Noise classification via the output of random quantum circuits

Abstract

A method for characterizing noise in a quantum system, the quantum system comprising a plurality of qubits and a plurality of entangled gates native to the quantum system, the method comprising generating a random quantum circuit on a quantum processor, the random quantum circuit comprising the plurality of entangled gates native to the quantum system. The method comprises running a simulation of the random quantum circuit multiple times on a classical computer to obtain an ideal result, and running the random quantum circuit multiple times on the quantum processor to obtain an experimental result. The method comprises grouping the experimental results based on the probability of the ideal result to obtain a first distribution, and grouping the experimental results based on the probability of the experimental results to obtain a second distribution. The method comprises characterizing the noise in the quantum system based on the first distribution and the second distribution.

Description

Technical Field

[0001] The presently claimed embodiments of the invention relate to systems and methods for noise classification, and more particularly to using random quantum circuits for noise classification. Background Art

[0002] Physical systems for quantum information processing are usually subjected to noise processes, which may affect their output in an undesirable manner. These noise processes have various origins, but can be roughly divided into two families: incoherent noise and coherent noise. Incoherent noise often arises from random processes and Markov (Markovian) processes (the probability of arriving at any future state depends only on the process of the current state). Incoherent noise is irreversible and memoryless. On the other hand, coherent noise can be corrected and is usually caused by the imperfect realization of the unitary operation required for quantum information processing. Coherent noise is repeatable and can be considered as over-rotation or under-rotation, originating from miscalibration or crosstalk.

[0003] Distinguishing between these two types of noise may be crucial for some quantum computing tasks. In the past, some methods have been developed that can classify noise, but they always lack scalability beyond just a few qubits. Scalable methods for characterizing quantum systems cannot distinguish between the noise types and therefore cannot be used to identify and mitigate coherent noise sources. Summary of the invention

[0004] According to an embodiment of the present invention, a method for characterizing noise in a quantum system includes a plurality of qubits and a plurality of entangled gates native to the quantum system, the method including generating a random quantum circuit on a quantum processor, the random quantum circuit including the plurality of entangled gates native to the quantum system. The method includes running a simulation of the random quantum circuit multiple times on a classical computer to obtain a corresponding plurality of ideal results, and running the random quantum circuit multiple times on the quantum processor to obtain a corresponding plurality of experimental results. The method includes grouping the plurality of experimental results based on the probability of the ideal results to obtain a first distribution, and grouping the plurality of experimental results based on the probability of the experimental results to obtain a second distribution. The method includes characterizing the noise in the quantum system based on the first distribution and the second distribution.

[0005] According to an embodiment of the present invention, a system for characterizing noise in a quantum system includes: a quantum processor including a plurality of qubits; a random quantum circuit including a plurality of entangled gates native to the quantum system; and a classical processor. The classical processor is configured to run a simulation of the random quantum circuit multiple times to obtain a corresponding plurality of ideal results, and to receive from the quantum circuit a plurality of experimental results corresponding to the quantum circuit acting multiple times on the plurality of qubits. The classical processor is configured to group the plurality of experimental results based on the probability of the ideal results to obtain a first distribution, and to group the plurality of experimental results based on the probability of the experimental results to obtain a second distribution. The classical processor is configured to characterize the noise in the quantum system based on the first distribution and the second distribution.

[0006] According to an embodiment of the present invention, a computer-readable medium includes computer executable code, which, when read by a computer, causes the computer to run a simulation of a random quantum circuit multiple times to obtain a corresponding plurality of ideal results, and receives from the quantum circuit a plurality of experimental results corresponding to the quantum circuit acting on a plurality of qubits multiple times. When read by the computer, the computer executable code further causes the computer to group the plurality of experimental results based on the probability of the ideal results to obtain a first distribution, group the plurality of experimental results based on the probability of the experimental results to obtain a second distribution, and characterize the noise in the quantum system based on the first distribution and the second distribution. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Figure 1 is a flow chart illustrating a method for characterizing noise in a quantum system according to an embodiment of the present invention.

[0008] Figure 2 is acting on six qubits ( Figure 2 Schematic diagram of an example of a random quantum circuit (circles in ).

[0009] Figure 3 is an example graph illustrating the Porter-Thomas distribution.

[0010] Figure 4 is an example graph illustrating the sorting of bit strings into bins.

[0011] Figure 5 is an example graph illustrating binning of four bit strings according to experimental probabilities.

[0012] Figure 6 is an example graph illustrating an ideal distribution.

[0013] Figure 7is an example graph illustrating an example distribution from a simulation with coherent noise binned by experimental probability.

[0014] Figure 8 is an example graph illustrating an example distribution from a simulation with coherent noise binned by ideal probability.

[0015] Fig. 9 is an example graph illustrating an example incoherent noise distribution, where incoherent noise results are binned according to their probability.

[0016] Fig.10 is an example graph illustrating a first average circuit success rate and a second average circuit success rate as a function of depth.

[0017] Fig.11 The first average circuit success rate and the second average circuit success rate obtained by experiment, and the first average circuit success rate and the second average circuit success rate obtained by simulation are shown.

[0018] Fig.12 is a schematic diagram of a system for characterizing noise in a quantum system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0019] Figure 1 1 is a flow chart illustrating a method 100 for characterizing noise in a quantum system according to an embodiment of the present invention. The quantum system includes a plurality of qubits and a plurality of entangled gates native to the quantum system. The method 100 includes generating a random quantum circuit 102. The random quantum circuit includes the plurality of entangled gates native to the quantum system. The method includes running a simulation of the random quantum circuit multiple times on a classical computer to obtain a corresponding plurality of ideal results 104. The method includes running the random quantum circuit multiple times to obtain a corresponding plurality of experimental results 106. The method includes grouping the plurality of experimental results based on the probability of the ideal results to obtain a first distribution 108. The method includes grouping the plurality of experimental results based on the probability of the experimental results to obtain a second distribution 110. The method includes characterizing the noise in the quantum system based on the first distribution and the second distribution 112.

[0020] According to an embodiment of the present invention, characterizing the noise in the quantum system includes quantizing coherent noise and incoherent noise in the quantum system.

[0021] According to an embodiment of the present invention, the random quantum circuit includes a plurality of random single-qubit rotations in addition to the entanglement gate native to the quantum system. The plurality of entanglement gates native to the quantum system may be, for example, a two-qubit CNOT gate. However, embodiments of the present invention are not limited to the two-qubit CNOT gate. Other entanglement gates may also be used.

[0022] Depending on the type of hardware employed, different quantum gates are easier to implement and more natural to use. Native gates refer to quantum gates that are a natural choice of gate for a given hardware. For example, in some hardware, the CNOT gate is the natural entanglement gate to be used. In other hardware, the CPHASE or CZ gate may be the natural entanglement gate to be used. Non-native gates require multiple native gates to implement. Native entanglement gates are implemented on qubits that are directly coupled to each other through hardware and do not require additional qubit SWAP to implement. In some hardware, specific qubits are directly coupled to other qubits through a physical resonator bus built into the hardware. Other hardware may have other connection schemes in which each qubit is coupled to every other qubit. Embodiments of the present invention use entanglement gates native to quantum systems to generate random quantum circuits.

[0023] According to an embodiment of the present invention, the random quantum circuit comprises alternating cycles of single-qubit rotations and two-qubit CNOT gates. Figure 2 is acting on six qubits ( Figure 2 Schematic diagram of an example of a random quantum circuit (circles in the figure). The random quantum circuit includes random unitary single qubit rotations 200, 202, 204, 206, 208, 2010 and CNOT gates 212, 214, 2016 acting on random pairs of connected qubits. The random unitary single qubit rotations 200-210 and CNOT gates 212, 214, 2016 are alternately applied to the qubit for x cycles. For sufficient depth x, the output distribution tends to the Porter-Thomas (PT) distribution. Figure 3 is a graph showing the Porter-Thomas distribution. N*p is plotted along the x-axis, where N=2 n , where n is the number of qubits in the quantum system and p is the probability of obtaining a particular outcome. The probability p is multiplied by N so that the x-axis label has order 1, rather than 1 / N, which can be a very small number. The probability of N*p, Pr(N*p), is plotted along the y-axis. For random quantum circuits that include randomly entangled unitary operators and have sufficient depth, the output distribution tends to a Porter-Thomas distribution, such as Figure 3 The distribution shown in .

[0024] According to an embodiment of the present invention, grouping a plurality of experimental results includes defining a plurality of bins such that when the plurality of ideal results are binned by ideal probabilities, for a Porter-Thomas distribution, the sum of the probabilities in each bin is equal. As described above, the method includes running a simulation of a random quantum circuit on a classical computer multiple times to obtain a corresponding plurality of ideal results. From the plurality of ideal results, for N=2 nThe ideal probability is determined for each of the possible outcomes. The ideal probabilities are used to generate bins. The bins are generated so that when the ideal outcomes are binned according to the ideal probabilities, the sum of the probabilities in each bin is equal for the Porter-Thomas distribution.

[0025] Figure 4 is an example graph showing the sorting of bit strings into bins. The jagged curve is an example of an ideal result plotted against its ideal probability to provide an ideal distribution 400. For example, a simulation can be run 1000 times on a classical computer, with each run having a corresponding bit string as the ideal output. The ideal outputs are used to determine the ideal probability corresponding to each possible bit string, and the probability of the ideal probabilities is the ideal distribution 400. The smooth curve 402 is the Porter-Thomas distribution. From Figure 4 It is clear from FIG. 4 that the ideal distribution 400 follows the Porter-Thomas distribution.

[0026] The ideal distribution 400 is used to generate the bins so that for the Porter-Thomas distribution, the sum of the probabilities in each bin is equal. Figure 4 , nine bins are generated: bin 1 404, bin 2 406, bin 3 408, bin 4 410, bin 5 412, bin 6 414, bin 7 416, bin 8 418, and bin 9 420. The bin edges are indicated by solid vertical lines. As described above, the ideal output is used to determine an ideal probability corresponding to each possible bit string. An example of such ideal probabilities for four possible bit strings is shown in Table 1. The ideal probability determines the bin to which the bit string is assigned, for example, based on the ideal probability, bit string x1 is assigned to bin 1, and based on the ideal probability, bit string 2 is assigned to bin 2.

[0027] Table 1 - Binning bit strings by ideal probability

[0028] <![CDATA[Bit string x j > Ideal probability * N warehouse# <![CDATA[x1:|000000>]]> 0.1265 1 <![CDATA[x2:|000001>]]> 0.9506 3 <![CDATA[x3:|000010>]]> 1.4793 4 <![CDATA[x4:|000011>]]> 0.6611 2

[0029] Once the bins have been generated, multiple experimental results generated by multiple runs of the random quantum circuit are assigned to the bins. The multiple experimental results are binned based on the probability of the ideal result and based on the probability of the experimental result. Although this example describes binning based on the ideal result first, and binning based on the experimental result second, embodiments of the present invention are not limited to a particular order.

[0030] According to an embodiment of the present invention, multiple experimental results are binned based on the probability of the ideal result to obtain a first distribution. For example, according to the ideal probability, each experimental result |000000> is binned in bin 1. According to the ideal probability, each experimental result |000001> is binned in bin 2. If p*N Pr(p*N) is different from the ideal value of a particular bit string, the resulting distribution (referred to as the "first distribution" in this article) may deviate from the ideal distribution. The deviation can be the result of coherent noise, incoherent noise, or a combination of both.

[0031] According to an embodiment of the present invention, multiple experimental results are binned based on the probability of the experimental results to obtain a second distribution. Table 2 shows an example of the experimental probability of four bit strings. For 1000 runs of a random quantum circuit acting on 6 qubits, 8 shots produce the experimental output x1:|000000>. Therefore, the experimental probability *N is Using the same bins as above, this places x1:|000000> in bin 1. The experimental probability *N of x2:|000001> is 1.216, which places x2 in bin 4.

[0032] Table 2 - Binning bit strings by experimental probability

[0033] <![CDATA[Bit string x j > Experimental probability * N warehouse# <![CDATA[x1:|000000>]]> 8 shots = 0.512 1 <![CDATA[x2:|000001>]]> 19 shots = 1.216 4 <![CDATA[x3:|000010>]]> 20 shots = 1.280 4 <![CDATA[x4:|000011>]]> 9 shots = 0.576 2

[0034] Figure 5 is an example graph illustrating the binning of four bit strings according to experimental probabilities. Multiple experimental results are binned based on the probabilities of the experimental results to obtain a second distribution. Binning by experimental probabilities provides an indication of how far the second distribution is from the ideal distribution. Coherent noise can be modeled as a small additional SU(2) gate in a random quantum circuit. The random quantum circuit still drives the probability distribution of the output toward Porter-Thomas, but "permutes" the bit strings within the Porter-Thomas distribution. For example, in Table 2, the bit string x2:|000001> is assigned to bin 4 based on the experimental probabilities, rather than bin 3 in Table 1. Coherent noise may change the probability associated with a particular result, but does not change the shape of the overall distribution. Therefore, binning by experimental probabilities is insensitive to coherent noise.

[0035] Figure 6 is a diagram of an example ideal distribution. Bit strings x1, x2, x3, and x4 output from a noise-free simulation are sorted into bin 1 600, bin 4 602, bin 6 604, and bin 7 606, respectively, according to their ideal probabilities. Bin edges are indicated by solid vertical lines. Summing over all bit strings and averaging over several circuits (jagged curve 608) reconstructs an ideal Porter-Thomas distribution (smooth curve 610).

[0036] Figure 7 is an illustration of an example distribution from a simulation with coherent noise binned by experimental probabilities. The experimental probabilities of the bit strings x1-x4 differ from the ideal (state vector computed) probabilities, and therefore the bit strings are assigned to different bins. However, when binning by the experimental probabilities of the bit strings, the Porter-Thomas distribution is still reconstructed.

[0037] Figure 8 is an illustration of an example distribution from a simulation with coherent noise binned by ideal probabilities. When we now sum the probabilities of the bit strings binned by ideal probabilities, we no longer construct a Porter-Thomas distribution. The sum of the probabilities is given by Figure 8 Note that the height of the vertical dashed lines of the bit strings x1-x4 is as Figure 7 However, because the bit strings have been assigned to different bins, the height of the vertical dashed lines no longer corresponds to the Porter-Thomas distribution 800. Figure 8 It is shown how binning by ideal probability is more discriminative than binning by experimental probability. Binning by ideal probability exploits the knowledge of which bit strings must go into which bins. Now, permuting the bit strings within the Porter-Thomas distribution will score poorly. Therefore, binning by ideal probability is sensitive to coherent noise, while binning by experimental probability is not.

[0038] Both binning methods are sensitive to incoherent noise. Incoherent noise will drive the distribution of the output towards a uniform distribution. In a uniform distribution, each outcome is equally likely. If the incoherent noise outcomes are binned according to their probability (i.e., the probability of the incoherent noise outcome), then the outcome is Fig. 9 The distribution shown. In the limit of an infinite number of results or "shots", a uniform distribution would be a vertical line at p*N = 1. However, with a finite number of shots, the shot noise is given a natural spread towards the vertical line, resulting in a Gaussian.

[0039] As described above, bins are generated based on an ideal distribution. In this document, the term "grouping" may refer to binning or allocation to bins. According to an embodiment of the present invention, the total number of bins is a polynomial in the number of qubits. The number of operations of the random quantum circuit is many times greater than the total number of bins. According to an embodiment of the present invention, the number of qubits is between 3 qubits and 100 qubits. A random quantum circuit according to an embodiment of the present invention may have a depth on the order of the number of qubits in the quantum system. The depth of a random quantum circuit is defined as the number of time steps required to run the random quantum circuit. Figure 2 As shown, the circuit can perform operations on multiple qubits during a single time step.

[0040] According to an embodiment of the present invention, characterizing noise includes: calculating a first distance from a first distribution to an ideal distribution, the ideal distribution being based on a simulation; calculating a second distance from a first incoherent noise distribution to the ideal distribution, the first incoherent noise distribution having equal probability for all possible incoherent noise results, wherein the incoherent noise results are grouped based on the probability of the ideal result; and calculating a first average circuit success rate based on the first distance and the second distance. For example, the average success rate may be defined as:

[0041]

[0042] where E is the experimentally obtained distribution (binned either by ideal probability or by experimental probability), I is the ideal distribution obtained from simulations on a classical computer, U is the uniform distribution corresponding to incoherent noise (binned either by ideal probability or by incoherent noise probability), and δ(A, B) is the variation distance between the distributions.

[0043] Therefore, the method according to an embodiment of the present invention includes calculating δ(E ideal prob , I), which is the first distance from the first distribution to the ideal distribution. The method includes calculating δ(U ideal prob , I), which is a second distance from the first incoherent noise distribution to the ideal distribution. The first incoherent noise distribution has equal probabilities for all possible incoherent noise results. However, the incoherent noise results are binned based on the probability of the ideal result (e.g., the ideal probability shown in Table 1). The method includes: calculating a first average circuit success rate based on the first distance and the second distance, for example using Equation 1.

[0044] According to an embodiment of the present invention, characterizing the noise further includes calculating δ(E experimental prob , I), which is the third distance from the second distribution to the ideal distribution. The method includes calculating δ(U incoherent noise prob , I), which is a fourth distance from the second incoherent noise distribution to the ideal distribution. The second incoherent noise distribution has equal probability for all possible incoherent noise results, and the incoherent noise results are grouped based on the probability of the incoherent noise results. Fig. 9 An example of a second incoherent noise distribution is shown in . The method includes calculating a second average circuit success rate based on the third distance and the fourth distance, for example using Equation 1. The method includes calculating a measure of coherent noise in the quantum system based on a difference between the first average circuit success rate and the second average circuit success rate.

[0045] Fig.10 is an example graph of a first average circuit success rate 1000 and a second average circuit success rate 1002 as a function of depth. The graphs are from a six-qubit ring (such as in Figure 21000 corresponds to binned output generation based on ideal probability, and the second average circuit success rate 1002 corresponds to binned output generation based on experimental probability. The value 1 on the y-axis indicates no noise, i.e., an ideal distribution. The distance 1004 between 1 and the second average circuit success rate 1002 is a measure of incoherent noise in the quantum system. The distance 1006 between the second average circuit success rate 1002 and the first average circuit success rate 1000 is a measure of coherent noise in the quantum system. The second average circuit success rate 1002 is sensitive to incoherent noise, but not to coherent noise. The first average circuit success rate 100 is sensitive to coherent noise in addition to incoherent noise. Therefore, when the results are binned by experimental probability and ideal probability, differences in average circuit success rates are observed in the quantum system.

[0046] Fig.11 The first average circuit success rate 1100 and the second average circuit success rate 1102 obtained by experiment, and the first average circuit success rate 1104 and the second average circuit success rate 1106 obtained by simulation are shown. The first average circuit success rate 1104 is obtained by simulating a device having T1 and T2 times corresponding to the T1 and T2 times of the quantum system. The first average circuit success rate 1104 is well consistent with the first average circuit success rate 1100 obtained by experiment. The second average circuit success rate 1106 is obtained by simulating 1% coherent noise in addition to the T1 and T2 times. The second average circuit success rate 1106 is consistent with the second average circuit success rate 1102. Fig.11 It is demonstrated how the methods and systems described herein can be used to characterize noise in quantum systems according to embodiments of the invention.

[0047] According to an embodiment of the present invention, a method for characterizing noise in a quantum system includes applying a continuous layer of randomized single-qubit and double-qubit unitary and sampling the resulting distribution. For sufficiently deep circuits, in the absence of any noise, the distribution will tend towards the Porter-Thomas distribution. However, the presence of coherent noise does not drive the noisy output distribution away from Porter-Thomas. Instead, it scrambles the labels. Incoherent noise will drive the output distribution towards a uniform distribution. Therefore, by binning the output results according to the expected ideal probability (obtained by simulating the circuit) and binning the output results according to the probability obtained experimentally, a quantitative separation between coherent noise and incoherent noise can be obtained. In contrast to the poor scalability of previous methods based on randomized benchmarks, this method can be reasonably easily scaled to more than 10-20 qubits.

[0048] Fig.121 is a schematic diagram of a system 1200 for characterizing noise in a quantum system according to an embodiment of the present invention. The system 1200 includes a quantum processor 1202 and a random quantum circuit 1210, the quantum processor including a plurality of qubits 1204, 1206, 1208, the random quantum circuit including a plurality of entangled gates native to the quantum system. The system 1200 includes a classical processor 1212, the classical processor being configured to run a simulation of the random quantum circuit 1210 multiple times to obtain a corresponding plurality of ideal results. The classical processor 1212 is further configured to receive a plurality of experimental results from the quantum circuit 1210, the experimental results corresponding to the quantum circuit 1210 acting on the plurality of qubits 1204, 1206, 1208 multiple times. The classical processor 1212 is further configured to group the plurality of experimental results based on the probability of the ideal results to obtain a first distribution, and to group the plurality of experimental results based on the probability of the experimental results to obtain a second distribution. The classical processor 1212 is further configured to characterize the noise in the quantum system based on the first distribution and the second distribution.

[0049] According to an embodiment of the present invention, the classical processor 1212 is configured to characterize the noise in the quantum system by quantizing the coherent noise and the incoherent noise in the quantum system. According to an embodiment of the present invention, the classical processor 1212 is configured to group the multiple experimental results by defining multiple bins so that when the multiple ideal results are binned by the ideal probability, the sum of the probabilities in each bin is equal for the Porter-Thomas distribution. The total number of the multiple bins can be a polynomial in the number of qubits of the quantum processor. The number of operations of the random quantum circuit 1210 can be greater than the total number of the multiple bins.

[0050] The quantum processor 1202 includes between 3 qubits and 100 qubits. Fig.12 The qubits 1204, 1206, 1208 schematically illustrated in FIG. 1 are merely examples. Embodiments of the present invention are not limited to Figure 2 and Fig.12 The number of qubits shown is not limited to a particular layout of qubits.

[0051] According to an embodiment of the present invention, random quantum circuit 1210 includes multiple random single qubit rotations. According to an embodiment of the present invention, the multiple entangled gates native to the quantum system are two-qubit CNOT gates. According to an embodiment of the present invention, random quantum circuit 1210 includes alternating cycles of single qubit rotations and two-qubit CNOT gates. The random quantum circuit 1210 can have a depth on the order of the number of qubits in the quantum system.

[0052] According to an embodiment of the present invention, the classical processor 1212 is configured to characterize noise by: calculating a first distance from a first distribution to an ideal distribution, the ideal distribution being based on a simulation; calculating a second distance from a first incoherent noise distribution to the ideal distribution, the first incoherent noise distribution having equal probability for all possible incoherent noise results, wherein the incoherent noise results are grouped based on the probability of the ideal result; and calculating a first average circuit success rate based on the first distance and the second distance. Fig.10 and Fig.11 This process according to an embodiment of the present invention is described.

[0053] According to an embodiment of the present invention, the classical processor 1212 is configured to characterize the noise by: calculating a third distance from a second distribution to an ideal distribution; calculating a fourth distance from a second incoherent noise distribution to the ideal distribution, wherein the second incoherent noise distribution has equal probability for all possible incoherent noise results, wherein the incoherent noise results are grouped based on the probability of the incoherent noise results; calculating a second average circuit success rate based on the third distance and the fourth distance; and calculating a measure of the coherent noise in the quantum system based on the difference between the first average circuit success rate and the second average circuit success rate. The above also refers to Fig.10 and Fig.11 This process according to an embodiment of the present invention is described.

[0054] The classical processor 1212 may be a dedicated "hardwired" device, or it may be a programmable device. For example, it may be, but is not limited to, a personal computer, a workstation, or any other suitable electronic device for a particular application. In some embodiments, it may be integrated into the unit, or it may be attachable, remote, and / or distributed.

[0055] According to an embodiment of the present invention, a computer-readable medium includes computer executable code, which, when read by a computer, causes the computer to run a simulation of a random quantum circuit multiple times to obtain a corresponding plurality of ideal results, and receives from the quantum circuit a plurality of experimental results corresponding to the quantum circuit acting on the plurality of qubits multiple times. When read by the computer, the computer executable code further causes the computer to group the plurality of experimental results based on the probability of the ideal results to obtain a first distribution, group the plurality of experimental results based on the probability of the experimental results to obtain a second distribution, and characterize the noise in the quantum system based on the first distribution and the second distribution.

[0056] According to an embodiment of the present invention, the computer executable code, when read by a computer, further causes the computer to generate data in order to construct the random quantum circuit in a quantum processor.

[0057] The methods disclosed herein measure and distinguish incoherent noise from coherent noise in quantum systems with more than three qubits using the binned output of random quantum circuits. Methods like the multi-qubit randomized benchmark (RB) require applying many native gates to a single multi-qubit Clifford gate until the point where decorrelation subdues the system before the necessary number of Cliffords can be applied. The methods disclosed herein can require a circuit depth that is only on the order of the number of qubits in the system.

[0058] According to an embodiment of the present invention, a random circuit is run, which includes alternating cycles of single-qubit SU(2) rotations and two-qubit CNOT gates, which drives the probability distribution of the resulting output states towards a "Porter-Thomas" distribution. The method relies on the fact that coherent noise will still drive the output distribution towards a Porter-Thomas distribution, while incoherent noise will drive the output distribution towards a uniform distribution. After running the experiment, the emissions are binned either by their ideal probabilities (computed from classical simulations) or by their experimental probabilities. The number of bins used can be a polynomial in the number of qubits, and the bin edges are defined so that for the Porter-Thomas distribution, the summed probabilities within each bin are equal between bins.

[0059] For each binning method (either by ideal probability or experimental probability), the distance from the ideal binning and the incoherent binning is calculated, and the fidelity is calculated. The difference in the fidelity of the two binning methods gives a measure of the coherent noise in the system. Thus, this method can quantitatively classify the noise in a quantum system into coherent noise and incoherent noise.

[0060] The description of various embodiments of the present invention has been presented for the purpose of illustration, but is not intended to be exhaustive or limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope of the described embodiments. The terms used herein are selected to best explain the principles of the embodiments, practical applications, or technical improvements over technologies found in the marketplace, or to enable other persons of ordinary skill in the art to understand the embodiments disclosed herein.

Claims

1. A method for characterizing noise in a quantum system, the quantum system comprising a plurality of qubits and a plurality of entangled gates native to the quantum system, the method comprising: generating a random quantum circuit on a quantum processor, the random quantum circuit comprising the plurality of entangled gates native to the quantum system; Running the simulation of the random quantum circuit multiple times on a classical computer to obtain corresponding multiple ideal results; Running the random quantum circuit multiple times on the quantum processor to obtain corresponding multiple experimental results; grouping the plurality of experimental results based on the probability of the ideal result to obtain a first distribution; grouping the plurality of experimental results based on the probabilities of the experimental results to obtain a second distribution; as well as characterizing noise in the quantum system based on the first distribution and the second distribution, Wherein, characterizing the noise in the quantum system comprises quantizing the coherent noise and the incoherent noise in the quantum system respectively, Wherein, characterizing the noise includes: calculating a first distance from the first distribution to an ideal distribution, the ideal distribution being based on the simulation; calculating a second distance from a first incoherent noise distribution to the ideal distribution, the first incoherent noise distribution having equal probability for all possible incoherent noise results, wherein the incoherent noise results are grouped based on the probability of the ideal result; and calculating a first average circuit success rate based on the first distance and the second distance, Wherein, characterizing the noise further includes: calculating a third distance from the second distribution to the ideal distribution; calculating a fourth distance from a second incoherent noise distribution to the ideal distribution, the second incoherent noise distribution having equal probability for all possible incoherent noise results, wherein the incoherent noise results are grouped based on their probabilities; calculating a second average circuit success rate based on the third distance and the fourth distance; and A measure of incoherent noise in the quantum system is calculated based on the second average circuit success rate, and a measure of coherent noise in the quantum system is calculated based on a difference between the first average circuit success rate and the second average circuit success rate.

2. The method for characterizing noise in a quantum system according to claim 1, wherein: The grouping of the plurality of experimental results includes defining a plurality of bins such that when the plurality of ideal results are binned by ideal probabilities, for a Porter-Thomas distribution, a sum of probabilities in each bin is equal.

3. The method for characterizing noise in a quantum system according to claim 2, wherein: The total number of the plurality of bins is a polynomial in the plurality of qubits.

4. The method for characterizing noise in a quantum system according to claim 1, wherein: The plurality of qubits is between 3 qubits and 100 qubits.

5. The method for characterizing noise in a quantum system according to claim 1, wherein: The random quantum circuit includes a plurality of random single qubit rotations.

6. The method for characterizing noise in a quantum system according to claim 1, wherein: The plurality of entanglement gates native to the quantum system are two-qubit CNOT gates.

7. The method for characterizing noise in a quantum system according to claim 1, wherein: The random quantum circuit includes alternating cycles of single-qubit rotations and two-qubit CNOT gates.

8. The method for characterizing noise in a quantum system according to claim 1, wherein: The random quantum circuit has a depth on the order of the number of qubits in the quantum system.

9. A system for characterizing noise in a quantum system, comprising: A quantum processor comprising a plurality of qubits; a random quantum circuit comprising a plurality of entangled gates native to the quantum system; as well as A classic processor, the classic processor being configured to: Running the simulation of the random quantum circuit multiple times to obtain corresponding multiple ideal results; receiving, from the quantum circuit, a plurality of experimental results corresponding to the quantum circuit acting on the plurality of qubits a plurality of times; grouping the plurality of experimental results based on the probability of the ideal result to obtain a first distribution; grouping the plurality of experimental results based on the probabilities of the experimental results to obtain a second distribution; as well as characterizing noise in the quantum system based on the first distribution and the second distribution, wherein the classical processor is configured to characterize the noise in the quantum system by quantizing the coherent noise and the incoherent noise in the quantum system respectively, Wherein, the classical processor is configured to characterize the noise by: calculating a first distance from the first distribution to an ideal distribution, the ideal distribution being based on the simulation; calculating a second distance from a first incoherent noise distribution to the ideal distribution, the first incoherent noise distribution having equal probability for all possible incoherent noise results, wherein the incoherent noise results are grouped based on the probability of the ideal result; and calculating a first average circuit success rate based on the first distance and the second distance, Wherein, the classical processor is further configured to characterize the noise by: calculating a third distance from the second distribution to the ideal distribution; calculating a fourth distance from a second incoherent noise distribution to the ideal distribution, the second incoherent noise distribution having equal probability for all possible incoherent noise results, wherein the incoherent noise results are grouped based on their probabilities; calculating a second average circuit success rate based on the third distance and the fourth distance; and A measure of incoherent noise in the quantum system is calculated based on the second average circuit success rate, and a measure of coherent noise in the quantum system is calculated based on a difference between the first average circuit success rate and the second average circuit success rate.

10. The system for characterizing noise in a quantum system according to claim 9, wherein: The classical processor is configured to group the plurality of experimental results by defining a plurality of bins such that when the plurality of ideal results are binned by ideal probabilities, for a Porter-Thomas distribution, a sum of probabilities in each bin is equal.

11. The system for characterizing noise in a quantum system according to claim 10, wherein: The total number of the plurality of bins is a polynomial in the plurality of qubits.

12. The system for characterizing noise in a quantum system according to claim 10, wherein: The number of times the random quantum circuit is executed is greater than a total number of the plurality of bins.

13. The system for characterizing noise in a quantum system according to claim 9, wherein: The plurality of qubits is between 3 qubits and 100 qubits.

14. The system for characterizing noise in a quantum system according to claim 9, wherein: The random quantum circuit includes a plurality of random single qubit rotations.

15. The system for characterizing noise in a quantum system according to claim 9, wherein: The plurality of entanglement gates native to the quantum system are two-qubit CNOT gates.

16. The system for characterizing noise in a quantum system according to claim 9, wherein: The random quantum circuit includes alternating cycles of single-qubit rotations and two-qubit CNOT gates.

17. The system for characterizing noise in a quantum system according to claim 9, wherein: The random quantum circuit has a depth on the order of the number of qubits in the quantum system.

18. A computer readable medium comprising computer executable code, which when read by a computer causes the computer to perform a method for characterizing noise in a quantum system, the quantum system comprising a plurality of qubits and a plurality of entangled gates native to the quantum system, the method comprising: Run the simulation of the random quantum circuit multiple times to obtain the corresponding multiple ideal results; receiving, from the quantum circuit, a plurality of experimental results corresponding to the quantum circuit acting on the plurality of qubits a plurality of times; grouping the plurality of experimental results based on the probability of the ideal result to obtain a first distribution; grouping the plurality of experimental results based on the probabilities of the experimental results to obtain a second distribution; as well as characterizing noise in the quantum system based on the first distribution and the second distribution, Wherein, characterizing the noise in the quantum system comprises quantizing the coherent noise and the incoherent noise in the quantum system respectively, Wherein, characterizing the noise includes: calculating a first distance from the first distribution to an ideal distribution, the ideal distribution being based on the simulation; calculating a second distance from a first incoherent noise distribution to the ideal distribution, the first incoherent noise distribution having equal probability for all possible incoherent noise results, wherein the incoherent noise results are grouped based on the probability of the ideal result; and calculating a first average circuit success rate based on the first distance and the second distance, Wherein, characterizing the noise further includes: calculating a third distance from the second distribution to the ideal distribution; calculating a fourth distance from a second incoherent noise distribution to the ideal distribution, the second incoherent noise distribution having equal probability for all possible incoherent noise results, wherein the incoherent noise results are grouped based on their probabilities; calculating a second average circuit success rate based on the third distance and the fourth distance; and A measure of incoherent noise in the quantum system is calculated based on the second average circuit success rate, and a measure of coherent noise in the quantum system is calculated based on a difference between the first average circuit success rate and the second average circuit success rate.

19. The computer-readable medium of claim 18, wherein: comprising computer executable code which, when read by a computer, further causes the computer to: Data is generated to construct the random quantum circuit in a quantum processor.

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