Quantum Computational Supremacy Research Articles

A reference architecture for quantum computing as a service

Quantum computers (QCs) aim to disrupt the status-quo of computing – replacing traditional systems and platforms that are driven by digital circuits and modular software – with hardware and software that operate on the principle of quantum mechanics. QCs that rely on quantum mechanics can exploit quantum circuits (i.e., quantum bits for manipulating quantum gates) to achieve ‘quantum computational supremacy’ over traditional, i.e., digital computing systems. Currently, the issues that impede mass-scale adoption of quantum systems are rooted in the fact that building, maintaining, and/or programming QCs is a complex and radically distinct engineering paradigm when compared to the challenges of classical computing and software engineering. Quantum service orientation is seen as a solution that synergises the research on service computing and quantum software engineering (QSE) to allow developers and users to build and utilise quantum software services based on pay-per-shot utility computing model. The pay-per-shot model represents a single execution of instruction on quantum processing unit and it allows vendors (e.g., Amazon Braket) to offer their QC platforms, simulators, and software services to end-users. This research contributes by (i) developing a reference architecture for enabling Quantum Computing as a Service (QCaaS), (ii) implementing microservices with the quantum-classic split pattern as an architectural use-case, and (iii) evaluating the architecture based on practitioners’ feedback. The proposed reference architecture follows a layered software pattern to support the three phases of service lifecycle namely development, deployment, and split of quantum software services. In the QSE context, the research focuses on unifying architectural methods and service-orientation patterns to promote reuse knowledge and best practices to tackle emerging and futuristic challenges of architecting QCaaS.

Scattershot multiboson correlation sampling with random photonic inner-mode multiplexing

Multiphoton interference is an essential phenomenon at the very heart not only of fundamental quantum optics and applications in quantum information processing and sensing but also of demonstrations of quantum computational supremacy in boson sampling experiments relying only on linear optical interferometers. However, scalable boson sampling experiments with either photon number states or squeezed states are challenged by the need to generate a large number of photons with fixed temporal and frequency spectra from one experimental run to another. Unfortunately, even the well-established standard multiplexing techniques employed to generate photons with fixed spectral properties are affected by the detrimental effects of losses, spectral distorsions and reduction in purity. Here, we employ sampling correlation measurements in the photonic inner modes, time and frequency, at the interferometer input and output to ensure the occurrence of multiphoton interference even with pure states of input photons with random spectral overlap from one sample to another. Indeed, by introducing a random multiplexing technique where photons are generated with random inner-mode parameters, it is possible to substantially enhance the probability to successfully generate samples and overcome the typical drawbacks in standard multiplexing. We also demonstrate the classical hardness of the resulting problem of scattershot multiboson correlation sampling based on this technique. Therefore, these results not only shed new light in the computational complexity of multiboson interference but also allow us to enhance the experimental scalability of boson sampling schemes. Furthermore, this research provides a new exciting route toward future demonstrations of quantum computational supremacy with scalable experimental resources as well as future applications in quantum information processing and sensing beyond boson sampling.

How do we quantify the utility of quantum algorithms?

Quantum computing advantage emerges not from brute force power, but from subtle differences in information processing that can occur for key bottleneck subroutines. In 2019, the Google Quantum AI team performed a landmark experiment demonstrating quantum computational supremacy (Arute et al., 2019) where they performed a quantum computation that, at the time, could not be done on a classical supercomputer. This was remarkable because it was achieved by a processor with only 53 qubits, an observation that emerged from theoretical work which identified that quantum computers could have a massive advantage for certain specially designed benchmarking tasks (Boixo et al., 2018; Bremner et al., 2016).

Efficient verification of Boson Sampling

The demonstration of quantum speedup, also known as quantum computational supremacy, that is the ability of quantum computers to outperform dramatically their classical counterparts, is an important milestone in the field of quantum computing. While quantum speedup experiments are gradually escaping the regime of classical simulation, they still lack efficient verification protocols and rely on partial validation. Here we derive an efficient protocol for verifying with single-mode Gaussian measurements the output states of a large class of continuous-variable quantum circuits demonstrating quantum speedup, including Boson Sampling experiments, thus enabling a convincing demonstration of quantum speedup with photonic computing. Beyond the quantum speedup milestone, our results also enable the efficient and reliable certification of a large class of intractable continuous-variable multimode quantum states.

Boson sampling with random numbers of photons

Multiphoton interference is at the very heart of quantum foundations and applications in quantum sensing and information processing. In particular, boson-sampling experiments have the potential to demonstrate quantum computational supremacy while relying on only multiphoton interference in linear optical interferometers. However, even when photonic losses are negligible, scalable experiments are challenged by the rapid decrease of the probability of the success of current schemes with probabilistic sources for a large number of single photons in each experimental sample. Remarkably, we show a boson sampling scheme in which the probability of success increases instead of decreasing with the number of input photons, eventually approaching a unit value even with nondeterministic sources. It is achieved by sampling measurements not only at the interferometer output but also over all the possible numbers of photons at each input port and, different from scattershot boson sampling, allowing a random number of occupied input ports from one experimental run to another. Therefore, these results provide an exciting route toward future demonstrations of quantum computational supremacy with scalable experimental resources.

Quantum Computers - An Emerging Cybersecurity Threat

Quantum computational supremacy may potentially endanger the current cryptographic protection methods. Although quantum computers are still far from a practical implementation in information processing and storage, they should not be overlooked in the context of cybersecurity. Quantum computers operate with qubits - units of information that are governed by the fundamental principles of quantum physics, such as quantum superposition of states and quantum coherence. In order to address the new challenge that quantum computers pose to cybersecurity, the very principles of their operation have to be understood and are overviewed in this contribution.

How many qubits are needed for quantum computational supremacy?

Quantum computational supremacy arguments, which describe a way for a quantum computer to perform a task that cannot also be done by a classical computer, typically require some sort of computational assumption related to the limitations of classical computation. One common assumption is that the polynomial hierarchy (PH) does not collapse, a stronger version of the statement thatP≠NP, which leads to the conclusion that any classical simulation of certain families of quantum circuits requires time scaling worse than any polynomial in the size of the circuits. However, the asymptotic nature of this conclusion prevents us from calculating exactly how many qubits these quantum circuits must have for their classical simulation to be intractable on modern classical supercomputers. We refine these quantum computational supremacy arguments and perform such a calculation by imposing fine-grained versions of the non-collapse conjecture. Our first two conjectures poly3-NSETH(a) and per-int-NSETH(b) take specific classical counting problems related to the number of zeros of a degree-3 polynomial innvariables overF2or the permanent of ann×ninteger-valued matrix, and assert that any non-deterministic algorithm that solves them requires2cntime steps, wherec∈{a,b}. A third conjecture poly3-ave-SBSETH(a′) asserts a similar statement about average-case algorithms living in the exponential-time version of the complexity classSBP. We analyze evidence for these conjectures and argue that they are plausible whena=1/2,b=0.999anda′=1/2.Imposing poly3-NSETH(1/2) and per-int-NSETH(0.999), and assuming that the runtime of a hypothetical quantum circuit simulation algorithm would scale linearly with the number of gates/constraints/optical elements, we conclude that Instantaneous Quantum Polynomial-Time (IQP) circuits with 208 qubits and 500 gates, Quantum Approximate Optimization Algorithm (QAOA) circuits with 420 qubits and 500 constraints and boson sampling circuits (i.e. linear optical networks) with 98 photons and 500 optical elements are large enough for the task of producing samples from their output distributions up to constant multiplicative error to be intractable on current technology. Imposing poly3-ave-SBSETH(1/2), we additionally rule out simulations with constant additive error for IQP and QAOA circuits of the same size. Without the assumption of linearly increasing simulation time, we can make analogous statements for circuits with slightly fewer qubits but requiring104to107gates.

The Road to Quantum Computational Supremacy

The main purpose of this paper is to examine some (potential) applications of quantum computation in AI and to review the interplay between quantum theory and AI. For the readers who are not familiar with quantum computation, a brief introduction to it is provided, and a famous but simple quantum algorithm is introduced so that they can appreciate the power of quantum computation. Also, a (quite personal) survey of quantum computation is presented in order to give the readers a (unbalanced) panorama of the field. The author hopes that this paper will be a useful map for AI researchers who are going to explore further and deeper connections between AI and quantum computation as well as quantum theory although some parts of the map are very rough and other parts are empty, and waiting for the readers to fill in.

Regimes of Classical Simulability for Noisy Gaussian Boson Sampling.

As a promising candidate for exhibiting quantum computational supremacy, Gaussian boson sampling (GBS) is designed to exploit the ease of experimental preparation of Gaussian states. However, sufficiently large and inevitable experimental noise might render GBS classically simulable. In this work, we formalize this intuition by establishing a sufficient condition for approximate polynomial-time classical simulation of noisy GBS-in the form of an inequality between the input squeezing parameter, the overall transmission rate, and the quality of photon detectors. Our result serves as a nonclassicality test that must be passed by any quantum computational supremacy demonstration based on GBS. We show that, for most linear-optical architectures, where photon loss increases exponentially with the circuit depth, noisy GBS loses its quantum advantage in the asymptotic limit. Our results thus delineate intermediate-sized regimes where GBS devices might considerably outperform classical computers for modest noise levels. Finally, we find that increasing the amount of input squeezing is helpful to evade our classical simulation algorithm, which suggests a potential route to mitigate photon loss.

Speedup in classical simulation of Gaussian boson sampling

Gaussian boson sampling is an alternative model for demonstrating quantum computational supremacy, where squeezed states are injected into every input mode, instead of applying single photons as in the case of standard boson sampling. Here by analyzing numerically the computational costs, we establish a lower bound for achieving quantum computational supremacy for a class of Gaussian boson-sampling problems. Specifically, we propose a more efficient method for calculating the transition probabilities, leading to a significant reduction of the simulation costs. Particularly, our numerical results indicate that one can simulate up to 18 photons for Gaussian boson sampling at the output subspace on a normal laptop, 20 photons on a commercial workstation with 256 cores, and about 30 photons for supercomputers. These numbers are significantly smaller than those in standard boson sampling, suggesting that Gaussian boson sampling could be experimentally-friendly for demonstrating quantum computational supremacy.

What the Quantum Computational Supremacy Experiment on a Quantum Computer Demonstrated

What the Quantum Computational Supremacy Experiment on a Quantum Computer Demonstrated

On the Classical Hardness of Spoofing Linear Cross-Entropy Benchmarking.

Recently, Google announced the first demonstration of quantum computational supremacy with a programmable superconducting processor. Their demonstration is based on collecting samples from the output distribution of a noisy random quantum circuit, then applying a statistical test to those samples called Linear Cross-Entropy Benchmarking (Linear XEB). This raises a theoretical question: How hard is it for a classical computer to spoof the results of the Linear XEB test? In this short note, we adapt an analysis of Aaronson and Chen to prove a conditional hardness result for Linear XEB spoofing. Specifically, we show that the problem is classically hard, assuming that there is no efficient classical algorithm that, given a random $n$-qubit quantum circuit $C$, estimates the probability of $C$ outputting a specific output string, say $0^n$, with mean squared error even slightly better than that of the trivial estimator that always estimates $1/2^n$. Our result automatically encompasses the case of noisy circuits.

Classically simulating near-term partially-distinguishable and lossy boson sampling

Boson sampling is the problem of sampling from the same distribution as indistinguishable single photons at the output of a linear optical interferometer. It is an example of a non-universal quantum computation which is believed to be feasible in the near term and cannot be simulated on a classical machine. Like all purported demonstrations of ‘quantum computational supremacy’, this motivates optimising classical simulation schemes for a realistic model of the problem, in this case boson sampling when the implementations experience lost or distinguishable photons. Although current simulation schemes for sufficiently imperfect boson sampling are classically efficient, in principle the polynomial runtime can be infeasibly large. In this work, we develop a scheme for classical simulation of boson sampling under uniform distinguishability and loss, based on the idea of sampling from distributions where at most k photons are indistinguishable. We show that asymptotically this scheme can provide a polynomial improvement in the runtime compared to classically simulating idealised boson sampling. More significantly, we show that in the regime considered experimentally relevant, our approach gives an substantial improvement in runtime over other classical simulation approaches.

Fine-grained quantum computational supremacy

(pp1089-1115) Tomoyuki Morimae and Suguru Tamaki doi: https://doi.org/10.26421/QIC19.13-14-2 Abstracts: Output probability distributions of several sub-universal quantum computing models cannot be classically efficiently sampled unless some unlikely consequences occur in classical complexity theory, such as the collapse of the polynomial-time hierarchy. These results, so called quantum supremacy, however, do not rule out possibilities of super-polynomial-time classical simulations. In this paper, we study ``fine-grained" version of quantum supremacy that excludes some exponential-time classical simulations. First, we focus on two sub-universal models, namely, the one-clean-qubit model (or the DQC1 model) and the HC1Q model. Assuming certain conjectures in fine-grained complexity theory, we show that for any a>0 output probability distributions of these models cannot be classically sampled within a constant multiplicative error and in 2^{(1-a)N+o(N)} time, where N is the number of qubits. Next, we consider universal quantum computing. For example, we consider quantum computing over Clifford and T gates, and show that under another fine-grained complexity conjecture, output probability distributions of Clifford-T quantum computing cannot be classically sampled in 2^{o(t)} time within a constant multiplicative error, where t is the number of T gates.

Quantum computational supremacy in the sampling of bosonic random walkers on a one-dimensional lattice

We study the sampling complexity of a probability distribution associated with an ensemble of identical noninteracting bosons undergoing a quantum random walk on a one-dimensional lattice. With uniform nearest-neighbor hopping we show that one can efficiently sample the distribution for times logarithmic in the size of the system, while for longer times there is no known efficient sampling algorithm. With time-dependent hopping and optimal control, we design the time evolution to approximate an arbitrary Haar-random unitary map analogous to that designed for photons in a linear optical network. This approach highlights a route to generating quantum complexity by optimal control only of a single-body unitary matrix. We study this in the context of two potential experimental realizations: a spinor optical lattice of ultracold atoms and a quantum gas microscope.

Classical simulation of photonic linear optics with lost particles

We explore the possibility of efficient classical simulation of linear optics experiments under the effect of particle losses. Specifically, we investigate the canonical boson sampling scenario in which an n-particle Fock input state propagates through a linear-optical network and is subsequently measured by particle-number detectors in the m output modes. We examine two models of losses. In the first model a fixed number of particles is lost. We prove that in this scenario the output statistics can be well approximated by an efficient classical simulation, provided that the number of photons that is left grows slower than . In the second loss model, every time a photon passes through a beamsplitter in the network, it has some probability of being lost. For this model the relevant parameter is s, the smallest number of beamsplitters that any photon traverses as it propagates through the network. We prove that it is possible to approximately simulate the output statistics already if s grows logarithmically with m, regardless of the geometry of the network. The latter result is obtained by proving that it is always possible to commute s layers of uniform losses to the input of the network regardless of its geometry, which could be a result of independent interest. We believe that our findings put strong limitations on future experimental realizations of quantum computational supremacy proposals based on boson sampling.

Dynamical Phase Transitions in Sampling Complexity.

We make the case for studying the complexity of approximately simulating (sampling) quantum systems for reasons beyond that of quantum computational supremacy, such as diagnosing phase transitions. We consider the sampling complexity as a function of time t due to evolution generated by spatially local quadratic bosonic Hamiltonians. We obtain an upper bound on the scaling of t with the number of bosons n for which approximate sampling is classically efficient. We also obtain a lower bound on the scaling of t with n for which any instance of the boson sampling problem reduces to this problem and hence implies that the problem is hard, assuming the conjectures of Aaronson and Arkhipov [Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing (ACM Press, New York, New York, USA, 2011), p.333]. This establishes a dynamical phase transition in sampling complexity. Further, we show that systems in the Anderson-localized phase are always easy to sample from at arbitrarily long times. We view these results in light of classifying phases of physical systems based on parameters in the Hamiltonian. Indoing so, we combine ideas from mathematical physics and computational complexity to gain insight into the behavior of condensed matter, atomic, molecular, and optical systems.

Verification of Many-Qubit States

Verification is a task to check whether a given quantum state is close to an ideal state or not. In this paper, we show that a variety of many-qubit quantum states can be verified with only sequential single-qubit measurements of Pauli operators. First, we introduce a protocol for verifying ground states of Hamiltonians. We next explain how to verify quantum states generated by a certain class of quantum circuits. We finally propose an adaptive test of stabilizers that enables the verification of all polynomial-time-generated hypergraph states, which include output states of the Bremner-Montanaro-Shepherd-type instantaneous quantum polynomial time (IQP) circuits. Importantly, we do not make any assumption that the identically and independently distributed copies of the same states are given: Our protocols work even if some highly complicated entanglement is created among copies in any artificial way. As applications, we consider the verification of the quantum computational supremacy demonstration with IQP models, and verifiable blind quantum computing.

Anticoncentration theorems for schemes showing a quantum speedup

One of the main milestones in quantum information science is to realise quantum devices that exhibit an exponential computational advantage over classical ones without being universal quantum computers, a state of affairs dubbed quantum speedup, or sometimes "quantum computational supremacy". The known schemes heavily rely on mathematical assumptions that are plausible but unproven, prominently results on anticoncentration of random prescriptions. In this work, we aim at closing the gap by proving two anticoncentration theorems and accompanying hardness results, one for circuit-based schemes, the other for quantum quench-type schemes for quantum simulations. Compared to the few other known such results, these results give rise to a number of comparably simple, physically meaningful and resource-economical schemes showing a quantum speedup in one and two spatial dimensions. At the heart of the analysis are tools of unitary designs and random circuits that allow us to conclude that universal random circuits anticoncentrate as well as an embedding of known circuit-based schemes in a 2D translation-invariant architecture.

Architectures for Quantum Simulation Showing a Quantum Speedup

One of the main aims in the field of quantum simulation is to achieve a quantum speedup, often referred to as "quantum computational supremacy", referring to the experimental realization of a quantum device that computationally outperforms classical computers. In this work, we show that one can devise versatile and feasible schemes of two-dimensional dynamical quantum simulators showing such a quantum speedup, building on intermediate problems involving non-adaptive measurement-based quantum computation. In each of the schemes, an initial product state is prepared, potentially involving an element of randomness as in disordered models, followed by a short-time evolution under a basic translationally invariant Hamiltonian with simple nearest-neighbor interactions and a mere sampling measurement in a fixed basis. The correctness of the final state preparation in each scheme is fully efficiently certifiable. We discuss experimental necessities and possible physical architectures, inspired by platforms of cold atoms in optical lattices and a number of others, as well as specific assumptions that enter the complexity-theoretic arguments. This work shows that benchmark settings exhibiting a quantum speedup may require little control in contrast to universal quantum computing. Thus, our proposal puts a convincing experimental demonstration of a quantum speedup within reach in the near term.