Loading data in a quantum device is required in several quantum computing applications. Without an efficient loading procedure, the cost to initialize the algorithms can dominate the overall computational cost. A circuit-based quantum random access memory named FF-QRAM can load M n-bit patterns with computational cost O(CMn) to load continuous data where C depends on the data distribution. In this work, we propose a strategy to load continuous data without post-selection with computational cost O(Mn). The proposed method is based on the probabilistic quantum memory, a strategy to load binary data in quantum devices, and the FF-QRAM using standard quantum gates, and is suitable for noisy intermediate-scale quantum computers.
Classical simulation of quantum circuits is crucial for evaluating and validating the design of new quantum algorithms. However, the number of quantum state amplitudes increases exponentially with the number of qubits, leading to the exponential growth of the memory requirement for the simulations. In this paper, we present a new data reduction technique to reduce the memory requirement of quantum circuit simulations. We apply our amplitude-aware lossy compression technique to the quantum state amplitude vector to trade the computation time and fidelity for memory space. The experimental resul…
In order to evaluate, validate, and refine the design of new quantum algorithms or quantum computers, researchers and developers need methods to assess their correctness and fidelity. This requires the capabilities of quantum circuit simulations. However, the number of quantum state amplitudes increases exponentially with the number of qubits, leading to the exponential growth of the memory requirement for the simulations. In this work, we present our memory-efficient quantum circuit simulation by using lossy data compression. Our empirical data shows that we reduce the memory requirement to 1…
In this paper, we will introduce the quantum circuit simulator we developed in C++ environment. We devise a novel method for efficient memory handling using linked list structures that enables us to simulate a quantum circuit of up to 20 qubits in a reasonable time. Our package can simulate the activity of any quantum circuit constructed by the user; it will also be used to understand the robustness of certain quantum algorithms such as Simons and Shors.
Memory effects are ubiquitous in nature and the class of memory circuit elements - which includes memristors, memcapacitors and meminductors - shows great potential to understand and simulate the associated fundamental physical processes. Here, we show that such elements can also be used in electronic schemes mimicking biologically-inspired computer architectures, performing digital logic and arithmetic operations, and can expand the capabilities of certain quantum computation schemes. In particular, we will discuss few examples where the concept of memory elements is relevant to the realizati…
Quantum supremacy in many applications using well-known quantum algorithms rely on availability of data in quantum format. Quantum Random Access Memory (QRAM), an equivalent of classical Random Access Memory (RAM), fulfills this requirement. However, the existing QRAM proposals either require qutrit technology and/or incur access challenges. We propose an approximate Parametric Quantum Circuit (PQC) based QRAM which takes address lines as input and gives out the corresponding data in these address lines as the output. We present two applications of the proposed PQC-based QRAM namely, storage o…
A quantum shift register circuit acts on a set of input qubits and memory qubits, outputs a set of output qubits and updated memory qubits, and feeds the memory back into the device for the next cycle (similar to the operation of a classical shift register). Such a device finds application as an encoding and decoding circuit for a particular type of quantum error-correcting code, called a quantum convolutional code. Building on the Ollivier-Tillich and Grassl-Roetteler encoding algorithms for quantum convolutional codes, I present a method to determine a quantum shift register encoding circuit…
Most research in quantum computing today is performed against simulations of quantum computers rather than true quantum computers. Simulating a quantum computer entails implementing all of the unitary operators corresponding to the quantum gates as tensors. For high numbers of qubits, performing tensor multiplications for these simulations becomes quite expensive, since $N$-qubit gates correspond to $2^{N}$-dimensional tensors. One way to accelerate such a simulation is to use field programmable gate array (FPGA) hardware to efficiently compute the matrix multiplications. Though FPGAs can effi…
We propose how to realize high-fidelity quantum storage using a hybrid quantum architecture including two coupled flux qubits and a nitrogen-vacancy center ensemble (NVE). One of the flux qubits is considered as the quantum computing processor and the NVE serves as the quantum memory. By separating the computing and memory units, the influence of the quantum computing process on the quantum memory can be effectively eliminated, and hence the quantum storage of an arbitrary quantum state of the computing qubit could be achieved with high fidelity. Furthermore the present proposal is robust with…
We present a theoretical proposal for a microwave driven circuit composed of superconducting resonators and qubits which shows a bistable behaviour, and we present a simple mechanism that allows single- or few-photon microwave pulses to work as Set- and Reset-signals that switch the circuit between its stable modes. The resulting system constitutes an ultra-low-energy Set-Reset flip-flop, and we show that its memory lifetime far exceeds the lifetime of states stored in any of its separate components.
Emerging quantum algorithms that process data require that classical input data be represented as a quantum state. These data-processing algorithms often follow the gate model of quantum computing--which requires qubits to be initialized to a basis state, typically $\lvert 0 \rangle$--and thus often employ state generation circuits to transform the initialized basis state to a data-representation state. There are many ways to encode classical data in a qubit, and the oft-applied approach of basis encoding does not allow optimization to the extent that other variants do. In this work, we thus c…
We investigate a hybrid quantum circuit where ensembles of cold polar molecules serve as long-lived quantum memories and optical interfaces for solid state quantum processors. The quantum memory realized by collective spin states (ensemble qubit) is coupled to a high-Q stripline cavity via microwave Raman processes. We show that for convenient trap-surface distances of a few $μ$m, strong coupling between the cavity and ensemble qubit can be achieved. We discuss basic quantum information protocols, including a swap from the cavity photon bus to the molecular quantum memory, and a deterministic …
Quantum computing is a rapidly expanding field with applications ranging from optimization all the way to complex machine learning tasks. Quantum memories, while lacking in practical quantum computers, have the potential to bring quantum advantage. In quantum machine learning applications for example, a quantum memory can simplify the data loading process and potentially accelerate the learning task. Quantum memory can also store intermediate quantum state of qubits that can be reused for computation. However, the depth, gate count and compilation time of quantum memories such as, Quantum Read…
A prerequisite for many quantum information processing tasks to truly surpass classical approaches is an efficient procedure to encode classical data in quantum superposition states. In this work, we present a circuit-based flip-flop quantum random access memory to construct a quantum database of classical information in a systematic and flexible way. For registering or updating classical data consisting of $M$ entries, each represented by $n$ bits, the method requires $O(n)$ qubits and $O(Mn)$ steps. With post-selection at an additional cost, our method can also store continuous data as proba…
We observe how an active (i.e., requring $2^n$ parallel control operations) QRAM-like effect $$\sum_{y=0}^{N-1} |y\rangle\langle y| \otimes U^y_{\text{result},\text{memory}_y}$$ can be realized, as a quantum circuit of depth $O(n+\sqrt m)$ (where $m$ is the size of the result register) plus the maximum over all~$z$ of the circuit depths of controlled-$U^z$ operations.
In this paper a storage method and a context-aware circuit simulation idea are presented for the sum of block diagonal matrices. Using the design technique for a generalized circuit for the Hamiltonian dynamics through the truncated series, we generalize the idea to (0-1) matrices and discuss the generalization for the real matrices. The presented circuit requires $O(n)$ number of quantum gates and yields the correct output with the success probability depending on the number of elements: for matrices with $poly(n)$, the success probability is $1/poly(n)$. Since the operations on the circuit a…
In this paper we describe, implement, and test the performance of distributed memory simulations of quantum circuits on the MSU Laconia Top500 supercomputer. Using OpenMP and MPI hybrid parallelization, we first use a distributed matrix-vector multiplication with one-dimensional partitioning and discuss the shortcomings of this method due to the exponential memory requirements in simulating quantum computers. We then describe a more efficient method that stores only the $2^n$ amplitudes of the $n$ qubit state vector $|ψ\rangle$ and optimize its single node performance. In our multi-node implem…
Random access memory is an indispensable device for classical information technology. Analog to this, for quantum information technology, it is desirable to have a random access quantum memory with many memory cells and programmable access to each cell. We report an experiment that realizes a random access quantum memory of 105 qubits carried by 210 memory cells in a macroscopic atomic ensemble. We demonstrate storage of optical qubits into these memory cells and their read-out at programmable times by arbitrary orders with fidelities exceeding any classical bound. Experimental realization of …
Quantum circuit simulations are critical for evaluating quantum algorithms and machines. However, the number of state amplitudes required for full simulation increases exponentially with the number of qubits. In this study, we leverage data compression to reduce memory requirements, trading computation time and fidelity for memory space. Specifically, we develop a hybrid solution by combining the lossless compression and our tailored lossy compression method with adaptive error bounds at each timestep of the simulation. Our approach optimizes for compression speed and makes sure that errors du…
To realize long-distance quantum communication and quantum network, it is required to have multiplexed quantum memory with many memory cells. Each memory cell needs to be individually addressable and independently accessible. Here we report an experiment that realizes a multiplexed DLCZ-type quantum memory with 225 individually accessible memory cells in a macroscopic atomic ensemble. As a key element for quantum repeaters, we demonstrate that entanglement with flying optical qubits can be stored into any neighboring memory cells and read out after a programmable time with high fidelity. Exper…
Significant advances in coherence have made superconducting quantum circuits a viable platform for fault-tolerant quantum computing. To further extend capabilities, highly coherent quantum systems could act as quantum memories for these circuits. A useful quantum memory must be rapidly addressable by qubits, while maintaining superior coherence. We demonstrate a novel superconducting microwave cavity architecture that is highly robust against major sources of loss that are encountered in the engineering of circuit QED systems. The architecture allows for near-millisecond storage of quantum sta…
Compared to quantum logic gates, quantum memory has received far less attention. Here, we explore the prognosis for a solid-state, scalable quantum dynamic random access memory (Q-DRAM), where the qubits are encoded by the spin orientations of single quantons in exchange-decoupled quantum dots. We address, in particular, various possibilities for implementing refresh cycles.
A random access memory (RAM) uses n bits to randomly address N=2^n distinct memory cells. A quantum random access memory (qRAM) uses n qubits to address any quantum superposition of N memory cells. We present an architecture that exponentially reduces the requirements for a memory call: O(log N) switches need be thrown instead of the N used in conventional (classical or quantum) RAM designs. This yields a more robust qRAM algorithm, as it in general requires entanglement among exponentially less gates, and leads to an exponential decrease in the power needed for addressing. A quantum optical i…
Circuit-based characterization of finite-temperature quantum phases and self-correcting quantum memory
Kavli Institute for Theoretical Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校卡弗里理论物理研究所）；Department of Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校物理系）；Kadanoff Center for Theoretical Physics & Enrico Fermi Institute, The University of Chicago（芝加哥大学卡达诺夫理论物理中心与恩里科·费米研究所）；Department of Physics, Stanford University（斯坦福大学物理系）
Many physical implementations of quantum computers impose stringent memory constraints in which 2-qubit operations can only be performed between qubits which are nearest neighbours in a lattice or graph structure. Hence, before a computation can be run on such a device, it must be mapped onto the physical architecture. That is, logical qubits must be assigned physical locations in the quantum memory, and the circuit must be replaced by an equivalent one containing only operations between nearest neighbours. In this paper, we give a new technique for quantum circuit mapping (a.k.a. routing), ba…
A "bucket brigade" architecture for a quantum random memory of $N=2^n$ memory cells needs $n(n+5)/2$ times of quantum manipulation on control circuit nodes per memory call. Here we propose a scheme, in which only average $n/2$ times manipulation is required to accomplish a memory call. This scheme may significantly decrease the time spent on a memory call and the average overall error rate per memory call. A physical implementation scheme for storing an arbitrary state in a selected memory cell followed by reading it out is discussed.
A novel concept of quantum random access memory (qRAM) employing a quantum walk is provided. Our qRAM relies on a bucket brigade scheme to access the memory cells. Introducing a bucket with chirality left and right as a quantum walker, and considering its quantum motion on a full binary tree, we can efficiently deliver the bucket to the designated memory cells, and fill the bucket with the desired information in the form of quantum superposition states. Our procedure has several advantages. First, we do not need to place any quantum devices at the nodes of the binary tree, and hence in our qRA…
We examine two proposals for marginally self-correcting quantum memory, the cubic code by Haah and the welded code by Michnicki. In particular, we prove explicitly that they are absent of topological order above zero temperature, as their Gibbs ensembles can be prepared via a short-depth quantum circuit from classical ensembles. Our proof technique naturally gives rise to the notion of free energy associated with excitations. Further, we develop a framework for an ergodic decomposition of Davies generators in CSS codes which enables formal reduction to simpler classical memory problems. We the…
