One of the critical limitations quantum computers are yet to overcome is quantum errors. Efforts have been made in quantum error correction fields to overcome them. However, since we are bound by the technology of this noisy intermediate-scale quantum era, it is important that we focus on the efficiency and optimization of our error correction circuits. In this paper, we present a way of extending quantum error correction circuits using quantum adders by utilizing the notion of majority voting over all the qubits. We use adder circuits and a comparator to achieve majority voting. We demonstrate how our proposed methodology exhibits a linear trend in the required number of quantum gates. Further, we confirm the accuracy and efficacy of our proposed methodology for optimizing the number of quantum gates through extensive simulation in IBM's Qiskit and compare them with existing literature.
One of the critical limitations quantum computers are yet to overcome is quantum errors. Efforts have been made in quantum error correction fields to overcome them. However, since we are bound by the technology of this noisy intermediate-scale quantum era, it is important that we focus on the efficiency and optimization of our error correction circuits. In this paper, we present a way of extending quantum error correction circuits using quantum adders by utilizing the notion of majority voting over all the qubits. We use adder circuits and a comparator to achieve majority voting. We demonstrate how our proposed methodology exhibits a linear trend in the required number of quantum gates. Further, we confirm the accuracy and efficacy of our proposed methodology for optimizing the number of quantum gates through extensive simulation in IBM's Qiskit and compare them with existing literature.
Quantum error correction comes from the marriage of quantum mechanics with the theory of error-correcting codes, which is still at the rudimentary stage tackling only 1 qubit to date. As, unlike the classical world, the extent of error in the quantum world is substantially high and unavoidable, scaling up the quantum error correction from 1 qubit to higher is of utmost significane. Therefore, to achive the scaling up, we present a general quantum error correction code that can be adapted for any number of quantum errors (bit-flip error to be specific in our case). This generalized code for bit-flip error correction realizes a delicate blending of using controlled-NOT gates with the notion of quantum entanglement. We augment the blending with majority voting in the final stage of the error correction. We demonstrate efficacy of our proposed error correction code through real experimentation in IBM Qiskit. Our experimental results up to 3-qubit bit-flip errors in the available Qiskit infrastructure confirm a total escape from errors using our proposed error correction code.
With the advent of efficient quantum algorithms and technological advances, design of quantum circuits has gained importance. Minimization of the gate count and the number of gate levels are the two major objectives in quantum circuit design. The peculiar nature of quantum decoherence that leads to quantum errors mandates completion of all the quantum gate operations within a time bound, hence reduction in the gate count and the number of circuit levels leads to lowering the errors and the overall cost in quantum circuits. In this paper, we propose the design of adder circuits using CNOT and CkNOT gates, with significant reduction in gate count and number of gate levels over their existing counterparts in the literature. We then present a software model for evaluating errors in quantum computing circuits and employ it for evaluating the error performance of our proposed quantum adder circuits.
Quantum error mitigation is an important technique to reduce the impact of noise in quantum computers. With more and more qubits being supported on quantum computers, there are two emerging fundamental challenges. First, the number of shots required for quantum algorithms with large numbers of qubits needs to increase in order to obtain a meaningful distribution or expected value of an observable. Second, although steady progress has been made in improving the fidelity of each qubit, circuits with a large number of qubits are likely to produce erroneous results. This low-shot, high-noise regime calls for highly scalable error mitigation techniques. In this paper, we propose a simple and effective mitigation scheme, qubit-wise majority vote, for quantum algorithms with a single correct output. We show that our scheme produces the maximum likelihood (ML) estimate under certain assumptions and bound the number of shots required. Our experimental results on real quantum devices confirm that our proposed approach requires fewer shots than existing ones, and can sometimes recover the correct answers even when they are not observed from the measurement results.
Quantum computing is an emerging technology that has the potential to achieve exponential speedups over their classical counterparts. To achieve quantum advantage, quantum principles are being applied to fields such as communications, information processing, and artificial intelligence. However, quantum computers face a fundamental issue since quantum bits are extremely noisy and prone to decoherence. Keeping qubits error free is one of the most important steps towards reliable quantum computing. Different stabilizer codes for quantum error correction have been proposed in past decades and several methods have been proposed to import classical error correcting codes to the quantum domain. Design of encoding and decoding circuits for the stabilizer codes have also been proposed. Optimization of these circuits in terms of the number of gates is critical for reliability of these circuits. In this paper, we propose a procedure for optimization of encoder circuits for stabilizer codes. Using the proposed method, we optimize the encoder circuit in terms of the number of 2-qubit gates used. The proposed optimized eight-qubit encoder uses 18 CNOT gates and 4 Hadamard gates, as compared to 14 single qubit gates, 33 2-qubit gates, and 6 CCNOT gates in a prior work. The encoder and decoder circuits are verified using IBM Qiskit. We also present encoder circuits for the Steane code and a 13-qubit code, that are optimized with respect to the number of gates used, leading to a reduction in number of CNOT gates by 1 and 8, respectively.
Quantum computers are able to efficiently solve certain problems that are very computationally demanding or even intractable on classical computers. With recent advances in quantum computing hardware, we are entering an exciting era where it is becoming possible to execute ‘useful’ quantum algorithms. However, quantum computers will continue to be noisy for the foreseeable future. In this paper, quantum adder circuits are used to evaluate three simple error mitigation methods: (1) error correction through the use of replicated circuits and a voter circuit, (2) error detection by encoding, which involves expanding the qubit space and partitioning it into orthogonal subspaces consisting of correct and incorrect code words, and (3) error mitigation by reducing circuit depth at the expense of increasing the number of qubits. These three mitigation methods are what we dub replication, encoding, and simplification, respectively. We find simplification to be most effective for implementing the simple quantum adders on the IBM Quantum Experience, while replication increases the gate count and the error count on current quantum devices. The encoding methods used in this study proved to be not effective for even the simple adder circuits that were implemented, suggesting the need to study and evaluate more sophisticated error correcting schemes.
The "Noisy intermediate-scale quantum" NISQ machine era primarily focuses on mitigating noise, controlling errors, and executing high-fidelity operations, hence requiring shallow circuit depth and noise robustness. Approximate computing is a novel computing paradigm that produces imprecise results by relaxing the need for fully precise output for error-tolerant applications including multimedia, data mining, and image processing. We investigate how approximate computing can improve the noise resilience of quantum adder circuits in NISQ quantum computing. We propose five designs of approximate quantum adders to reduce depth while making them noise-resilient, in which three designs are with carryout, while two are without carryout. We have used novel design approaches that include approximating the Sum only from the inputs (pass-through designs) and having zero depth, as they need no quantum gates. The second design style uses a single CNOT gate to approximate the SUM with a constant depth of O(1). We performed our experimentation on IBM Qiskit on noise models including thermal, depolarizing, amplitude damping, phase damping, and bitflip: (i) Compared to exact quantum ripple carry adder without carryout the proposed approximate adders without carryout have improved fidelity ranging from 8.34% to 219.22%, and (ii) Compared to exact quantum ripple carry adder with carryout the proposed approximate adders with carryout have improved fidelity ranging from 8.23% to 371%. Further, the proposed approximate quantum adders are evaluated in terms of various error metrics.