous compared to the situation with no quantum code. We obtained our results using a quantum simulator with custom noise models considering different numbers of noisy qubits.

State-Independent Nonadiabatic Geometric Quantum Gates

Quantum computation has demonstrated advantages over classical computation for special hard problems, where a set of universal quantum gates is essential. Geometric phases, which have built-in resilience to local noise, have been used to construct quantum gates with excellent performance. However, this advantage has been smeared in previous schemes. Here, we propose a state-independent nonadiabatic geometric quantum-gate scheme that is able to realize a more fully geometric gate than previous approaches, allowing for the cancelation of dynamical phases accumulated by an arbitrary state. Numerical simulations demonstrate that our scheme has significantly stronger gate robustness than the previous geometric and dynamical ones. Meanwhile, we give a detailed physical implementation of our scheme with the Rydberg atom system based on the Rydberg blockade effect, specifically for multiqubit control-phase gates, which exceeds the fault-tolerance threshold of multiqubit quantum gates within the considered error range. Therefore, our scheme provides a promising way for fault-tolerant quantum computation in atomic systems.

Error-Divisible Two-Qubit Gates

We introduce a simple widely applicable formalism for designing ``error-divisible'' two-qubit gates: a quantum gate set where fractional rotations have proportionally reduced error compared to the full entangling gate. In current noisy intermediate-scale quantum (NISQ) algorithms, performance is largely constrained by error proliferation at high circuit depths, of which two-qubit gate error is generally the dominant contribution. Further, in many hardware implementations, arbitrary two-qubit rotations must be composed from multiple two-qubit stock gates, further increasing error. This work introduces a set of criteria, and example wave forms and protocols to satisfy them, using superconducting qubits with tunable couplers for constructing continuous gate sets with significantly reduced leakage and dynamic $ZZ$ errors for small-angle rotations. If implemented at scale, NISQ-algorithm performance could be significantly improved by our error-divisible gate protocols.

Measurement-based interleaved randomised benchmarking using IBM processors

Quantum computers have the potential to outperform classical computers in a range of computational tasks, such as prime factorisation and unstructured searching. However, real-world quantum computers are subject to noise. Quantifying noise is of vital importance, since it is often the dominant factor preventing the successful realisation of advanced quantum computations. Here we propose and demonstrate an interleaved randomised benchmarking protocol for measurement-based quantum computers that can be used to estimate the fidelity of any single-qubit measurement-based gate. We tested the protocol on IBM superconducting quantum processors by estimating the fidelity of the Hadamard and T gates—a universal single-qubit gate set. Measurements were performed on entangled cluster states of up to 31 qubits. Our estimated gate fidelities show good agreement with those calculated from quantum process tomography. By artificially increasing noise, we were able to show that our protocol detects large noise variations in different implementations of a gate.

Low-overhead code concatenation approaches for universal quantum computation

Fault-tolerant quantum circuit design can be done by using a set of transversal gates. However, as there is no quantum error correction code with a universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state distillation, gauge fixing, code switching, code concatenation and pieceable fault tolerance are well-known examples of such approaches. However, the overhead of these approaches is one of the main bottlenecks for large-scale quantum computation. In this paper, two approaches for universal fault-tolerant quantum computation, mainly based on code concatenation, are proposed. The first approach combines the code concatenation approach with code switching, pieceable fault tolerance or magic state distillation and the second approach extends the nonuniformity of the concatenated codes by allowing to apply CNOT gates between different codes. The proposed approaches outperform the code concatenation approach in terms of both number of qubits and code distance and have also significantly less resource overhead than magic state distillation. This is achieved at the cost of reducing the effective distance of the concatenated code for implementing non-transversal gates.

Implementation of a Frenkel exciton-based controlled phase shifter

Frenkel excitons are of interest for ultrafast switching applications due to the femtosecond timescale at which coherent exciton transfer between chromophores takes place. The Frenkel Hamiltonian, which governs the dynamics of Frenkel excitons, belongs to a class of Hamiltonians that enable universal quantum computation. It is thus of interest to determine how a complete set of exciton-based gates for quantum computing could be constructed as aggregates of chromophores. We demonstrate that a controlled phase shifter can be constructed as a pair of exciton transmission lines that employ two types of chromophores and that are cross coupled by a two-exciton interaction. This element facilitates the construction of controlled basis-change gates, thereby enabling the implementation of a complete set of exciton-based gates for universal quantum computation.

Hardness of Braided Quantum Circuit Optimization in the Surface Code

Large-scale quantum information processing requires the use of quantum error correcting codes to mitigate the effects of noise in quantum devices. Topological error-correcting codes, such as surface codes, are promising candidates as they can be implemented using only local interactions in a two-dimensional array of physical qubits. Procedures such as defect braiding and lattice surgery can then be used to realize a fault-tolerant universal set of gates on the logical space of such topological codes. However, error correction also introduces a significant overhead in computation time, the number of physical qubits, and the number of physical gates. While optimizing fault-tolerant circuits to minimize this overhead is critical, the computational complexity of such optimization problems remains unknown. This ambiguity leaves room for doubt surrounding the most effective methods for compiling fault-tolerant circuits for a large-scale quantum computer. In this paper, we show that the optimization of a special subset of braided quantum circuits is NP-hard by a polynomial-time reduction of the optimization problem into a specific problem called Planar Rectilinear 3SAT.