This work proposes numerical tests which determine whether a two-qubit operator has an atypically simple quantum circuit. Specifically, we describe formulae, written in terms of matrix coefficients, characterizing operators implementable with exactly zero, one, or two controlled-not (CNOT) gates and all other gates being one-qubit. We give an algorithm for synthesizing two-qubit circuits with optimal number of CNOT gates, and illustrate it on operators appearing in quantum algorithms by Deutsch-Josza, Shor and Grover. In another application, our explicit numerical tests allow timing a given Hamiltonian to compute a CNOT modulo one-qubit gates, when this is possible.
We examine how dissipation and gate timing errors affect the fidelity of a sequence of SWAP gates on a chain of interacting qubits in comparison to noise in the interqubit interaction. Although interqubit interaction noise and gate timing errors are always present in any qubit platform, dissipation is a special case that can arise in multivalley semiconductor spin qubit systems, such as Si-based qubits, where dissipation may be used as a general model for valley leakage. In our Hamiltonian, each qubit is coupled via Heisenberg exchange to every other qubit in the chain, with the strength of th…
Quantum algorithms need to be compiled to respect the constraints imposed by quantum processors, which is known as the mapping problem. The mapping procedure will result in an increase of the number of gates and of the circuit latency, decreasing the algorithm's success rate. It is crucial to minimize mapping overhead, especially for Noisy Intermediate-Scale Quantum (NISQ) processors that have relatively short qubit coherence times and high gate error rates. Most of prior mapping algorithms have only considered constraints such as the primitive gate set and qubit connectivity, but the actual g…
Even if a logical network consists of thermodynamically reversible gate operations, the computation process may have high dissipation rate if the gate implementation is controlled by external clock signals. It is an open question whether the global clocking mechanism necessarily envolves irreversible processes. However, one can show that it is not possible to extract any timing information from a micro-physical clock without disturbing it. Applying recent results of quantum information theory we can show a hardware-independent lower bound on the timing information that is necessarily destroyed…
We demonstrate a simple pulse shaping technique designed to improve the fidelity of spin-dependent force operations commonly used to implement entangling gates in trapped-ion systems. This extension of the Mølmer-Sørensen gate can theoretically suppress the effects of certain frequency and timing errors to any desired order and is demonstrated through Walsh modulation of a two-qubit entangling gate on trapped atomic ions. The technique is applicable to any system of qubits coupled through collective harmonic oscillator modes.
We address the problem of constructing dynamically corrected gates for non-Markovian open quantum systems in settings where limitations on the available control inputs and/or the presence of control noise make existing analytical approaches unfeasible. By focusing on the important case of singlet-triplet electron spin qubits, we show how ideas from optimal control theory may be used to automate the synthesis of dynamically corrected gates that simultaneously minimize the system's sensitivity against both decoherence and control errors. Explicit sequences for effecting robust single-qubit rotat…
Controlled phase (CPHASE) gates can in principle be realized with trapped neutral atoms by making use of the Rydberg blockade. Achieving the ultra-high fidelities required for quantum computation with such Rydberg gates is however compromised by experimental inaccuracies in pulse amplitudes and timings, as well as by stray fields that cause fluctuations of the Rydberg levels. We report here a comparative study of analytic and numerical pulse sequences for the Rydberg CPHASE gate that specifically examines the robustness of the gate fidelity with respect to such experimental perturbations. Anal…
We analyze the coupling of two qubits via an epitaxial semiconducting junction. In particular, we consider three configurations that include pairs of transmons or gatemons as well as gatemon-like two qubits formed by an epitaxial four-terminal junction. These three configurations provide an electrical control of the interaction between the qubits by applying voltage to a metallic gate near the semiconductor junction and can be utilized to naturally realize a controlled-Z gate (CZ). We calculate the fidelity and timing for such CZ gate. We demonstrate that in the absence of decoherence, the CZ …
The error threshold for fault tolerant quantum computation with concatenated encoding of qubits is penalized by internal communication overhead. Many quantum computation proposals rely on nearest-neighbour communication, which requires excess gate operations. For a qubit stripe with a width of L+1 physical qubits implementing L levels of concatenation, we find that the error threshold of 2.1x10^-5 without any communication burden is reduced to 1.2x10^-7 when gate errors are the dominant source of error. This ~175X penalty in error threshold translates to an ~13X penalty in the amplitude and ti…
A comparison of gate fidelities between different spin qubit types defined in quantum dots and a donor under different control errors is reported. We studied five qubit types, namely the quantum dot spin qubit, the double quantum dot singlet-triplet qubit, the double quantum dot hybrid qubit, the donor qubit and the quantum dot spin-donor qubit. For each one, we derived analytical time sequences that realize single qubit rotations along the principal axis of the Bloch sphere. We estimated the effects of control errors on the gate fidelity by using a Gaussian noise model. Then we compared the g…
Quantum systems have potential to demonstrate significant computational advantage, but current quantum devices suffer from the rapid accumulation of error that prevents the storage of quantum information over extended periods. The unintentional coupling of qubits to their environment and each other adds significant noise to computation, and improved methods to combat decoherence are required to boost the performance of quantum algorithms on real machines. While many existing techniques for mitigating error rely on adding extra gates to the circuit, calibrating new gates, or extending a circuit…
The Hamiltonian control of n qubits requires precision control of both the strength and timing of interactions. Compensation pulses relax the precision requirements by reducing unknown but systematic errors. Using composite pulse techniques designed for single qubits, we show that systematic errors for n qubit systems can be corrected to arbitrary accuracy given either two non-commuting control Hamiltonians with identical systematic errors or one error-free control Hamiltonian. We also examine composite pulses in the context of quantum computers controlled by two-qubit interactions. For quantu…
It is known that it is possible to encode a logical qubit over many physical qubits such that it is immune to the effects of collective decoherence, and it is possible to perform universal quantum computation using these `decoherence-free' qubits. However, current proposed methods of performing gates on these encoded qubits could be difficult to implement, or could take too much time to perform. Here we investigate whether exploiting ring-exchange interactions, which may be naturally present, can simplify the implementation of these gates in any way. Using a ring exchange interaction, we have …
We derive an encoded universality representation for a generalized anisotropic exchange Hamiltonian that contains cross-product terms in addition to the usual two-particle exchange terms. The recently developed algebraic approach is used to show that the minimal universality-generating encodings of one logical qubit are based on three physical qubits. We show how to generate both single- and two-qubit operations on the logical qubits, using suitably timed conjugating operations derived from analysis of the commutator algebra. The timing of the operations is seen to be crucial in allowing simpl…
This study examines the possibility of finding perfect entanglers for a Hamiltonian which corresponds to several quantum information platforms of interest at the present time. However, in this study, we use a superconducting circuit that stands out from other quantum-computing devices, especially because Transmon qubits can be coupled via capacitors or microwave cavities, which enable us to combine high coherence, fast gates, and high flexibility in its design parameters. There are currently two factors limiting the performance of superconducting processors: timing mismatch and the limitation …
The feasibility of high-fidelity single-qubit operations of a hole spin in a quantum dot molecule by electric g tensor control is demonstrated. Apart from a constant external magnetic field the proposed scheme allows for an exclusively electric control of the hole spin. Realistic electric gate bias profiles are identified for various qubit operations using process-tomography-based optimal control. They are shown to be remarkably robust against decoherence and dissipation arising from the interaction of the hole with host-lattice nuclear spins and phonons, with a fidelity loss of $\approx$ 1 pe…
Quantum Hashing Circuit Optimization for Arbitrary Qubit Connectivity Graphs Based on 1-Covering Path
Kazan Federal University（喀山联邦大学）；Zavoisky Physical-Technical Institute, FRC Kazan Scientific Center of RAS（扎沃伊斯基物理技术研究所，俄罗斯科学院喀山科学中心）；University of Messina（墨西拿大学）
High-fidelity gate operations are essential to the realization of a fault-tolerant quantum computer. In addition, the physical resources required to implement gates must scale efficiently with system size. A longstanding goal of the superconducting qubit community is the tight integration of a superconducting quantum circuit with a proximal classical cryogenic control system. Here we implement coherent control of a superconducting transmon qubit using a Single Flux Quantum (SFQ) pulse driver cofabricated on the qubit chip. The pulse driver delivers trains of quantized flux pulses to the qubit …
A new method for simulation of a binary homogeneous Markov process using a quantum computer was proposed. This new method allows using the distinguished properties of the quantum mechanical systems -- superposition, entanglement and probability calculations. Implementation of an algorithm based on this method requires the creation of a new quantum logic gate, which creates entangled state between two qubits. This is a two-qubit logic gate and it must perform a predefined rotation over the X-axis for the qubit that acts as a target, where the rotation accurately represents the transient probabi…
