Multi-qubit Operations Research Articles

Exploring multi-qubit analogue operations through acoustic wave dynamics

Quantum computing harnesses quantum phenomena like superposition and entanglement to surpass classical computers, showing promise across various fields. Current techniques utilize qubits in quantum circuits for parallel information processing, though managing and measuring these systems poses significant challenges. We propose a novel approach to simplify executing complex quantum algorithms without relying on multiple quantum gate operations. Our method introduces logical phi-bits—classical counterparts to qubits, using nonlinear acoustic waves in an externally driven acoustic metastructure. We demonstrate that complex multi-phi-bit unitary operations, akin to those in quantum circuits, can be conducted through a single action on this metastructure. This method starkly contrasts traditional quantum computing, which requires decomposed sequences of qubit gates for equivalent operations. The phi-bit system simplifies processes that are typically complex in quantum mechanics, potentially enhancing robustness and ease of implementation. Our results indicate that phi-bits could expand computational models by merging classical wave dynamics with quantum computational principles, thereby widening the potential of computational technologies. This research advances quantum-analogue computation and introduces new prospects for utilizing wave physics in information processing, thereby challenging and expanding existing paradigms in both classical and quantum computing. [Funding: NSF grant 2204382, 2204400, and 2242925.]

Empowering a qudit-based quantum processor by traversing the dual bosonic ladder

High-dimensional quantum information processing has emerged as a promising avenue to transcend hardware limitations and advance the frontiers of quantum technologies. Harnessing the untapped potential of the so-called qudits necessitates the development of quantum protocols beyond the established qubit methodologies. Here, we present a robust, hardware-efficient, and scalable approach for operating multidimensional solid-state systems using Raman-assisted two-photon interactions. We then utilize them to construct extensible multi-qubit operations, realize highly entangled multidimensional states including atomic squeezed states and Schrödinger cat states, and implement programmable entanglement distribution along a qudit array. Our work illuminates the quantum electrodynamics of strongly driven multi-qudit systems and provides the experimental foundation for the future development of high-dimensional quantum applications such as quantum sensing and fault-tolerant quantum computing.

Applicability of measurement-based quantum computation towards physically-driven variational quantum eigensolver

Variational quantum algorithms are considered one of the most promising methods for obtaining near-term quantum advantages; however, most of these algorithms are only expressed in the conventional quantum circuit scheme. The roadblock to developing quantum algorithms with the measurement-based quantum computation (MBQC) scheme is resource cost. Recently, we discovered that the realization of multi-qubit rotation operations only requires a constant number of single-qubit measurements with the MBQC scheme, providing a potential advantage in terms of resource cost. The structure of the Hamiltonian variational ansatz aligns well with this characteristic. Thus, we propose an efficient measurement-based quantum algorithm for quantum many-body system simulation tasks, called measurement-based Hamiltonian variational ansatz (MBHVA). We then demonstrate its effectiveness, efficiency, and advantages with the two-dimensional Heisenberg model and the Fermi–Hubbard chain. Numerical experiments show that MBHVA can have similar performance as circuit-based ansatz, and is expected to reduce operation counts during execution compared to quantum circuits, bringing the advantage of running time. We conclude that the MBQC scheme is potentially feasible for achieving near-term quantum advantages in the noisy intermediate-scale quantum era, especially in the presence of large multi-qubit rotation operations.

Synthetiq: Fast and Versatile Quantum Circuit Synthesis

To implement quantum algorithms on quantum computers it is crucial to decompose their operators into the limited gate set supported by those computers. Unfortunately, existing works automating this essential task are generally slow and only applicable to narrow use cases.We present Synthetiq, a method to synthesize quantum circuits implementing a given specification over arbitrary finite gate sets, which is faster and more versatile than existing works. Synthetiq utilizes Simulated Annealing instantiated with a novel, domain-specific energy function that allows developers to leverage partial specifications for better efficiency. Synthetiq further couples this synthesis method with a custom simplification pass, to ensure efficiency of the found circuits. We experimentally demonstrate that Synthetiq can generate better implementations than were previously known for multiple relevant quantum operators including RCCCX, CCT, CCiSWAP, C√SWAP, and C√iSWAP. Our extensive evaluation also demonstrates Synthetiq frequently outperforms a wide variety of more specialized tools in their own domains, including (i) ‍the well-studied task of synthesizing fully specified operators in the Clifford+T gate set, (ii) ‍є-approximate synthesis of multi-qubit operators in the same gate set, and (iii) ‍synthesis tasks with custom gate sets. On all those tasks, Synthetiq is typically one to two orders of magnitude faster than previous state-of-the-art and can tackle problems that were previously out of the reach of any synthesis tool.

Rapid single-shot parity spin readout in a silicon double quantum dot with fidelity exceeding 99%

Silicon-based spin qubits offer a potential pathway toward realizing a scalable quantum computer owing to their compatibility with semiconductor manufacturing technologies. Recent experiments in this system have demonstrated crucial technologies, including high-fidelity quantum gates and multiqubit operation. However, the realization of a fault-tolerant quantum computer requires a high-fidelity spin measurement faster than decoherence. To address this challenge, we characterize and optimize the initialization and measurement procedures using the parity-mode Pauli spin blockade technique. Here, we demonstrate a rapid (with a duration of a few μs) and accurate (with >99% fidelity) parity spin measurement in a silicon double quantum dot. These results represent a significant step forward toward implementing measurement-based quantum error correction in silicon.

Experimental Realization of Nonunitary Multiqubit Operations

Experimental Realization of Nonunitary Multiqubit Operations

Logical states for fault-tolerant quantum computation with propagating light.

To harness the potential of a quantum computer, quantum information must be protected against error by encoding it into a logical state that is suitable for quantum error correction. The Gottesman-Kitaev-Preskill (GKP) qubit is a promising candidate because the required multiqubit operations are readily available at optical frequency. To date, however, GKP qubits have been demonstrated only at mechanical and microwave frequencies. We realized a GKP state in propagating light at telecommunication wavelength and verified it through homodyne measurements without loss corrections. The generation is based on interference of cat states, followed by homodyne measurements. Our final states exhibit nonclassicality and non-Gaussianity, including the trident shape of faint instances of GKP states. Improvements toward brighter, multipeaked GKP qubits will be the basis for quantum computation with light.

A versatile device for implementing the optical quantum gates in multiple degrees of freedom

Optical quantum logic gates are the basic elements for building optical quantum computer. Usually, to implement different logic gates, different optical elements and frameworks are needed. Here, we propose a versatile device that a modified Sagnac interferometer composed of a spatial light modulator (SLM) for implementing multiple optical gates within a classical light framework. We demonstrate that the device can manipulate the polarization and full-field spatial modes of photons to perform multi-qubit logic operations. And versatile conversions between different logic gates are achieved by simply altering the hologram imposed on SLM. Our device shows a good performance in exploring the photon’s full degrees of freedom, which makes it an appropriate candidate for integrated optical computing.

Effect of fast noise on the fidelity of trapped-ion quantum gates

High-fidelity single- and multiqubit operations compose the backbone of quantum information processing. This fidelity is based on the ability to couple single- or two-qubit levels in an extremely coherent and precise manner. A necessary condition for coherent quantum evolution is a highly stable local oscillator driving these transitions. Here we study the effect of fast noise, that is, noise at frequencies much higher than the local oscillator linewidth, on the fidelity of one- and two-qubit gates in a trapped-ion system. We analyze and measure the effect of fast noise on single-qubit operations, including resonant $\ensuremath{\pi}$ rotations and off-resonant sideband transitions. We further numerically analyze the effect of fast phase noise on the M\o{}lmer-S\o{}rensen two-qubit gate. We find a unified and simple way to estimate the performance of all of these operations through a single parameter given by the noise power spectral density at the qubit response frequency. While our analysis focuses on phase noise and on trapped-ion systems, it is relevant for other sources of fast noise as well as for other qubit systems in which spinlike qubits are coupled by a common bosonic field. Our analysis can help in guiding the design of quantum hardware platforms and gates, improving their fidelity towards fault-tolerant quantum computing.

Comparison of spontaneous emission in trapped-ion multiqubit gates at high magnetic fields

Penning traps have been used for performing quantum simulations and sensing with hundreds of ions and provide a promising route toward scaling up trapped ion quantum platforms because of the ability to trap and control hundreds or thousands of ions in two- and three-dimensional crystals. In both Penning traps and the more common radiofrequency Paul traps, lasers are often used to drive multiqubit entangling operations. A leading source of decoherence in these operations is off-resonant spontaneous emission. While many trapped ion quantum computers or simulators utilize clock qubits, other systems, especially those with high magnetic fields such as Penning traps, rely on Zeeman qubits, which require a more complex calculation of this decoherence. We therefore examine theoretically the impacts of spontaneous emission on quantum gates performed with trapped-ion ground-state Zeeman qubits in a high magnetic field. In particular, we consider two types of gates---light-shift $({\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{i}^{z}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{j}^{z})$ gates and M\o{}lmer-S\o{}rensen $({\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{i}^{x}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{j}^{x})$ gates---obtained with laser beams directed approximately perpendicular to the magnetic field (the quantization axis) and compare the decoherence errors in each. Within each gate type, we also compare different operating points with regard to the detunings, polarizations, and required intensity of the laser beams used to drive the gates. We show that both gates can have similar performance at their optimal operating conditions at high magnetic fields and examine the experimental feasibility of various operating points. By examining the magnetic field dependence of each gate, we demonstrate that, when the $P$ state fine-structure splitting is large compared to the Zeeman splittings, the theoretical performance of the M\o{}lmer-S\o{}rensen gate is significantly better than that of the light-shift gate. Additionally, for the light-shift gate, we make an approximate comparison between the fidelities that can be achieved at high fields with the fidelities of state-of-the-art two-qubit trapped ion quantum gates. We show that, with regard to spontaneous emission, the achievable infidelity with our current configuration is about an order of magnitude larger than that of the best low-field gates, but we also discuss several alternative configurations with potential error rates that are comparable with those for state-of-the-art trapped ion gates.

Imaginary-time evolution with quantum nondemolition measurements: Multiqubit interactions via measurement nonlinearities

We show that quantum nondemolition (QND) measurements can be used to realize measurement-based imaginary-time evolution. In our proposed scheme, repeated weak QND measurements are used to estimate the energy of a given Hamiltonian. Based on this estimated energy, adaptive unitary operations are applied such that only the targeted energy eigenstates are fixed points of the evolution. In this way, the system is deterministically driven towards the desired state. The nonlinear nature of the QND measurement, which allows for producing interactions between systems, is explicitly derived in terms of measurement operators. We show that for suitable interaction times, single-qubit QND Hamiltonians can be converted to effective multiqubit imaginary time operations. We illustrate our techniques with the example of preparing a four-qubit cluster state, which is prepared using only collective single-qubit QND measurements and single-qubit adaptive operations.

Scalable fast benchmarking for individual quantum gates with local twirling

With the development of controllable quantum systems, fast and practical characterization of multi-qubit gates has become essential for building high-fidelity quantum computing devices. The usual way to fulfill this requirement via randomized benchmarking demands complicated implementation of numerous multi-qubit twirling gates. How to efficiently and reliably estimate the fidelity of a quantum process remains an open problem. This work thus proposes a character-cycle benchmarking protocol and a character-average benchmarking protocol using only local twirling gates to estimate the process fidelity of an individual multi-qubit operation. Our protocols were able to characterize a large class of quantum gates including and beyond the Clifford group via the local gauge transformation, which forms a universal gate set for quantum computing. We demonstrated numerically our protocols for a non-Clifford gate—controlled- ( T X ) and a Clifford gate—five-qubit quantum error-correcting encoding circuit. The numerical results show that our protocols can efficiently and reliably characterize the gate process fidelities. Compared with the cross-entropy benchmarking, the simulation results show that the character-average benchmarking achieves three orders of magnitude improvements in terms of sampling complexity.

Noise-resilient edge modes on a chain of superconducting qubits.

Inherent symmetry of a quantum system may protect its otherwise fragile states. Leveraging such protection requires testing its robustness against uncontrolled environmental interactions. Using 47 superconducting qubits, we implement the one-dimensional kicked Ising model, which exhibits nonlocal Majorana edge modes (MEMs) with [Formula: see text] parity symmetry. We find that any multiqubit Pauli operator overlapping with the MEMs exhibits a uniform late-time decay rate comparable to single-qubit relaxation rates, irrespective of its size or composition. This characteristic allows us to accurately reconstruct the exponentially localized spatial profiles of the MEMs. Furthermore, the MEMs are found to be resilient against certain symmetry-breaking noise owing to a prethermalization mechanism. Our work elucidates the complex interplay between noise and symmetry-protected edge modes in a solid-state environment.

Classically Replaceable Operations

Quantum information science provides powerful technologies beyond the scope of classical physics. In practice, accurate control of quantum operations is a challenging task with current quantum devices. The implementation of high fidelity and multi-qubit quantum operations consumes massive resources and requires complicated hardware design to fight against noise. An approach to alleviating this problem is to replace quantum operations with classical processing. Despite the common practice of this approach, rigorous criteria to determine whether a given quantum operation is replaceable classically are still missing. In this work, we define the classically replaceable operations in four general scenarios. In each scenario, we provide their necessary and sufficient criteria and point out the corresponding classical processing. For a practically favorable case of unitary classically replaceable operations, we show that the replaced classical processing is deterministic. Beyond that, we regard the irreplaceability of quantum operations by classical processing as a quantum resource and relate it to the performance of a channel in a non-local game, as manifested in a robustness measure.

Ground-State Preparation and Energy Estimation on Early Fault-Tolerant Quantum Computers via Quantum Eigenvalue Transformation of Unitary Matrices

Under suitable assumptions, the algorithms in [Lin, Tong, Quantum 2020] can estimate the ground state energy and prepare the ground state of a quantum Hamiltonian with near-optimal query complexities. However, this is based on a block encoding input model of the Hamiltonian, whose implementation is known to require a large resource overhead. We develop a tool called quantum eigenvalue transformation of unitary matrices with real polynomials (QET-U), which uses a controlled Hamiltonian evolution as the input model, a single ancilla qubit and no multi-qubit control operations, and is thus suitable for early fault-tolerant quantum devices. This leads to a simple quantum algorithm that outperforms all previous algorithms with a comparable circuit structure for estimating the ground state energy. For a class of quantum spin Hamiltonians, we propose a new method that exploits certain anti-commutation relations and further removes the need of implementing the controlled Hamiltonian evolution. Coupled with Trotter based approximation of the Hamiltonian evolution, the resulting algorithm can be very suitable for early fault-tolerant quantum devices. We demonstrate the performance of the algorithm using IBM Qiskit for the transverse field Ising model. If we are further allowed to use multi-qubit Toffoli gates, we can then implement amplitude amplification and a new binary amplitude estimation algorithm, which increases the circuit depth but decreases the total query complexity. The resulting algorithm saturates the near-optimal complexity for ground state preparation and energy estimating using a constant number of ancilla qubits (no more than 3).

Nuclear spin polarization and control in hexagonal boron nitride

Electron spins in van der Waals materials are playing a crucial role in recent advances in condensed-matter physics and spintronics. However, nuclear spins in van der Waals materials remain an unexplored quantum resource. Here we report optical polarization and coherent control of nuclear spins in a van der Waals material at room temperature. We use negatively charged boron vacancy ([Formula: see text]) spin defects in hexagonal boron nitride to polarize nearby nitrogen nuclear spins. We observe the Rabi frequency of nuclear spins at the excited-state level anti-crossing of [Formula: see text] defects to be 350 times larger than that of an isolated nucleus, and demonstrate fast coherent control of nuclear spins. Further, we detect strong electron-mediated nuclear-nuclear spin coupling that is five orders of magnitude larger than the direct nuclear-spin dipolar coupling, enabling multi-qubit operations. Our work opens new avenues for the manipulation of nuclear spins in van der Waals materials for quantum information science and technology.

Superconducting circuit architecture for digital-analog quantum computing

We propose a superconducting circuit architecture suitable for digital-analog quantum computing (DAQC) based on an enhanced NISQ family of nearest-neighbor interactions. DAQC makes a smart use of digital steps (single qubit rotations) and analog blocks (parametrized multiqubit operations) to outperform digital quantum computing algorithms. Our design comprises a chain of superconducting charge qubits coupled by superconducting quantum interference devices (SQUIDs). Using magnetic flux control, we can activate/deactivate exchange interactions, double excitation/de-excitations, and others. As a paradigmatic example, we present an efficient simulation of an ell times h fermion lattice (with 2<ell leq h), using only 2(2ell +1)^{2}+24 analog blocks. The proposed architecture design is feasible in current experimental setups for quantum computing with superconducting circuits, opening the door to useful quantum advantage with fewer resources.

Fault-Tolerant Parity Readout on a Shuttling-Based Trapped-Ion Quantum Computer

Quantum error correction requires the detection of errors by reliable measurements of suitable multi-qubit correlation operators. Here, we experimentally demonstrate a fault-tolerant weight-4 parity check measurement scheme. An additional 'flag' qubit serves to detect errors occurring throughout the parity measurement, which would otherwise proliferate into uncorrectable weight-2 errors on the qubit register. We achieve a flag-conditioned parity measurement single-shot fidelity of 93.2(2)\%. Deliberately injecting bit and phase-flip errors, we show that the fault-tolerant protocol is capable of reliably intercepting such faults. For holistic benchmarking of the parity measurement scheme, we use entanglement witnessing to show that the implemented circuit generates genuine six-qubit multi-partite entanglement. The fault-tolerant parity measurement scheme is an essential building block in a broad class of stabilizer quantum error correction protocols, including topological color codes. Our hardware platform is based on atomic ions stored in a segmented microchip ion trap. The qubit register is dynamically reconfigured via shuttling operations, enabling effective full connectivity without operational cross-talk, which provides key capabilities for scalable fault-tolerant quantum computing.

Feasibility study of quantum computing using trapped electrons

We investigate the feasibility of using electrons in a linear Paul trap as qubits in a future quantum computer. We discuss the necessary experimental steps to realize such a device through a concrete design proposal, including trapping, cooling, electronic detection, spin readout, and single- and multiqubit gate operations. Numeric simulations indicate that two-qubit Bell-state fidelities of order 99.99% can be achieved assuming reasonable experimental parameters.

Single shot i-Toffoli gate in dispersively coupled superconducting qubits

Quantum algorithms often benefit from the ability to execute multi-qubit (&amp;gt;2) gates. To date, such multi-qubit gates are typically decomposed into single- and two-qubit gates, particularly in superconducting qubit architectures. The ability to perform multi-qubit operations in a single step could vastly improve the fidelity and execution time of many algorithms. Here, we propose a single shot method for executing an i-Toffoli gate, a three-qubit gate with two control and one target qubit, using currently existing superconducting hardware. We show numerical evidence for a process fidelity over 99.5% and a gate time of 450 ns for superconducting qubits interacting via tunable couplers. Our method can straight forwardly be extended to implement gates with more than two control qubits at similar fidelities.